Journal articles: 'Electrons Wave functions'

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CHUEV, G. N., M. V. FEDOROV, H. J. LUO, D. KOLB, and E. G. TIMOSHENKO. "3D WAVELET TREATMENT OF SOLVATED BIPOLARON AND POLARON." Journal of Theoretical and Computational Chemistry 04, no. 03 (September 2005): 751–67. http://dx.doi.org/10.1142/s0219633605001787.

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Three-dimensional discrete tensor wavelets are applied to calculate wave functions of excess electrons solvated in polar liquids. Starting from the Hartree–Fock approximation for the electron wave functions and from the linear response to the solute charge for the solvent, we have derived the approximate free energy functional for the excess electrons. The orthogonal Coifman basis set is used to minimize the free energy functional and to approximate the electron wave functions. The scheme is applied to the calculation of the properties of the solvated electron and the singlet bipolaron formation. The obtained results indicate that the proposed algorithm is fast and rather efficient for calculating the electronic structure of the solvated molecular solutes.

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McMorran, Benjamin J., Amit Agrawal, Peter A. Ercius, Vincenzo Grillo, Andrew A. Herzing, Tyler R. Harvey, Martin Linck, and Jordan S. Pierce. "Origins and demonstrations of electrons with orbital angular momentum." Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences 375, no. 2087 (February 28, 2017): 20150434. http://dx.doi.org/10.1098/rsta.2015.0434.

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The surprising message of Allen et al. (Allen et al. 1992 Phys. Rev. A 45 , 8185 ( doi:10.1103/PhysRevA.45.8185 )) was that photons could possess orbital angular momentum in free space, which subsequently launched advancements in optical manipulation, microscopy, quantum optics, communications, many more fields. It has recently been shown that this result also applies to quantum mechanical wave functions describing massive particles (matter waves). This article discusses how electron wave functions can be imprinted with quantized phase vortices in analogous ways to twisted light, demonstrating that charged particles with non-zero rest mass can possess orbital angular momentum in free space. With Allen et al. as a bridge, connections are made between this recent work in electron vortex wave functions and much earlier works, extending a 175 year old tradition in matter wave vortices. This article is part of the themed issue ‘Optical orbital angular momentum’.

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Repetsky, S., I. Vyshyvana, S. Kruchinin, and S. Bellucci. "Tight-binding model in the theory of disordered crystals." Modern Physics Letters B 34, no. 19n20 (July 8, 2020): 2040065. http://dx.doi.org/10.1142/s0217984920400655.

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This paper presents a new method of describing electronic spectrum, thermodynamic potential, and electrical conductivity of disordered crystals based on the Hamiltonian of multi-electron system and diagram method for Green’s functions finding. Electronic states of a system were described by multi-band tight-binding model. The Hamiltonian of a system is defined on the basis of the wave functions of electron in the atom nucleus field. Electrons scattering on the oscillations of the crystal lattice are taken into account. The proposed method includes long-range Coulomb interaction of electrons at different sites of the lattice. Precise expressions for Green’s functions, thermodynamic potential and conductivity tensor are derived using diagram method. Cluster expansion is obtained for density of states, free energy, and electrical conductivity of disordered systems. We show that contribution of the electron scattering processes to clusters is decreasing along with increasing number of sites in the cluster, which depends on small parameter. The computation accuracy is determined by renormalization precision of the vertex parts of the mass operators of electron-electron and electron-phonon interactions. This accuracy also can be determined by small parameter of cluster expansion for Green’s functions of electrons and phonons.

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Vovk, Ilia A., Vladimir V. Lobanov, Aleksandr P. Litvin, Mikhail Yu Leonov, Anatoly V. Fedorov, and Ivan D. Rukhlenko. "Band Structure and Intersubband Transitions of Three-Layer Semiconductor Nanoplatelets." Nanomaterials 10, no. 5 (May 12, 2020): 933. http://dx.doi.org/10.3390/nano10050933.

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This paper presents the first general theory of electronic band structure and intersubband transitions in three-layer semiconductor nanoplatelets. We find a dispersion relation and wave functions of the confined electrons and use them to analyze the band structure of core/shell nanoplatelets with equal thicknesses of the shell layers. It is shown that the energies of electrons localized inside the shell layers can be degenerate for certain electron wave vectors and certain core and shell thicknesses. We also show that the energies of intersubband transitions can be nonmonotonic functions of the core and shell thicknesses, exhibiting pronounced local minima and maxima which can be observed in the infrared absorption spectra. Our results will prove useful for the design of photonic devices based on multilayered semiconductor nanoplatelets operating at infrared frequencies.

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Herzfeld, Judith, and Solen Ekesan. "Exchange potentials for semi-classical electrons." Physical Chemistry Chemical Physics 18, no. 44 (2016): 30748–53. http://dx.doi.org/10.1039/c6cp06100a.

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Electrostatic terms in the Hamiltonian make substantial contributions to the exchange energy because the antisymmetric wave functions for electrons of like spin that occupy different floating orbitals have depleted electron density between the orbitals (black curve vs. red curve).

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Gebhard, Florian. "Gutzwiller wave functions for correlated electrons: theory and applications." Philosophical Magazine 86, no. 13-14 (May 2006): 1847–76. http://dx.doi.org/10.1080/14786430500070438.

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CRUZ, H. "RELATIVISTIC CORRECTIONS TO ELECTRON DWELL TIME IN DOUBLE BARRIER HETEROSTRUCTURES." Modern Physics Letters B 05, no. 28 (December 10, 1991): 1865–72. http://dx.doi.org/10.1142/s0217984991002240.

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In this work, we have studied relativistic corrections to electron tunneling in double barrier heterostructures through analytical solutions of a Dirac-type equation as effective-mass equation for electrons in the conduction band. It is found that relativistic wave functions for electrons give us small but significant shifts in the electron dwell time obtained through a transfer matrix method of calculation.

