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Journal articles on the topic 'Open system density matrix theory'

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Published: 4 June 2021

Last updated: 8 February 2022

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1

STEFANESCU, E., A. SǍNDULESCU, and W. GREINER. "QUANTUM TUNNELING IN OPEN SYSTEMS." International Journal of Modern Physics E 02, no. 01 (March 1993): 233–58. http://dx.doi.org/10.1142/s0218301393000078.

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We study the barrier penetrability in the frame of the Lindblad theory of open quantum systems. In addition to the diagonal elements of the density matrix, leading to the Gamow’s formula, new terms, describing energy dissipation and spectral line broadening effects are obtained. It is shown that the presence of a dissipative environment increase the barrier penetrability, in accordance with a very simple physical interpretation: for a system initially found in its ground state the dissipation can lead only to transitions to the reaction channels where lower-energy levels exist.

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2

ISAR, A., A. SANDULESCU, H. SCUTARU, E. STEFANESCU, and W. SCHEID. "OPEN QUANTUM SYSTEMS." International Journal of Modern Physics E 03, no. 02 (June 1994): 635–714. http://dx.doi.org/10.1142/s0218301394000164.

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The damping of the harmonic oscillator is studied in the framework of the Lindblad theory for open quantum systems. A generalization of the fundamental constraints on quantum mechanical diffusion coefficients which appear in the master equation for the damped quantum oscillator is presented; the Schrödinger, Heisenberg and Weyl-Wigner-Moyal representations of the Lindblad equation are given explicitly. On the basis of these representations it is shown that various master equations for the damped quantum oscillator used in the literature are particular cases of the Lindblad equation and that not all of these equations are satisfying the constraints on quantum mechanical diffusion coefficients. Analytical expressions for the first two moments of coordinate and momentum are obtained by using the characteristic function of the Lindblad master equation. The master equation is transformed into Fokker-Planck equations for quasiprobability distributions and a comparative study is made for the Glauber P representation, the antinormal ordering Q representation, and the Wigner W representation. The density matrix is represented via a generating function, which is obtained by solving a timedependent linear partial differential equation derived from the master equation. Illustrative examples for specific initial conditions of the density matrix are provided. The solution of the master equation in the Weyl-Wigner-Moyal representation is of Gaussian type if the initial form of the Wigner function is taken to be a Gaussian corresponding (for example) to a coherent wavefunction. The damped harmonic oscillator is applied for the description of the charge equilibration mode observed in deep inelastic reactions. For a system consisting of two harmonic oscillators the time dependence of expectation values, Wigner function and Weyl operator, are obtained and discussed. In addition models for the damping of the angular momentum are studied. Using this theory to the quantum tunneling through the nuclear barrier, besides Gamow’s transitions with energy conservation, additional transitions with energy loss are found. The tunneling spectrum is obtained as a function of the barrier characteristics. When this theory is used to the resonant atom-field interaction, new optical equations describing the coupling through the environment of the atomic observables are obtained. With these equations, some characteristics of the laser radiation absorption spectrum and optical bistability are described.

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3

Sargsyan, V. V., Z. Kanokov, G. G. Adamian, and N. V. Antonenko. "Application of the theory of open quantum systems in nuclear physics." International Journal of Modern Physics: Conference Series 49 (January 2019): 1960008. http://dx.doi.org/10.1142/s2010194519600085.

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Projectile-nucleus capture by a target nucleus at bombarding energies in the vicinity of the Coulomb barrier is treated with the reduced-density-matrix formalism. The effects of dissipation and fluctuations on the capture process are taken self-consistently into account within the quantum model suggested. The excitation functions for the capture in the reactions [Formula: see text]O, [Formula: see text]F, [Formula: see text]Mg, [Formula: see text]Si, [Formula: see text]S, [Formula: see text]Ca, [Formula: see text]Ti, [Formula: see text]Cr [Formula: see text] [Formula: see text]Pb are calculated and compared with the experimental data.

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4

Scheid, Werner, Aurelian Isar, and Aurel Sandulescu. "Diffusion and dissipation by linear momentum in spherical environment." International Journal of Modern Physics B 28, no. 11 (March 26, 2014): 1450077. http://dx.doi.org/10.1142/s0217979214500775.

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An open quantum system is studied consisting of a particle moving in a spherical space with an infinite wall. With the theory of Lindblad the system is described by a density matrix which gets affected by operators with diffusive and dissipative properties depending on the linear momentum and density matrix only. It is shown that an infinite number of basis states leads to an infinite energy because of the infinite unsteadiness of the potential energy at the infinite wall. Therefore only a solution with a finite number of basis states can be performed. A slight approximation is introduced into the equation of motion in order that the trace of the density matrix remains constant in time. The equation of motion is solved by the method of searching eigenvalues. As a side-product two sums over the zeros of spherical Bessel functions are found.