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TAVERNIER, M. B., E. ANISIMOVAS, and F. M. PEETERS. "ELECTRON-VORTEX INTERACTION IN A QUANTUM DOT." International Journal of Modern Physics B 18, no. 27n29 (November 30, 2004): 3633–36. http://dx.doi.org/10.1142/s0217979204027177.

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Small numbers N<5 of two-dimensional Coulomb-interacting electrons trapped in a parabolic potential placed in a perpendicular magnetic field are investigated. The reduced wave function of this system, which is obtained by fixing the positions of N-1 electrons, exhibits strong correlations between the electrons and the zeros. These zeros are often called vortices. An exact-diagonalization scheme is used to obtain the wave functions and the results are compared with results obtained from the recently proposed rotating electron molecule (REM) theory. We find that the vortices gather around the fixed electrons and repel each other, which is to a much lesser extend so for the REM results.

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Trinh, Lang Hoang, Tao Van Chau, Chien Hoang Le, Hong Thi Yen Huynh, and Tram Ngoc Huynh. "Positron annihilation rate in single atom with slater type orbital approximation." Science and Technology Development Journal 16, no. 4 (December 31, 2013): 43–51. http://dx.doi.org/10.32508/stdj.v16i4.1595.

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A theoretical approximation for the structure of many-positron and manyelectron atoms in bound states is presented. The purpose of this theory is to permit the calculation of positron lifetimes from annihilation enhancement factor which is directly estimated by pair correlation function for each element atom, but not analytical form of correlation functions which depend upon homogeneous electron gas Monte– Carlo simulation data. We therefore used a modified orbital approximation for the electrons and positron. The orbital modification consisting of explicit electronpositron and electron-electron correlation in each elec-tronic orbital was used for the electrons and positron wave functions. The kinetic energies of the electrons and positron were treated on the same footing, and the Born-Oppenheimer approximation was applied to the nuclei. In this paper we treated only those systems for the valance electrons in the real spatial coordinate of the atom or molecule. The complex of many-particle problem was solved by the Schrongdinger of one particle equation which is derived by Kohn–Sham approximation and single particle wave function of Slater type orbital. As a result of this model, the positron annihilation rate and lifetime in some atoms, Ti, Zn and Zr, were calculated.

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Ortega, J. E., A. Mugarza, V. Pérez-Dieste, V. Repain, S. Rousset, and A. Mascaraque. "Probing wave functions at step superlattices: confined versus propagating electrons." Materials Science and Engineering: B 96, no. 2 (November 2002): 154–58. http://dx.doi.org/10.1016/s0921-5107(02)00308-2.

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Shul'ga, N. F., V. V. Syshchenko, A. I. Tarnovsky, and A. Yu Isupov. "Wave functions of channeling electrons in regular and chaotic cases." Journal of Physics: Conference Series 732 (July 2016): 012028. http://dx.doi.org/10.1088/1742-6596/732/1/012028.

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Shul'ga, N. F., V. V. Syshchenko, A. I. Tarnovsky, and A. Yu Isupov. "Wave functions of channeling electrons in regular and chaotic cases." Journal of Physics: Conference Series 732 (July 2016): 012034. http://dx.doi.org/10.1088/1742-6596/732/1/012034.

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Tripathi, Arvind K., Rajendra P. Singhal, and Onkar N. Singh II. "The generation of Ganymede's diffuse aurora through pitch angle scattering." Annales Geophysicae 35, no. 2 (February 22, 2017): 239–52. http://dx.doi.org/10.5194/angeo-35-239-2017.

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Abstract. Diffuse auroral intensities of neutral atomic oxygen OI λ1356 Å emission on Ganymede due to whistler mode waves are estimated. Pitch angle diffusion of magnetospheric electrons into the loss cone due to resonant wave–particle interaction of whistler mode waves is considered, and the resulting electron precipitation flux is calculated. The analytical yield spectrum approach is used for determining the energy deposition of electrons precipitating into the atmosphere of Ganymede. It is found that the intensities (4–30 R) calculated from the precipitation of magnetospheric electrons observed near Ganymede are inadequate to account for the observational intensities (≤ 100 R). This is in agreement with the conclusions reached in previous works. Some acceleration mechanism is required to energize the magnetospheric electrons. In the present work we consider the heating and acceleration of magnetospheric electrons by electrostatic waves. Two particle distribution functions (Maxwellian and kappa distribution) are used to simulate heating and acceleration of electrons. Precipitation of a Maxwellian distribution of electrons can produce about 70 R intensities of OI λ1356 Å emission for electron temperature of 150 eV. A kappa distribution can also yield a diffuse auroral intensity of similar magnitude for a characteristic energy of about 100 eV. The maximum contribution to the estimated intensity results from the dissociative excitation of O2. Contributions from the direct excitation of atomic oxygen and cascading in atomic oxygen are estimated to be only about 1 and 2 % of the total calculated intensity, respectively. The findings of this work are relevant for the present JUNO and future JUICE missions to Jupiter. These missions will provide new data on electron densities, electron temperature and whistler mode wave amplitudes in the magnetosphere of Jupiter near Ganymede.

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CIFTJA, ORION. "ANALYTIC WAVE FUNCTIONS FOR THE HALF-FILLED LOWEST LANDAU LEVEL." International Journal of Modern Physics B 24, no. 18 (July 20, 2010): 3489–99. http://dx.doi.org/10.1142/s0217979210055469.

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We consider a two-dimensional strongly correlated electronic system in a strong perpendicular magnetic field at half-filling of the lowest Landau level (LLL). We seek to build a wave function that, by construction, lies entirely in the Hilbert space of the LLL. Quite generally, a wave function of this nature can be built as a linear combination of all possible Slater determinants formed by using the complete set of single-electron states that belong to the LLL. However, due to the vast number of Slater determinant states required to form such basis functions, the expansion is impractical for any but the smallest systems. Thus, in practice, the expansion must be truncated to a small number of Slater determinants. Among many possible LLL Slater determinant states, we note a particular special class of such wave functions in which electrons occupy either only even, or only odd angular momentum states. We focus on such a class of wave functions and obtain analytic expressions for various quantities of interest. Results seem to suggest that these special wave functions, while interesting and physically appealing, are unlikely to be a very good approximation for the exact ground state at half-filling factor. The overall quality of the description can be improved by including other additional LLL Slater determinant states. It is during this process that we identify another special family of suitable LLL Slater determinant states to be used in an enlarged expansion.