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5

Zenichowski, Karl, Jadranka Dokić, Tillmann Klamroth, and Peter Saalfrank. "Current versus temperature-induced switching of a single molecule: Open-system density matrix theory for 1,5-cyclooctadiene on Si(100)." Journal of Chemical Physics 136, no. 9 (March 7, 2012): 094705. http://dx.doi.org/10.1063/1.3692229.

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6

Czerwiński, Artur, and Andrzej Jamiołkowski. "Dynamic Quantum Tomography Model for Phase-Damping Channels." Open Systems & Information Dynamics 23, no. 04 (December 2016): 1650019. http://dx.doi.org/10.1142/s1230161216500190.

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In this paper we propose a dynamic quantum tomography model for open quantum systems with evolution given by phase-damping channels. Mathematically, these channels correspond to completely positive trace-preserving maps defined by the Hadamard product of the initial density matrix with a time-dependent matrix which carries the knowledge about the evolution. Physically, there is a strong motivation for considering this kind of evolution because such channels appear naturally in the theory of open quantum systems. The main idea behind a dynamic approach to quantum tomography claims that by performing the same kind of measurement at some time instants one can obtain new data for state reconstruction. Thus, this approach leads to a decrease in the number of distinct observables which are required for quantum tomography; however, the exact benefit for employing the dynamic approach depends strictly on how the quantum system evolves in time. Algebraic analysis of phase-damping channels allows one to determine criteria for quantum tomography of systems in question. General theorems and observations presented in the paper are accompanied by a specific example, which shows step by step how the theory works. The results introduced in this paper can potentially be applied in experiments where there is a tendency to look at quantum tomography from the point of view of economy of measurements, because each distinct kind of measurement requires, in general, preparing a separate setup.

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7

Naicker, V., and F. Petruccione. "A Lie Symmetry Analysis of the Caldeira-Leggett Model." Open Systems & Information Dynamics 17, no. 04 (December 2010): 409–17. http://dx.doi.org/10.1142/s1230161210000254.

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An important model in the theory of open quantum systems is the Caldeira-Leggett quantum Brownian motion model for the behaviour of a massive quantum particle weakly interacting with a bath of harmonic oscillators. The model is formulated in terms of a (1 + 2) dimensional partial differential equation (PDE) for the reduced density matrix of the particle. In this paper we analyze this PDE from the perspective of Lie symmetry groups. A Lie point symmetry analysis is performed and a number of canonical reductions are obtained. Of note are new analytic solutions to the model obtained by mapping the model to the linear diffusion equation.

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8

TOPOL, I. A., and V. I. POLYAKOV. "Method for Molecular Electronic State Multiplet Structure Calculation in the Space of Xα-SW-Orbitals." International Journal of Modern Physics C 02, no. 01 (March 1991): 510–14. http://dx.doi.org/10.1142/s0129183191000792.

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The SCF-Xα-scattered wave method (Xα-SW) as well as other versions of the density function approach cannot give a proper description of the open-shell many-electron energy levels and thus it is not always possible to reproduce electron spectra adequately by this method. We propose the following way to overcome this drawback of the X α-SW method. First one- and two-particle molecular integrals with Xα-SW molecular orbitals (MO) are calculated numerically. Then these integrals are used to evaluate Hamiltonian matrix elements (both diagonal and off-diagonal) in the basis of configuration state functions. The present scheme allows us to describe molecular electronic spectra in various approximations: a) one-configurational frozen orbitals approach; b) ΔSCF; c) configuration interaction (CI). Our method gives an opportunity to go beyond the muffin-tin (MT) approximation for a potential; inherent in the X α-SW method. In the X α-SW-MO basis it is simple enough to construct the full electron Hamiltonian matrix elements for various open-shell systems.

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9

Rohr, Daniel R., and Katarzyna Pernal. "Open-shell reduced density matrix functional theory." Journal of Chemical Physics 135, no. 7 (August 21, 2011): 074104. http://dx.doi.org/10.1063/1.3624609.

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10

Ying-Hua, Ji, and Liu Yong-Mei. "Reduced density matrix identification of open quantum system." Optik 159 (April 2018): 162–68. http://dx.doi.org/10.1016/j.ijleo.2018.01.066.

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11

Zhou, Yongxi, and Matthias Ernzerhof. "Open-system Kohn-Sham density functional theory." Journal of Chemical Physics 136, no. 9 (March 7, 2012): 094105. http://dx.doi.org/10.1063/1.3687922.

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12

Man'ko, V. I., V. A. Sharapov, and E. V. Shchukin. "Tomographic representation of evolution equation for density matrix of open system." Physics Letters A 309, no. 3-4 (March 2003): 176–82. http://dx.doi.org/10.1016/s0375-9601(03)00020-3.

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13

Huisinga, Wilhelm, Lorenzo Pesce, Ronnie Kosloff, and Peter Saalfrank. "Faber and Newton polynomial integrators for open-system density matrix propagation." Journal of Chemical Physics 110, no. 12 (March 22, 1999): 5538–47. http://dx.doi.org/10.1063/1.478451.