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Dragoman, Daniela. "Tunable fractional Fourier transform implementation of electronic wave functions in atomically thin materials." Beilstein Journal of Nanotechnology 9 (June 19, 2018): 1828–33. http://dx.doi.org/10.3762/bjnano.9.174.

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A tunable fractional Fourier transform of the quantum wave function of electrons satisfying either the Schrödinger or the Dirac equation can be implemented in an atomically thin material by a parabolic potential distribution applied on a direction transverse to that of electron propagation. The difference between the propagation lengths necessary to obtain a fractional Fourier transform of a given order in these two cases could be seen as a manifestation of the Berry phase. The Fourier transform of the electron wave function is a particular case of the fractional Fourier transform. If the input and output wave functions are discretized, this configuration implements in one step the discrete fractional Fourier transform, in particular the discrete Fourier transform, and thus can act as a coprocessor in integrated logic circuits.

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Дурнев, М. В. "Влияние электрон-дырочной асимметрии на электронную структуру спиральных краевых состояний в квантовой яме HgTe/HgCdTe." Физика твердого тела 62, no. 3 (2020): 447. http://dx.doi.org/10.21883/ftt.2020.03.49012.629.

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We study the effects of electron-hole asymmetry on the electronic structure of helical edge states in HgTe/HgCdTe quantum wells. In the framework of the four-band kp-model, which takes into account the absence of a spacial inversion centre, we obtain analytical expressions for the energy spectrum and wave functions of edge states, as well as the effective g-factor tensor and matrix elements of electro-dipole optical transitions between the spin branches of the edge electrons. We show that when two conditions - electron-hole asymmetry and the absence of an inversion centre - are simultaneously satisfied, the spectrum of edge electrons deviates from the linear one, and we obtain the corresponding corrections.

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Shul’ga, N. F., V. V. Syshchenko, A. I. Tarnovsky, and A. Yu Isupov. "Structure of the channeling electrons wave functions under dynamical chaos conditions." Nuclear Instruments and Methods in Physics Research Section B: Beam Interactions with Materials and Atoms 370 (March 2016): 1–9. http://dx.doi.org/10.1016/j.nimb.2015.12.040.

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Ryabinkin, Ilya G., and Viktor N. Staroverov. "Accurate explicitly correlated wave functions for two electrons in a square." Journal of Chemical Physics 135, no. 1 (July 7, 2011): 014106. http://dx.doi.org/10.1063/1.3603451.

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Gidopoulos, Nikitas I., and E. K. U. Gross. "Electronic non-adiabatic states: towards a density functional theory beyond the Born–Oppenheimer approximation." Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences 372, no. 2011 (March 13, 2014): 20130059. http://dx.doi.org/10.1098/rsta.2013.0059.

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A novel treatment of non-adiabatic couplings is proposed. The derivation is based on a theorem by Hunter stating that the wave function of the complete system of electrons and nuclei can be written, without approximation, as a Born–Oppenheimer (BO)-type product of a nuclear wave function, X ( R ), and an electronic one, Φ R ( r ), which depends parametrically on the nuclear configuration R . From the variational principle, we deduce formally exact equations for Φ R ( r ) and X ( R ). The algebraic structure of the exact nuclear equation coincides with the corresponding one in the adiabatic approximation. The electronic equation, however, contains terms not appearing in the adiabatic case, which couple the electronic and the nuclear wave functions and account for the electron–nuclear correlation beyond the BO level. It is proposed that these terms can be incorporated using an optimized local effective potential.

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Rieth, M., and W. Schommers. "Electronic States of Nano-Systems." International Journal of Modern Physics B 11, no. 06 (March 10, 1997): 767–77. http://dx.doi.org/10.1142/s0217979297000435.

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Electronic properties of open but well-defined nano-systems have been studied quantum-mechanically. The energy states, electronic densities and the quantum-mechanical currents of such systems are dependent on the wave functions at the boundaries of the systems, the number of electrons inside the system, and the size of the system.

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Jagarlamudi, V. K., T. Dudok de Wit, C. Froment, V. Krasnoselskikh, A. Larosa, L. Bercic, O. Agapitov, et al. "Whistler wave occurrence and the interaction with strahl electrons during the first encounter of Parker Solar Probe." Astronomy & Astrophysics 650 (June 2021): A9. http://dx.doi.org/10.1051/0004-6361/202039808.

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Aims. We studied the properties and occurrence of narrowband whistler waves and their interaction with strahl electrons observed between 0.17 and 0.26 au during the first encounter of Parker Solar Probe. Methods. We used Digital Fields Board band-pass filtered (BPF) data from FIELDS to detect the signatures of whistler waves. Additionally parameters derived from the particle distribution functions measured by the Solar Wind Electrons Alphas and Protons (SWEAP) instrument suite were used to investigate the plasma properties, and FIELDS suite measurements were used to investigate the electromagnetic (EM) fields properties corresponding to the observed whistler signatures. Results. We observe that the occurrence of whistler waves is low, nearly ~1.5% and less than 0.5% in the analyzed peak and average BPF data, respectively. Whistlers occur highly intermittently and 80% of the whistlers appear continuously for less than 3 s. The spacecraft frequencies of the analyzed waves are less than 0.2 electron cyclotron frequency (fce). The occurrence rate of whistler waves was found to be anticorrelated with the solar wind bulk velocity. The study of the duration of the whistler intervals revealed an anticorrelation between the duration and the solar wind velocity, as well as between the duration and the normalized amplitude of magnetic field variations. The pitch-angle widths (PAWs) of the field-aligned electron population referred to as the strahl are broader by at least 12 degrees during the presence of large amplitude narrowband whistler waves. This observation points toward an EM wave electron interaction, resulting in pitch-angle scattering. PAWs of strahl electrons corresponding to the short duration whistlers are higher compared to the long duration whistlers, indicating short duration whistlers scatter the strahl electrons better than the long duration ones. Parallel cuts through the strahl electron velocity distribution function (VDF) observed during the whistler intervals appear to depart from the Maxwellian shape typically found in the near-Sun strahl VDFs. The relative decrease in the parallel electron temperature and the increase in PAW for the electrons in the strahl energy range suggests that the interaction with whistler waves results in a transfer of electron momentum from the parallel to the perpendicular direction.