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14

Nakata, Maho, Masahiro Ehara, Koji Yasuda, and Hiroshi Nakatsuji. "Direct determination of second-order density matrix using density equation: Open-shell system and excited state." Journal of Chemical Physics 112, no. 20 (May 22, 2000): 8772–78. http://dx.doi.org/10.1063/1.481531.

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15

Lari, B., and H. Hassanabadi. "Specific heat and thermal entanglement in an open quantum system." Modern Physics Letters A 34, no. 11 (April 9, 2019): 1950059. http://dx.doi.org/10.1142/s0217732319500597.

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In this paper, the density matrix is obtained using the non-Markovian master equation method for a system consisting of two-qubit modeling with the Heisenberg XXZ chain, which involves the Dzyaloshinskii–Moriya interaction and is exposed to the bosonic baths. Also, using the proposed formula for calculating the specific heat through the density matrix of the open quantum system, the specific heat is calculated. The quantum entanglement behavior with time and coupling constant is investigated. It is observed that the specific heat at low temperatures becomes negative when the system is exposed to the environment. The time behavior of quantum entanglement for this model showed that the entanglement decreases to zero with increasing time.

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16

MINAHAN, JOSEPH A. "MATRIX MODELS AND ONE-DIMENSIONAL OPEN STRING THEORY." International Journal of Modern Physics A 08, no. 20 (August 10, 1993): 3599–614. http://dx.doi.org/10.1142/s0217751x93001466.

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We propose a random matrix model as a representation for D = 1 open strings. We show that the model with one flavor of boundary fields is equivalent to N fermions with spin in a central potential that also includes a long-range ferromagnetic interaction between the fermions that falls off as 1/(rij)2. We also generalize this theory to contain an arbitrary number of flavors. For an appropriate choice of the matrix model potential the ground state of the system can be found. Using this potential, we calculate the free energy in the double scaling limit and show that the free energy expansion has the expected form for a theory of open and closed strings if the boundary field mass and couplings have a logarithmic divergence. We then examine the critical properties of this theory and show that the length of the boundary around a hole remains finite, even near the critical point. We also argue that unlike critical string theory or a D = 0 theory, the open string coupling constant is a free parameter.

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17

SEVERIN, LUKAS, M. S. S. BROOKS, and BÖRJE JOHANSSON. "THEORY OF ORBITAL SPLITTING IN METALS." International Journal of Modern Physics B 07, no. 01n03 (January 1993): 255–57. http://dx.doi.org/10.1142/s021797929300055x.

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A theory for orbital splitting is derived from a statistical Hartree-Fock (HF) treatment of open shell interactions. In a scaling procedure, where the HF spinpolarization matrix is replaced by the corresponding local spin density matrix, an expression for the orbital splitting is derived which is well suited for implementation in the standard ab initio calculational scheme. Results for Co metal as well as for the itinerant 5f ferromagnet US is presented, which are in good agreement with experiment.

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18

Ungar, A. A. "The density matrix for mixed state qubits and hyperbolic geometry." Quantum Information and Computation 2, no. 6 (October 2002): 513–14. http://dx.doi.org/10.26421/qic2.6-5.

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Density matrices for mixed state qubits, parametrized by the Bloch vector in the open unit ball of the Euclidean 3-space, are well known in quantum information and computation theory. By presenting new identities for the qubit density matrix we indicate its intimate relationship with M\"obius addition and scalar multiplication. The latter, in turn, form the algebraic setting for the Poincar\'e ball model of hyperbolic geometry so that, as a result, the qubit density matrix is linked to hyperbolic geometry.

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19

Boendgen, Gisela, and Peter Saalfrank. "STM-Induced Desorption of Hydrogen from a Silicon Surface: An Open-System Density Matrix Study." Journal of Physical Chemistry B 102, no. 41 (October 1998): 8029–35. http://dx.doi.org/10.1021/jp9823695.

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20

Zenichowski, Karl, Tillmann Klamroth, and Peter Saalfrank. "Open-system density matrix description of an STM-driven atomic switch: H on Si(100)." Applied Physics A 93, no. 2 (November 2008): 319–33. http://dx.doi.org/10.1007/s00339-008-4833-3.

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21

MORAWETZ, KLAUS, VÁCLAV ŠPIČKA, and PAVEL LIPAVSKÝ. "NONLOCAL KINETIC THEORY." International Journal of Modern Physics B 15, no. 10n11 (May 10, 2001): 1744–47. http://dx.doi.org/10.1142/s0217979201006288.

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The short time behavior of a disturbed system is influenced by off-shell motion and characterized by the reduced density matrix possessing high energetic tails. After this short time regime the time evolution is controlled by small gradients. This leads to a nonlocal Boltzmann equation for the quasiparticle distribution and a functional relating the latter one to the reduced density matrix. The nonlocalities are presented as time and space shifts arising from gradient expansion and are leading to virial corrections in the thermodynamical limit.