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Сухарев, А. Г. "Симметрия икосаэдра и оптические свойства фуллерена С-=SUB=-60-=/SUB=-." Оптика и спектроскопия 129, no. 2 (2021): 132. http://dx.doi.org/10.21883/os.2021.02.50550.204-20.

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The electron transitions property of the fullerene molecule is considered. Because of electron jumps between nearest neighbor is possible, the interaction of the $\pi$- electrons produces the appearance of the collective states, having truncated icosahedron symmetry. The irreducible representations of the icosahedral group allow us to subdivide the state functions into groups with separate energy sublevel. The good approximation of the wave functions for the irreducible representations developed by means of spherical functions superposition. The optical properties is presented by formula of the excitation cross-section for electronic levels and by formula of the spontaneous relaxation time, received with help of matrix element calculation. Because of Jahn–Teller effect, a time of non-radiative transition is much less than radiative relaxation time. The interaction with phonon spectrum produces the spontaneously broken symmetry and restricts electronic-emission spectrum, while the absorption in optical spectrum exists. Transfer of energy from electron states into phonon oscillations produces the thermal radiation. However, it is possible to solve problem of electron state decay.

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Yang, Jian, and Wu-Pei Su. "A Microscopic Hierarchy Theory of the Fractional Quantum Hall Effect." International Journal of Modern Physics B 11, no. 06 (March 10, 1997): 707–28. http://dx.doi.org/10.1142/s021797929700040x.

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In this paper we present a microscopic hierarchy theory of the fractional quantum Hall effect. The wave functions of the ground state and the collective excitation states are obtained in terms of the electron coordinates. Working in the subspace spanned by the quasiparticles of the 1/m L Laughlin ground state, with m L an odd integer, it is shown that there exists a simple mapping between electron states in the quasiparticle subspace and states of an auxiliary boson system which is defined such that the number of the bosons is the same as that of the quasiparticles and the total magnetic flux quanta seen by the bosons equals the number of electrons. For the auxiliary boson system, one can write down the Laughlin state as well as the density wave states, analogous to the electron system at filling factor 1/m L . By mapping these states onto the quasiparticle subspace of the electrons, we find that the resulting wave functions provide a quite good description for the ground state and the collective excitations respectively of the original electron system at filling factor ν=1/(m L (± 1/2p)) with p a positive integer. This construction of the ground state and the collective excitation states can be repeated for higher filling factors. The theory presented in this paper can be viewed as a microscopic realization of Haldane's original hierarchy picture.

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Berggren, K. F., and M. Pepper. "Electrons in one dimension." Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences 368, no. 1914 (March 13, 2010): 1141–62. http://dx.doi.org/10.1098/rsta.2009.0226.

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In this article, we present a summary of the current status of the study of the transport of electrons confined to one dimension in very low disorder GaAs–AlGaAs heterostructures. By means of suitably located gates and application of a voltage to ‘electrostatically squeeze’ the electronic wave functions, it is possible to produce a controllable size quantization and a transition from two-dimensional transport. If the length of the electron channel is sufficiently short, then transport is ballistic and the quantized subbands each have a conductance equal to the fundamental quantum value 2 e 2 / h , where the factor of 2 arises from the spin degeneracy. This mode of conduction is discussed, and it is shown that a number of many-body effects can be observed. These effects are discussed as in the spin-incoherent regime, which is entered when the separation of the electrons is increased and the exchange energy is less than kT . Finally, results are presented in the regime where the confinement potential is decreased and the electron configuration relaxes to minimize the electron–electron repulsion to move towards a two-dimensional array. It is shown that the ground state is no longer a line determined by the size quantization alone, but becomes two distinct rows arising from minimization of the electrostatic energy and is the precursor of a two-dimensional Wigner lattice.

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Fáth, Gábor, and Stephen B. Haley. "Interacting electrons in magnetic fields: Tracking potentials and Jastrow-product wave functions." Physical Review B 58, no. 3 (July 15, 1998): 1405–13. http://dx.doi.org/10.1103/physrevb.58.1405.

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Ullah, Nazakat. "Momentum space distribution of electrons in an atom using hydrogenic wave functions." Pramana 41, no. 2 (August 1993): 171–74. http://dx.doi.org/10.1007/bf02847588.

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Ohmi, Norichika, and Masashi Hayakawa. "On the generation of quasi-electrostatic half-electron-gyrofrequency VLF emissions in the magnetosphere." Journal of Plasma Physics 35, no. 3 (June 1986): 351–73. http://dx.doi.org/10.1017/s0022377800011405.

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A theoretical study is made of the generation mechanism of quasi-electrostatic VLF emissions observed in the distant magnetosphere, with frequency greater than half the electron gyrofrequency and with wave normal around the cold plasma oblique resonance cone. The two-component plasma is treated, composed of cold electrons and hot electrons with bi-Maxwellian and loss-cone distribution functions. The effects of various plasma parameters on the instability characteristics are examined in order to estimate their relative importance in determining the properties of unstable waves. It is found that both types of hot plasma distribution function can account for quasi-electrostatic half-gyrofrequency emissions. The frequency where the maximum growth rate occurs is mainly determined by the temperature anisotropy of the hot plasma, and the wave normal angle where maximum growth is expected is determined by the temperature of the hot plasma and the ratio of the cold to hot plasma densities. These theoretical considerations form the basis of a suggested plasma model which is able to explain our experimental direction-finding results.