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22

Ueda, Masahito. "Nonequilibrium open-system theory for continuous photodetection processes: A probability-density-functional description." Physical Review A 41, no. 7 (April 1, 1990): 3875–90. http://dx.doi.org/10.1103/physreva.41.3875.

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23

Wang Lu-Xia and Chang Kai-Nan. "Study on electron transfer in a heterogeneous system using a density matrix theory approach." Acta Physica Sinica 63, no. 13 (2014): 137302. http://dx.doi.org/10.7498/aps.63.137302.

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24

Dutta, Nirupam, A. K. Chaudhuri, and P. K. Panigrahi. "Effect of high frequency modes of medium on an open quantum system." Modern Physics Letters A 31, no. 02 (January 10, 2016): 1650002. http://dx.doi.org/10.1142/s0217732316500024.

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We present a method to calculate the real time effective propagator of a generic open quantum system, immersed in a medium using a wave function based framework. The medium is characterized by a set of harmonic oscillators having a continuous span of frequencies. This technique has been applied to the Caldeira–Leggett model showing that high frequency modes of the medium do not contribute towards decay of the population of states of the open system. In fact, they cause a Rabi-type oscillation. Moreover, our wave function based approach provides an excellent alternative to conventional formalisms involving the density matrix.

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25

Zhao, Chao-Ying, Qi-Zhi Guo, and Wei-Han Tan. "A novel entanglement criterion of two-qubit system." International Journal of Modern Physics B 34, no. 05 (February 17, 2020): 2050022. http://dx.doi.org/10.1142/s0217979220500228.

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The “separability problem” in quantum information theory is a quite important and well-known hard problem. The low-dimensional system satisfies the PPT criterion. However, the high-dimensional system problem has been shown to be NP-hard problem. In general, it is very difficult to find the analytic solution of the density matrix for the high-dimensional system. Therefore, getting an analytic solution for two-qubit system is an interesting and useful problem. We propose a novel criterion for separability and entanglement-verification of two-qubit system. We expressed the density matrix by a sum of a principal density matrix and six separable density matrices. The necessary and sufficient conditions for the two-qubit system include that if the four involved coefficients [Formula: see text], [Formula: see text], [Formula: see text], [Formula: see text] and the principal density matrix [Formula: see text] are separable, then the two-qubit system is separable, otherwise the two-qubit system is entangled. Finally, our criterion results in a totally different conclusion compared to Horodecki’s criterion. We believe that the new criterion is more stringent than existing PPT methods.

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26

Ring, P. "Covariant density functional theory for rare isotopes." HNPS Proceedings 14 (December 5, 2019): 25. http://dx.doi.org/10.12681/hnps.2244.

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Modern methods for the description of the nuclear many-body system use the concepts of density functional theory (DFT) and of effective field theory (EFT). The covariant version of this theory is based on a density functional which takes into account Lorentz symmetry in a self-consistent way. Pairing correlations play an important role in all open-shell configurations. They are included in relativistic Hartree Bogoliubov (RHB) theory by an effective residual interaction of finite range. With a minimal number of phenomenological parameters this theory allows a very successful phenomenological description of ground state properties of nuclei all over the periodic table. Recently this method has also been extended for the investigations of excited states, such as collective vibrations and rotations.

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27

KIM, HYUN-JOO, and DOIL JUNG. "SPECTRAL DENSITY SCALING OF FLUCTUATING INTERFACES." Modern Physics Letters B 27, no. 27 (October 15, 2013): 1350197. http://dx.doi.org/10.1142/s0217984913501972.

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In this paper, covariance matrices of heights measured relative to the average height of growing self-affine surfaces in the steady state are investigated in the framework of random matrix theory. We show that the spectral density of the covariance matrix scales as ρ(λ) ~ λ-ν deviating from the prediction of random matrix theory and has a scaling form, ρ(λ, L) = λ-ν f(λ/Lϕ) for the lateral system size L, where the scaling function f(x) approaches a constant for λ ≪ Lϕ and zero for Lϕ≪λ< λ max . The values of exponents obtained by numerical simulations are ν ≈ 1.70 and ϕ ≈ 1.51 for the Edward–Wilkinson class and ν ≈ 1.61 and ϕ ≈ 1.76 for the Kardar–Parisi–Zhang class, respectively. The distribution of the largest eigenvalues follows a scaling form as ρ(λ max , L) = 1/Lb f max ((λ max - La)/Lb), which is different from the Tracy–Widom distribution of random matrix theory while the exponents a and b are given by the same values for the two different classes.

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MAVROMATOS, NICK E., and RICHARD J. SZABO. "NONLINEAR SCHRÖDINGER DYNAMICS OF MATRIX D-BRANES." International Journal of Modern Physics A 16, no. 02 (January 20, 2001): 209–50. http://dx.doi.org/10.1142/s0217751x01002348.