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Zhang, Yuanhao, Quanlan Xiao, Huilin He, Junpei Zhang, Guoping Dong, Junbo Han, and Jianrong Qiu. "Simultaneous luminescence modulation and magnetic field detection via magneto-optical response of Eu3+-doped NaGdF4 nanocrystals." Journal of Materials Chemistry C 3, no. 39 (2015): 10140–45. http://dx.doi.org/10.1039/c5tc02364e.

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FUBINI, S., and C. A. LÜTKEN. "VERTEX OPERATORS IN THE FRACTIONAL QUANTUM HALL EFFECT." Modern Physics Letters A 06, no. 06 (February 28, 1991): 487–500. http://dx.doi.org/10.1142/s0217732391000506.

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A second quantized formalism for electrons confined to a plane in a strong perpendicular magnetic field is constructed using vertex operators. They are seen to arise naturally from a holomorphic representation of Laughlin’s first quantized wave functions, since they have the unique properties of creating coherent states, satisfying anyonic statistics and factorizing matrix elements. While open string vertex operators are sufficient for representing Laughlin’s “ground state” wave functions, it is shown that the vertex operators appearing in the theory of closed strings are needed in order to represent both types of anyonic excitations (quasi-holes and quasi-electrons) which appear in the theory of the fractional quantum Hall effect.

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Pradhan, B. "Charge Density Wave and Spin Density Wave in Two-Orbital Model for Iron-Based Superconductors." SPIN 08, no. 02 (June 2018): 1850007. http://dx.doi.org/10.1142/s2010324718500078.

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We present a mean-field theoretical model study for the coexistence of the two strongly interacting charge density wave (CDW) and spin density wave (SDW) for iron-based superconductors in the under-doped region before the onset of the superconductivity in the system. The analytic expressions for the temperature dependence of the CDW and SDW order parameters are derived by using Zubarev’s technique of double-time single particle Green’s functions and solved self-consistently. Their interplay is studied by varying both the CDW and SDW coupling constants. Further, the electronic density of states (DOS) for the conduction electrons are studied in the pure CDW and SDW states and coexistence state for the cases, where the CDW transition temperature is greater than the SDW transition temperature and vice versa, which show two gap parameters.

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Do, Thi-Nga, Danhong Huang, Po-Hsin Shih, Hsin Lin, and Godfrey Gumbs. "Atomistic Band-Structure Computation for Investigating Coulomb Dephasing and Impurity Scattering Rates of Electrons in Graphene." Nanomaterials 11, no. 5 (May 1, 2021): 1194. http://dx.doi.org/10.3390/nano11051194.

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In this paper, by introducing a generalized quantum-kinetic model which is coupled self-consistently with Maxwell and Boltzmann transport equations, we elucidate the significance of using input from first-principles band-structure computations for an accurate description of ultra-fast dephasing and scattering dynamics of electrons in graphene. In particular, we start with the tight-binding model (TBM) for calculating band structures of solid covalent crystals based on localized Wannier orbital functions, where the employed hopping integrals in TBM have been parameterized for various covalent bonds. After that, the general TBM formalism has been applied to graphene to obtain both band structures and wave functions of electrons beyond the regime of effective low-energy theory. As a specific example, these calculated eigenvalues and eigen vectors have been further utilized to compute the Bloch-function form factors and intrinsic Coulomb diagonal-dephasing rates for induced optical coherence of electron-hole pairs in spectral and polarization functions, as well as the energy-relaxation time from extrinsic impurity scattering of electrons for non-equilibrium occupation in band transport.

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Hannibal, L., E. Rebhan, and C. Kielhorn. "Bifurcation of BGK waves in a plasma of cold ions and electrons." Journal of Plasma Physics 52, no. 1 (August 1994): 1–22. http://dx.doi.org/10.1017/s0022377800017748.

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For the simple model of cold electrons streaming against cold ions the complete set of nonlinear stationary waves is expressed in terms of elliptic functions. The conditions for their dynamical connection to a uniform neutral plasma state are taken into account, and the conditions for the neglect of the magnetic field are analysed. The range of existence of stationary waves is found to be confined to the stable regime of the two-stream instability, but covers only part of it. All nonlinear BGK waves that are found within the limits of the model can be shown to bifurcate from the two-stream instability, some of them also exhibiting secondary and further bifurcations. As an exceptional case, all bifurcations can be treated exactly. Close to the linear regime, all nonlinear modes turn out to be unstable. The corresponding instability is caused by a wave decay that transports energy from low to high wavenumbers of the Fourier modes constituting the wave. From the two-stream solutions four- stream solutions with exactly vanishing magnetic field are derived.

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Christov, Ivan P. "Spatial Entanglement of Fermions in One-Dimensional Quantum Dots." Entropy 23, no. 7 (July 7, 2021): 868. http://dx.doi.org/10.3390/e23070868.

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The time-dependent quantum Monte Carlo method for fermions is introduced and applied in the calculation of the entanglement of electrons in one-dimensional quantum dots with several spin-polarized and spin-compensated electron configurations. The rich statistics of wave functions provided by this method allow one to build reduced density matrices for each electron, and to quantify the spatial entanglement using measures such as quantum entropy by treating the electrons as identical or distinguishable particles. Our results indicate that the spatial entanglement in parallel-spin configurations is rather small, and is determined mostly by the spatial quantum nonlocality introduced by the ground state. By contrast, in the spin-compensated case, the outermost opposite-spin electrons interact like bosons, which prevails their entanglement, while the inner-shell electrons remain largely at their Hartree–Fock geometry. Our findings are in close correspondence with the numerically exact results, wherever such comparison is possible.

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Miraglia, J. E., M. G. Bustamante, and P. A. Macri. "Approximate wave functions for two electrons in the continuum of a Coulomb charge." Physical Review A 60, no. 6 (December 1, 1999): 4532–41. http://dx.doi.org/10.1103/physreva.60.4532.

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Nascimento, Marco Antonio Chaer. "The Valence-Bond (VB) Model and Its Intimate Relationship to the Symmetric or Permutation Group." Molecules 26, no. 15 (July 27, 2021): 4524. http://dx.doi.org/10.3390/molecules26154524.