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We formulate an effective Schrödinger wave equation describing the quantum dynamics of a system of D0-branes by applying the Wilson renormalization group equation to the world sheet partition function of a deformed σ-model describing the system, which includes the quantum recoil due to the exchange of string states between the individual D-particles. We arrive at an effective Fokker–Planck equation for the probability density with diffusion coefficient determined by the total kinetic energy of the recoiling system. We use Galilean invariance of the system to show that there are three possible solutions of the associated nonlinear Schrödinger equation depending on the strength of the open string interactions among the D-particles. When the open string energies are small compared to the total kinetic energy of the system, the solutions are governed by freely-propagating solitary waves. When the string coupling constant reaches a dynamically determined critical value, the system is described by minimal uncertainty wavepackets which describe the smearing of the D-particle coordinates due to the distortion of the surrounding space–time from the string interactions. For strong string interactions, bound state solutions exist with effective mass determined by an energy-dependent shift of the static BPS mass of the D0-branes.

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29

Baldsiefen, Tim, and E. K. U. Gross. "Minimization procedure in reduced density matrix functional theory by means of an effective noninteracting system." Computational and Theoretical Chemistry 1003 (January 2013): 114–22. http://dx.doi.org/10.1016/j.comptc.2012.09.001.

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30

Swiatkowski, Marcin, Tomasz Sieranski, Marta Bogdan, and Rafal Kruszynski. "Structural Insights into Influence of Isomerism on Properties of Open Shell Cobalt Coordination System." Molecules 24, no. 18 (September 16, 2019): 3357. http://dx.doi.org/10.3390/molecules24183357.

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The two coordination compounds of cobalt were designed and synthesized. The substrates were carefully selected to allow gentle tuning of the molecular structure of the designed compounds. The crystal, molecular and supramolecular structure of studied compounds has been determined and discussed. The spectroscopic and thermal properties of designed coordination compounds have been studied and their application as precursors for the synthesis of cobalt oxide nanoparticles has been demonstrated. It was proven that not only are parameters of conversion of the precursor to nanoparticles important, but also small changes in molecular structure can considerably affect the size of formed particles. For unambiguous determination of the influence of compounds structure on their UV-Vis radiation absorption, density functional theory and time-dependent density functions theory calculations have been performed. The complexity of the correct ab-initio reflection of the open shell molecular system was outlined and discussed. The results obtained from density functional theory (DFT) calculations have been also employed for discussion of the bonding properties.

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31

Baer, Roi, and Martin Head-Gordon. "Sparsity of the Density Matrix in Kohn-Sham Density Functional Theory and an Assessment of Linear System-Size Scaling Methods." Physical Review Letters 79, no. 20 (November 17, 1997): 3962–65. http://dx.doi.org/10.1103/physrevlett.79.3962.

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Yu, Kuang, and Emily A. Carter. "Extending density functional embedding theory for covalently bonded systems." Proceedings of the National Academy of Sciences 114, no. 51 (December 4, 2017): E10861—E10870. http://dx.doi.org/10.1073/pnas.1712611114.

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Quantum embedding theory aims to provide an efficient solution to obtain accurate electronic energies for systems too large for full-scale, high-level quantum calculations. It adopts a hierarchical approach that divides the total system into a small embedded region and a larger environment, using different levels of theory to describe each part. Previously, we developed a density-based quantum embedding theory called density functional embedding theory (DFET), which achieved considerable success in metals and semiconductors. In this work, we extend DFET into a density-matrix–based nonlocal form, enabling DFET to study the stronger quantum couplings between covalently bonded subsystems. We name this theory density-matrix functional embedding theory (DMFET), and we demonstrate its performance in several test examples that resemble various real applications in both chemistry and biochemistry. DMFET gives excellent results in all cases tested thus far, including predicting isomerization energies, proton transfer energies, and highest occupied molecular orbital–lowest unoccupied molecular orbital gaps for local chromophores. Here, we show that DMFET systematically improves the quality of the results compared with the widely used state-of-the-art methods, such as the simple capped cluster model or the widely used ONIOM method.

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LAWANDE, S. V., and Q. V. LAWANDE. "PATH INTEGRAL DERIVATION OF AN EXACT MASTER EQUATION." Modern Physics Letters B 09, no. 02 (January 20, 1995): 87–94. http://dx.doi.org/10.1142/s0217984995000097.

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The Feynman propagator in coherent states representation is obtained for a system of a single harmonic oscillator coupled to a reservoir of N oscillators. Using this propagator, an exact master equation is obtained for the evolution of the reduced density matrix for the open system of the oscillator.

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MATSUO, YUTAKA. "LONG OPEN STRING AND NON-SINGLET SECTOR IN MATRIX QUANTUM MECHANICS." International Journal of Modern Physics A 23, no. 14n15 (June 20, 2008): 2091–98. http://dx.doi.org/10.1142/s0217751x08040639.

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Recently Maldacena conjectured that the long folded open string in noncritical string theory is described by the non-singlet sectors of matrix quantum mechanics. In this paper, we first describe how to obtain the exact wave functions of this system when the sign of the potential is reverted, based on a work with Y. Hatsuda. The wave functions are labeled by three Young diagrams and the degeneracy associated with it is given by the group theoretical quantities. In the second part, based on a work with J.-E. Bourgine, K. Hosomichi and I. Kostov, we derive the scattering amplitude of two long strings and which coincides with the result from the Liouville theory. It generalizes the result of the one-body scattering by Kostov and uses the relation with the two-matrix model correlation functions.

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35

Finger, Karin, and Peter Saalfrank. "Vibrationally excited products after the photodesorption of NO from Pt(111): a two-mode open-system density matrix approach." Chemical Physics Letters 268, no. 3-4 (April 1997): 291–99. http://dx.doi.org/10.1016/s0009-2614(97)00189-9.

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Sik Noh, Hyun, Sang Koo You, and Chul Koo Kim. "Finite Temperature Many-Particle Theory of Condensed Matter Systems in the Functional Schrödinger Picture." International Journal of Modern Physics B 11, no. 15 (June 20, 1997): 1829–37. http://dx.doi.org/10.1142/s0217979297000940.

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A finite temperature many-particle theory of condensed matter systems is formulated using the functional Schrödinger picture. Using the interacting electron gas as a model system, we solve the equation of motion for the density matrix variationally with a Gaussian type trial density matrix. We show that the present formalism yields the finite temperature Hartree–Fock results both for the para- and ferromagnetic states in a simple and convenient fashion. Implications of the present results and future prospects are also discussed.

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37

Eleuch, Hichem, and Ingrid Rotter. "EXCEPTIONAL POINTS IN OPEN AND PT-SYMMETRIC SYSTEMS." Acta Polytechnica 54, no. 2 (April 30, 2014): 106–12. http://dx.doi.org/10.14311/ap.2014.54.0106.

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Exceptional points (EPs) determine the dynamics of open quantum systems and cause also PT symmetry breaking in PT symmetric systems. From a mathematical point of view, this is caused by the fact that the phases of the wavefunctions (eigenfunctions of a non-Hermitian Hamiltonian) relative to one another are not rigid when an EP is approached. The system is therefore able to align with the environment to which it is coupled and, consequently, rigorous changes of the system properties may occur. We compare analytically as well as numerically the eigenvalues and eigenfunctions of a 2 × 2 matrix that is characteristic either of open quantum systems at high level density or of PT symmetric optical lattices. In both cases, the results show clearly the influence of the environment on the system in the neighborhood of EPs. Although the systems are very different from one another, the eigenvalues and eigenfunctions indicate the same characteristic features.

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38

Nest, Mathias, and Peter Saalfrank. "Open-system density matrix description of femtosecond laser desorption of electronically and vibrationally relaxing adsorbates: Single- and two-pulse scenarios." Journal of Chemical Physics 116, no. 16 (April 22, 2002): 7189–99. http://dx.doi.org/10.1063/1.1462608.

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39

Wood, Christopher J., Jacob D. Biamonte, and David G. Cory. "Tensor networks and graphical calculus for open quantum systems." Quantum Information and Computation 15, no. 9&10 (July 2015): 759–811. http://dx.doi.org/10.26421/qic15.9-10-3.

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We describe a graphical calculus for completely positive maps and in doing so review the theory of open quantum systems and other fundamental primitives of quantum information theory using the language of tensor networks. In particular we demonstrate the construction of tensor networks to pictographically represent the Liouville-superoperator, Choi-matrix, process-matrix, Kraus, and system-environment representations for the evolution of quantum states, review how these representations interrelate, and illustrate how graphical manipulations of the tensor networks may be used to concisely transform between them. To further demonstrate the utility of the presented graphical calculus we include several examples where we provide arguably simpler graphical proofs of several useful quantities in quantum information theory including the composition and contraction of multipartite channels, a condition for whether an arbitrary bipartite state may be used for ancilla assisted process tomography, and the derivation of expressions for the average gate fidelity and entanglement fidelity of a channel in terms of each of the different representations of the channel.

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Caravelli, Francesco, Bin Yan, Luis Pedro García-Pintos, and Alioscia Hamma. "Energy storage and coherence in closed and open quantum batteries." Quantum 5 (July 15, 2021): 505. http://dx.doi.org/10.22331/q-2021-07-15-505.

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We study the role of coherence in closed and open quantum batteries. We obtain upper bounds to the work performed or energy exchanged by both closed and open quantum batteries in terms of coherence. Specifically, we show that the energy storage can be bounded by the Hilbert-Schmidt coherence of the density matrix in the spectral basis of the unitary operator that encodes the evolution of the battery. We also show that an analogous bound can be obtained in terms of the battery's Hamiltonian coherence in the basis of the unitary operator by evaluating their commutator. We apply these bounds to a 4-state quantum system and the anisotropic XY Ising model in the closed system case, and the Spin-Boson model in the open case.

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41

Tong, M. D., and W. K. Chen. "Perfect Multivariable Feedback Theory." Journal of Circuits, Systems and Computers 07, no. 02 (April 1997): 129–51. http://dx.doi.org/10.1142/s0218126697000103.