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VB and molecular orbital (MO) models are normally distinguished by the fact the first looks at molecules as a collection of atoms held together by chemical bonds while the latter adopts the view that each molecule should be regarded as an independent entity built up of electrons and nuclei and characterized by its molecular structure. Nevertheless, there is a much more fundamental difference between these two models which is only revealed when the symmetries of the many-electron Hamiltonian are fully taken into account: while the VB and MO wave functions exhibit the point-group symmetry, whenever present in the many-electron Hamiltonian, only VB wave functions exhibit the permutation symmetry, which is always present in the many-electron Hamiltonian. Practically all the conflicts among the practitioners of the two models can be traced down to the lack of permutation symmetry in the MO wave functions. Moreover, when examined from the permutation group perspective, it becomes clear that the concepts introduced by Pauling to deal with molecules can be equally applied to the study of the atomic structure. In other words, as strange as it may sound, VB can be extended to the study of atoms and, therefore, is a much more general model than MO.

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Agafonov, A. I. "Massless Composite Bosons Formed by the Coupled Electron-Positron Pairs and Two-Photon Angular Correlations in the Colliding Beam Reaction e-e+→Bγγ with Emission of the Massless Boson." Advances in High Energy Physics 2018 (June 24, 2018): 1–18. http://dx.doi.org/10.1155/2018/6137380.

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The approach in which the electron and positron are treated as ordinary, different particles, each being characterized by the complete set of the Dirac plane waves, is examined. This completely symmetric representation that is beyond the standard QED makes it necessary to choose another solution of the Dirac equation for the free particle propagator as compared to that used currently. The Bethe-Salpeter equation with these particle propagators is solved in the ladder approximation. A new solution has been found represented by the massless composite bosons formed by the coupled electron-positron pairs with the coupling equal to the fine structure constant. It has been demonstrated that (1) the massless boson states have normalizable complex wave functions which are transversely compressed plane waves; (2) the transverse radius of the wave functions diverges as the boson energy goes to zero; that is, the composite bosons cannot be at rest; (3) increasing the boson energy results in an extension of the transverse wave function in the momentum space and a corresponding contraction of the real space coordinate wave function. The new reaction e-e+→Bγγ is investigated with the products composed of the massless composite boson and two photons. The cross-section of this reaction is derived for nonrelativistic colliding beams of spin-polarized electrons and positrons. In this case the 2γ angular correlation spectrum is characterized by a narrow peak with the full-width-at-half-maximum not exceeding 0.2 mrad. It is shown that in order to distinguish between the conventional annihilation of the singlet electron-positron pair with the two-photon emission and the new examined reaction yielding the three particles, experiments are proposed with the extremely nonrelativistic colliding beams.

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GURVITZ, S. A., H. J. LIPKIN, and Ya S. PRAGER. "THE PAULI PRINCIPLE AND QUANTUM TRANSPORT." Modern Physics Letters B 08, no. 21n22 (September 20, 1994): 1377–85. http://dx.doi.org/10.1142/s0217984994001345.

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A new method using Fock space wave functions is proposed for studying resonant tunneling in semiconductor quantum wells. The use of binary occupation numbers as dynamical variables, rather than properties of individual electrons, manifestly takes account of electron statistics, which enables investigation of the influence of the Pauli principle on resonant tunneling in the presence of inelastic scattering. Applied to the evaluation of the resonant current in semiconductor heterostructures, our approach predicts considerable deviations from the one-electron and rate equations pictures.

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HILKE, M., and M. RUIZ-ALTABA. "THE COULOMB GAS FOR EXCITED STATES IN THE FRACTIONAL QUANTUM HALL EFFECT." Modern Physics Letters B 05, no. 19 (August 20, 1991): 1307–11. http://dx.doi.org/10.1142/s021798499100160x.

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We follow Fubini's suggestion to use vertex operators for describing electrons and holes in the two-dimensional set-up appropriate for the description of the fractional quantum Hall effect, i.e., on the gauge-fixed magnetic plane. Laughlin's wave function is thus reproduced as the correlator of primary conformal fields, represented as exponentials of a free scalar field. We generalize an Ansatz by Halperin and present a new wave function describing the ground-state and the excited states of a system of unpolarized electrons. We realize these wave functions as correlators of normal-ordered exponentials of two free fields. We also give an explicit representation for the creation operator of an excitation.

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Makhoute, Abdelkader, Driss Khalil, and Imane Ajana. "Laser-Assisted (e, 2e) Collisions in the Symmetric/Asymmetric Coplanar Geometry." Atoms 7, no. 2 (April 2, 2019): 40. http://dx.doi.org/10.3390/atoms7020040.

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In this review, we present a comprehensive survey of laser-assisted (e, 2e) reactions. The influence of a laser field on the dynamics of (e, 2e) collisions in atomic hydrogen is analyzed in the symmetric and asymmetric coplanar geometries. Particular attention is devoted to the construction of the dressed (laser-modified) target wave functions, in both the initial and final states. The calculation is performed in the framework of Coulomb-Volkov-Born approximation, where the initial and final electrons are described by Volkov wave functions, while the interaction of the incident electron with the target atom is treated in the first and the second Born approximation. The state of the ejected electron is described by a Volkov/Coulomb-Volkov wave function. A detailed account is also given of the techniques we have used to evaluate the scattering amplitudes. The influence of the laser parameters (frequency, intensity, and direction of polarization) on the angular distribution of the ejected electron is discussed, and a number of illustrative examples are given. The structure of the triple differential cross section in the vicinity of resonances is also analyzed.

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Lokot, Lyubov E. "Particle-hole pair and beelectron states in ZnO/(Zn,Mg)O quantum wells and Dirac materials." JOURNAL OF ADVANCES IN PHYSICS 10, no. 1 (August 5, 2015): 2583–604. http://dx.doi.org/10.24297/jap.v10i1.1344.

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In this paper a theoretical studies of the space separation of electron and hole wave functions in the quantum well ZnO/Mg(0.27)Zn(0.73)O are presented. For this aim the self-consistent solution of the SchrÃ¶dinger equations for electrons and holes and the Poisson equations at the presence of spatially varying quantum well potential due to the piezoelectric effect and local exchange-correlation potential is found. The one-dimensional Poisson equation contains the Hartree potential which includes the one-dimensional charge density for electrons and holes along the polarization field distribution. The three-dimensional Poisson equation contains besides the one-dimensional charge density for electrons and holes the exchange-correlation potential which is built on convolutions of a plane-wave part of wave functions in addition. The shifts of the Hartree valence band spectrums and the conduction band spectrum with respect to the flat band spectrums as well as the Hartree-Fock band spectrums with respect to the Hartree ones are found. An overlap integrals of the wave functions of holes and electron with taking into account besides the piezoelectric effects the exchange-correlation effects in addition is greater than an overlap integral of Hartree ones. The Hartree particles distribute greater on edges of quantum well than Hartree-Fock particles. It is found that an effective mass of heavy hole of Mg(0.27)Zn(0.73)O under biaxial strain is greater than an effective-mass of heavy hole of ZnO. It is calculated that an electron mass is less than a hole mass. It is found that the Bohr radius is grater than the localization range particle-hole pair, and the excitons may be spontaneously created.SchrÃ¶dinger equation for pair of two massless Dirac particles when magnetic field is applied in Landau gauge is solved exactly. In this case the separation of center of mass and relative motion is obtained. Landau quantization $\epsilon=\pm\,B\sqrt{l}$ for pair of two Majorana fermions coupled via a Coulomb potential from massless chiral Dirac equation in cylindric coordinate is found. The root ambiguity in energy spectrum leads into Landau quantization for beelectron, when the states in which the one simultaneously exists are allowed. The tachyon solution with imaginary energy in Cooper problem ($\epsilon^{2}<0$) is found.

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King, Andrew W., Adam L. Baskerville, and Hazel Cox. "Hartree–Fock implementation using a Laguerre-based wave function for the ground state and correlation energies of two-electron atoms." Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences 376, no. 2115 (February 5, 2018): 20170153. http://dx.doi.org/10.1098/rsta.2017.0153.

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An implementation of the Hartree–Fock (HF) method using a Laguerre-based wave function is described and used to accurately study the ground state of two-electron atoms in the fixed nucleus approximation, and by comparison with fully correlated (FC) energies, used to determine accurate electron correlation energies. A variational parameter A is included in the wave function and is shown to rapidly increase the convergence of the energy. The one-electron integrals are solved by series solution and an analytical form is found for the two-electron integrals. This methodology is used to produce accurate wave functions, energies and expectation values for the helium isoelectronic sequence, including at low nuclear charge just prior to electron detachment. Additionally, the critical nuclear charge for binding two electrons within the HF approach is calculated and determined to be Z HF C =1.031 177 528. This article is part of the theme issue ‘Modern theoretical chemistry’.

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QIN, SHAOJIN, ZHAOBIN SU, and BINGSHEN WANG. "STUDY ON THE MOST PROBABLE DISTRIBUTION FOR LAUGHLIN WAVE FUNCTIONS." Modern Physics Letters B 07, no. 10 (April 30, 1993): 679–87. http://dx.doi.org/10.1142/s0217984993000655.

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We show that, up to a global phase freedom, the most probable distribution of electrons given by the maxima of modulus square of Laughlin wave function (LWF), which is known to be a wave function for an incompressible liquid state of fractional Hall effect, has a triangular lattice structure. We introduce the Gaussian approximation for the modulus square of LWF. We find that the radial distribution function calculated from the Gaussian approximation has a form close to that of LWF at ν = 1, 1/3 and close to a crystal-like behavior when ν becomes smaller. We interprete the underlying physics to be that in the incompressible liquid regime, the "hidden" triangular lattice is smeared away by the quantum phase fluctuation, and as a precursor for liquid-crystal transition when the filling ν decreases towards the crystallization regime, it might manifest itself to be a sort of correlated short-range ordered density fluctuation.

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Meng, Zhaoyue, Richard M. Thorne, and Danny Summers. "Ion-acoustic wave instability driven by drifting electrons in a generalized Lorentzian distribution." Journal of Plasma Physics 47, no. 3 (June 1992): 445–64. http://dx.doi.org/10.1017/s002237780002434x.

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A generalized Lorentzian (kappa) particle distribution function is useful for modelling plasma distributions with a high-energy tail that typically occur in space. The modified plasma dispersion function is employed to study the instability of ion-acoustic waves driven by electron drift in a hot isotropic unmagnetized plasma modelled by a kappa distribution. The real and imaginary parts of the wave frequency ω0 + ιγ are obtained as functions of the normalized wavenumber kλD, where λD is the electron Debye length. Marginal stability conditions for instability are obtained for different ion-to-electron temperature ratios. The results for a kappa distribution are compared with the classical results for a Maxwellian. In all cases studied the ion-acoustic waves are strongly damped at short wavelengths, kλD ≫ 1, but they can be destabilized at long wavelengths. The instability for both the kappa and Maxwellian distributions can be quenched by increasing the ion-electron temperature ratio Ti/Te. However, both the marginally unstable electron drift velocities and the growth rates of unstable waves can differ significantly between a generalized Lorentzian and a Maxwellian plasma; these differences are also influenced by the value of Ti/Te.

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Fliszár, S., N. Desmarais, and G. Dancausse. "Valence and core region energies of atoms in Hartree–Fock theory." Canadian Journal of Chemistry 70, no. 2 (February 1, 1992): 537–46. http://dx.doi.org/10.1139/v92-076.