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The paper nicely combines the state-space description with the input-output description and elegantly formulates the multivariable feedback theory as well as obtains a number of useful results for modern network and control theory. In particular, it reveals various kinds of duality between a multivariable feedback network and its associated inverse network, such as structure duality, transfer function matrix (determinant) duality and duality on controllability (observability). It also thoroughly studies four pairs of the (null) return difference matrices of a multivariable feedback network and its associated inverse network, and presents not only the dual properties about these (null) return diferrence matrices and their respective determinants, but also treats the relationships among these determinants, the characteristic polynomials of a closed-loop network (the multivariable feedback network), its associated closed-loop inverse network, and their respective corresponding open-loop networks. Finally, the stability criteria, the testing criteria for a minimum-phase matrix and the sensitivity matrices are discussed. Although all of these results are obtained for a continuous system, they are also suitable for a discrete system provided that we use the z-transformation instead of the Laplace transformation.

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DALLEY, S., C. V. JOHNSON, T. R. MORRIS, and A. WÄTTERSTAM. "UNITARY MATRIX MODELS AND 2D QUANTUM GRAVITY." Modern Physics Letters A 07, no. 29 (September 21, 1992): 2753–62. http://dx.doi.org/10.1142/s0217732392002226.

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The KdV and modified KdV integrable hierarchies are shown to be different descriptions of the same 2D gravitational system — open-closed string theory. Non-perturbative solutions of the multicritical unitary matrix models map to non-singular solutions of the 'renormalization group' equation for the string susceptibility, [Formula: see text]. We also demonstrate that the large-N solutions of unitary matrix integrals in external fields, studied by Gross and Newman, equal the non-singular pure closed-string solutions of [Formula: see text].

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43

Youcef-Toumi, Kamal, and Haruhiko Asada. "The Design of Open-Loop Manipulator Arms With Decoupled and Configuration-Invariant Inertia Tensors." Journal of Dynamic Systems, Measurement, and Control 109, no. 3 (September 1, 1987): 268–75. http://dx.doi.org/10.1115/1.3143854.

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A manipulator design theory for reduced dynamic complexity is presented. The kinematic structure and mass distribution of a manipulator arm are designed so that the inertia matrix in the equation of motion becomes diagonal and/or invariant for an arbitrary arm configuration. For the decoupled and invariant inertia matrix, the system can be treated as a linear, single-input, single-output system with constant parameters. Consequently, control of the manipulator arm is simplified, and more importantly, the reduced dynamic complexity permits improved control performance. First, the problem of designing such an arm with a decoupled and/or configuration-invariant inertia matrix is defined. The inertia matrix is then analyzed in relation to the kinematic structure and mass properties of the arm links. Necessary conditions for a decoupled and/or configuration-invariant manipulator inertia matrix are then obtained. Using the necessary conditions, the kinematic structure and mass properties are found which reduce the inertia matrix to a constant diagonal form. Possible arm designs for decoupled and/or invariant inertia matrices are then determined for 2 and 3 degree-of-freedom manipulators.

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RING, GERARD J. F. "The hyperbolic theory of light scattering, tensile strength, and density in paper." November 2011 11, no. 11 (December 1, 2011): 9–18. http://dx.doi.org/10.32964/tj10.11.9.

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The hyperbolic theory of light scattering, tensile strength, and density in paper describes a sheet of paper as a matrix of cellulose with a characteristic material strength and open and closed pores dispersed through the cellulose, forming solid foam. This paper presents two principle hyperbolic equations. The first describes the conservation of tensile strength and the second describes the conservation of mass as functions of light scattering. Three additional equations are derived. The first relates tensile strength to sheet density, the second relates light scattering to total pore volume, and the third relates tensile strength to total pore volume. The conservation of tensile strength equation varies with processing for a given cellulose pulp. Variable refining levels at constant levels of wet-pressing produce separate curves for each wet-pressing level. Correspondingly, variable wet-pressing levels produce separate curves for each level of constant refining. Hydrolyzing pulps or cutting fibers to shorten the average degree of cellulose polymerization shifts the curves to lower tensile strengths. The conservation of mass equation results in a single curve, regardless of processing or reduction in the degree of cellulose polymerization. The concept of relative bonded area measurement using light scattering as developed by Ingmanson and Thode is shown to be invalid for paper by this hyperbolic theory. The validity of relative bonded area by any technique is also questioned.

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Khadyko, Mikhail, Stéphane Dumoulin, and Odd Sture Hopperstad. "Slip System Interaction Matrix and its Influence on the Macroscopic Response of Al Alloys." Materials Science Forum 794-796 (June 2014): 566–71. http://dx.doi.org/10.4028/www.scientific.net/msf.794-796.566.

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In numerical models based on the crystal plasticity theory, various rules are implemented to describe hardening on the slip system level. The rules used are often variations of the Mecking-Kocks law, where the statistically stored dislocation density is the single internal variable. The dislocation density evolution equation consists of two terms representing accumulation and annihilation of dislocations. The accumulation term depends on a scalar parameter and an interaction matrix, which describes the contribution of all slip systems to the accumulation of the dislocations on a given slip system. Physically this matrix represents the relative strength of various dislocation locks which form when dislocations from different slip systems interact. The numerical values of the elements of the interaction matrix are rather hard to establish, but this has been done experimentally for different alloys and also based on numerical simulations. The obtained values, found in literature, are very different from each other. We use some new experimental data in an attempt to establish the influence of the numerical values of the elements of the interaction matrix on the hardening of a polycrystal.

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Strunz, Walter T. "Finite Temperature Dynamics of the Total State in an Open System Model." Open Systems & Information Dynamics 12, no. 01 (March 2005): 65–80. http://dx.doi.org/10.1007/s11080-005-0487-1.

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We determine the dynamics of the total state of a system and environment for an open system model, at finite temperature. Based on a partial Husimi representation, our framework describes the full dynamics very efficiently through equations in the Hilbert space of the open system only. We briefly review the zero-temperature case and present the corresponding new finite temperature theory, within the usual Born-Markov approximation. As we will show, from a reduced point of view, our approach amounts to the derivation of a stochastic Schrödinger equation description of the dynamics. We show how the reduced density operator evolves according to the expected (finite temperature) master equation of Lindblad form.

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Ganesan, Timothy, Pandian Vasant, Pratik Sanghvi, Joshua Thomas, and Igor Litvinchev. "Random Matrix Generators for Optimizing a Fuzzy Biofuel Supply Chain System." Journal of Advanced Engineering and Computation 4, no. 1 (March 31, 2020): 33. http://dx.doi.org/10.25073/jaec.202041.268.

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Complex industrial systems often contain various uncertainties. Hence sophisticated fuzzy optimization (metaheuristics) techniques have become commonplace; and are currently indispensable for effective design, maintenance and operations of such systems. Unfortunately, such state-of-the-art techniques suffer several drawbacks when applied to largescale problems. In line of improving the performance of metaheuristics in those, this work proposes the fuzzy random matrix theory (RMT) as an add-on to the cuckoo search (CS) technique for solving the fuzzy large-scale multiobjective (MO) optimization problem; biofuel supply chain. The fuzzy biofuel supply chain problem accounts for uncertainties resulting from fluctuations in the annual electricity generation output of the biomass power plant [kWh/year]. The details of these investigations are presented and analyzed.This is an Open Access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium provided the original work is properly cited.

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48

Dorofeyev, Illarion. "Relaxation of two coupled quantum oscillators to quasi-equilibrium states based on path integrals." Canadian Journal of Physics 92, no. 10 (October 2014): 1208–22. http://dx.doi.org/10.1139/cjp-2013-0708.

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This paper addresses the problem of relaxation of open quantum systems. Using the path integral methods, we found an analytical expression for the time-dependent density matrix of two coupled quantum oscillators interacting with different baths of oscillators. The expression for density matrix was found in the linear regime with respect to the coupling constant between selected oscillators. Time dependent spatial variances and covariances were investigated analytically and numerically. It was shown that asymptotic variances in the long-time limit are always in accordance with the fluctuation dissipation theorem despite their initial values. In the weak coupling approach there is good reason to believe that subsystems are asymptotically in equilibrium at their own temperatures despite the arbitrary difference in temperatures within the whole system.

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49

Witten, Edward. "Matrix models and deformations of JT gravity." Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 476, no. 2244 (December 2020): 20200582. http://dx.doi.org/10.1098/rspa.2020.0582.

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Recently, it has been found that Jackiw-Teitelboim (JT) gravity, which is a two-dimensional theory with bulk action − 1 / 2 ∫ d 2 x g ϕ ( R + 2 ) , is dual to a matrix model, that is, a random ensemble of quantum systems rather than a specific quantum mechanical system. In this article, we argue that a deformation of JT gravity with bulk action − 1 / 2 ∫ d 2 x g ( ϕ R + W ( ϕ ) ) is likewise dual to a matrix model. With a specific procedure for defining the path integral of the theory, we determine the density of eigenvalues of the dual matrix model. There is a simple answer if W (0) = 0, and otherwise a rather complicated answer.

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GONZÁLEZ-DÍAZ, PEDRO F., and SALVADOR ROBLES-PÉREZ. "QUANTUM THEORY OF AN ACCELERATING UNIVERSE." International Journal of Modern Physics D 17, no. 08 (August 2008): 1213–28. http://dx.doi.org/10.1142/s0218271808012772.

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We review some of the well-known features of quantum cosmology, such as the factor ordering problem, the wave function and the density matrix, for a dark-energy-dominated universe, where analytical solutions can be obtained. For the particular case of the phantom universe, we suggest a quantum system in which the usual notion of locality (nonlocality) of quantum information theory has to be extended. In that case, we deal also with a quantum description where the existence of a nonchronal region around the big rip singularity is explicitly accounted for.

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