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The subdivision of an atom into an inner core and an outer valence region reveals an interesting statistical aspect about the Hartree–Fock (HF) eigenvalues, εi, and the electron populations in the valence region, [Formula: see text] namely [Formula: see text] where Tv and [Formula: see text] are, respectively, the kinetic energy and the nuclear-electronic potential energy of the [Formula: see text] valence electrons, [Formula: see text] the interelectronic repulsion confined within the valence region, while [Formula: see text] is the repulsion between the core electrons and those of the valence region. This relationship (and a similar one for the core region) holds for any number of electrons arbitrarily assigned to the core, but is accurate only for HF (or near-HF) wave functions. This leads to a definition of the valence region energy, [Formula: see text] which, however, cannot be compared to the energy actually required for the removal of the outer electrons, because relaxation is not accounted for. An accurate energy expression has also been derived, [Formula: see text] which measures the actual withdrawal of the valence electrons. The latter expression requires the use of discrete values of Nc, the number of electrons assigned to the core, namely Nc = 2 for the first-row and Nc = 10 e for the second-row elements. Keywords: atoms, core–valence separation.

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Kafoněk, Tomáš. "New Solutions of Lorentz Transformation III." Scientific Review, no. 72 (March 9, 2021): 15–19. http://dx.doi.org/10.32861/sr.72.15.19.

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This work is my third part of the hypothesis which was originally based on the basic assumptions of the Lorentz transformation and has various consequences. In this first part of the hypothesis [1], I calculated a wave function from the general assumptions of the Lorentz transformation. This wave function describes the spatiotemporal deformations and I use it also in my second part of the hypothesis [2] to calculate the interference and diffraction which resulted in an equation that is not based on complex functions, as is the case with standard calculations. This equation we can examine also, for example, in the context of electron levels in an atom, because interference and diffraction are phenomena related to Young’s experiment, and the wave properties of electrons have been demonstrated.

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Abourabia, Aly M., and Rabab A. Shahein. "Shock pattern solutions for viscous-collisional plasma ion acoustic waves in view of the linear theory of the non-equilibrium thermodynamics." Canadian Journal of Physics 89, no. 6 (June 2011): 673–87. http://dx.doi.org/10.1139/p11-037.

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In the framework of irreversible thermodynamics, we study nonlinear ion-acoustic waves (IAWs) in viscous and collisional plasmas. Electrons, which form the background, are assumed to be nonthermal. On account of ion viscosity and ion-electron collisions, we investigate using ion fluid equations. We study the effects of the nonthermally distributed electrons β and the temperature ratio σ (= Ti/Te) on the stability, where the stability for Burger’s equation is analyzed by two methods: the phase portrait method and irreversible thermodynamics relations at different values of σ and β. We usa a reductive perturbation technique, where the nonlinear evolution of an IAW is governed by the driven Burger equation. This equation is solved exactly by using two methods: the tanh-function method and the Cole–Hopf transformation. Both methods produce shock wave solutions, their results compared, and good agreement exists in most predictions. The analytical calculations show that an IAW propagates as a shock wave with subsonic speed. The flow velocity, pressure, number density, electrostatic potential, and thermodynamic characteristics are estimated and illustrated as functions of time t and the distance x. It is found via the tanh-function method that the amplitudes of the sought-for functions of the system are suppressed and move towards an equilibrium state at the highest value of β. The tanh-function method reveals an advantage over the Cole–Hopf method in the viscous and collisional cases of IAWs, where it satisfies the stability conditions at the highest value of β with the chosen σ values when applied to evaluate the Onsager relation.

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Fedotkin, S. N. "Corrections to the wave functions of atomic electrons in the potential of Thomas - Fermi." Nuclear Physics and Atomic Energy 19, no. 4 (December 25, 2018): 336–40. http://dx.doi.org/10.15407/jnpae2018.04.336.

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Marechal, Y. "Adiabatic wave functions beyond the Born–Oppenheimer approximation: Phase linking between electrons and nuclei." Journal of Chemical Physics 83, no. 1 (July 1985): 247–54. http://dx.doi.org/10.1063/1.449816.

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SHUKLA, PADMA K., and BENGT ELIASSON. "Clustering of ions at atomic dimensions in quantum plasmas." Journal of Plasma Physics 79, no. 4 (December 20, 2012): 359–66. http://dx.doi.org/10.1017/s0022377812001110.

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AbstractBy means of particle simulations of the equations of motion for ions interacting among themselves under the influence of newly discovered Shukla–Eliasson attractive force (SEAF) in a dense quantum plasma, we demonstrate that the SEAF can bring ions closer at atomic dimensions. We present simulation results of the dynamics of an ensemble of ions in the presence of the SEAF without and with confining external potentials and collisions between ions and degenerate electrons. Our particle simulations reveal that under the SEAF, ions attract each other, come closer, and form ionic clusters in the bath of degenerate electrons that shield ions. Furthermore, an external confining potential produces robust ion clusters that can have cigar- and ball-like shapes, which remain stable when the confining potential is removed. The stability of ion clusters is discussed. Our results may have applications to solid density plasmas (density exceeding 1023 per cm3), where the electrons will be degenerate and quantum forces due to the electron recoil effect caused by the overlapping of electron wave functions and electron tunneling through the Bohm potential, electron-exchange and electron-exchange and electron correlations associated with electron-1/2 spin effect, and the quantum statistical pressure of the degenerate electrons play a decisive role.

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Yüksel, Zeynep, and M. Çağatay Tufan. "Estimating the effect of electron beam interactions with biological tissues." Canadian Journal of Physics 96, no. 12 (December 2018): 1338–48. http://dx.doi.org/10.1139/cjp-2018-0093.

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The stopping power and range for electrons in matter are the most important parameters in predicting the consequences of the electrons interacting with matter. In this work, we used our previously developed method to calculate these parameters. In our calculation method, the main parameter is the velocity-dependent electronic charge density of the target, which we obtained by using Roothaan–Hartree–Fock (RHF) wave functions. For range calculations, we used the continuous slowdown approach (CSDA), which neglects the energy-loss fluctuations so the incident particle loses its energy in a medium continuously at a rate equal to the total stopping power. The stopping power and CSDA range values have been calculated for electrons incident on brain, breast, and eye tissues. Obtained results have been compared with the available data.

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Journal articles on the topic 'Electrons Wave functions'

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