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Artykuły w czasopismach na temat „Gaussian ansatz”

Autor: Grafiati

Data publikacji: 7 września 2024

Data aktualizacji: 31 lipca 2025

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1

Wang, Meng-Jong. "The Gaussian ansatz and beyond." Il Nuovo Cimento A 104, no. 3 (1991): 449–52. http://dx.doi.org/10.1007/bf02799149.

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GUPTA, SOURENDU, and A. IRBÄCK. "FINITE SIZE SCALING ON THE ISING COEXISTENCE LINE." International Journal of Modern Physics C 03, no. 05 (1992): 1119–24. http://dx.doi.org/10.1142/s0129183192000749.

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We report tests of finite-size scaling ansatzes in the low temperature phase of the two-dimensional Ising model. For moments of the magnetisation density, we find good agreement with the new ansatz of Borgs and Kotecký, and clear evidence of violations of the double Gaussian ansatz. We note that certain consequences of the convexity of the free energy are not adequately treated in either of these approaches.

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3

BISWAS, S., A. SHAW, and D. BISWAS. "SCHRÖDINGER–WHEELER–DEWITT EQUATION IN MULTIDIMENSIONAL COSMOLOGY." International Journal of Modern Physics D 10, no. 04 (2001): 585–93. http://dx.doi.org/10.1142/s0218271801001372.

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We study multidimensional cosmology to obtain the wavefunction of the universe using wormhole dominance proposal. Using a prescription for time we obtain the Schrödinger–Wheeler–DeWitt equation without any reference to WD equation and WKB ansatz for WD wavefunction. It is found that the Hartle–Hawking or wormhole-dominated boundary conditions serve as a seed for inflation as well as for Gaussian type ansatz to Schrödinger–Wheeler–DeWitt equation.

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4

Dinda, P. Tchofo, K. Nakkeeran, and A. B. Moubissi. "Optimized Hermite-gaussian ansatz functions for dispersion-managed solitons." Optics Communications 187, no. 4-6 (2001): 427–33. http://dx.doi.org/10.1016/s0030-4018(00)01135-4.

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5

BISWAS, S., A. SHAW, and B. MODAK. "TIME IN QUANTUM GRAVITY." International Journal of Modern Physics D 10, no. 04 (2001): 595–606. http://dx.doi.org/10.1142/s0218271801001384.

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The Wheeler–DeWitt equation in quantum gravity is timeless in character. In order to discuss quantum to classical transition of the universe, one uses a time prescription in quantum gravity to obtain a time contained description starting from Wheeler–DeWitt equation and WKB ansatz for the WD wavefunction. The approach has some drawbacks. In this work, we obtain the time-contained Schrödinger–Wheeler–DeWitt equation without using the WD equation and the WKB ansatz for the wavefunction. We further show that a Gaussian ansatz for SWD wavefunction is consistent with the Hartle–Hawking or wormhole

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6

Preuss, Roland, and Udo von Toussaint. "Outlier-Robust Surrogate Modeling of Ion–Solid Interaction Simulations." Entropy 25, no. 4 (2023): 685. http://dx.doi.org/10.3390/e25040685.

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Data for complex plasma–wall interactions require long-running and expensive computer simulations. Furthermore, the number of input parameters is large, which results in low coverage of the (physical) parameter space. Unpredictable occasions of outliers create a need to conduct the exploration of this multi-dimensional space using robust analysis tools. We restate the Gaussian process (GP) method as a Bayesian adaptive exploration method for establishing surrogate surfaces in the variables of interest. On this basis, we expand the analysis by the Student-t process (TP) method in order to impro

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7

Wu, Shu-Guang, and Yang Zhang. "The Nonlinear Field Equation of the Three-point Correlation Function of Galaxies: to the Second Order of Density Perturbation." Research in Astronomy and Astrophysics 22, no. 4 (2022): 045015. http://dx.doi.org/10.1088/1674-4527/ac55ff.

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Abstract Based on the field theory of density fluctuation under Newtonian gravity, we obtain analytically the nonlinear equation of 3-pt correlation function ζ of galaxies in a homogeneous, isotropic, static universe. The density fluctuation has been kept up to second order. By the Fry–Peebles ansatz and the Groth-Peebles ansatz, the equation of ζ becomes closed and differs from the Gaussian approximate equation. Using the boundary condition inferred from the data of SDSS, we obtain the solution ζ(r, u, θ) at fixed u = 2, which exhibits a shallow U-shape along the angle θ and, nevertheless, de

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8

Darewych, J. W., and A. D. Polozov. "Variational solution of bound states in a charged interacting scalar-field theory." Canadian Journal of Physics 66, no. 11 (1988): 969–71. http://dx.doi.org/10.1139/p88-155.

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Two interacting [Formula: see text] scalar fields in N spatial dimensions are investigated using the Gaussian variational approximation. The interaction is taken to be in the form [Formula: see text]. Two-particle bound-state solutions are obtained in the domain g < 2λ for N = 1 and 2. The nonrelativistic limit, which is also the weak-coupling limit, is shown to correspond to an attractive delta-function interaction. For N = 3, the Gaussian ansatz suggests triviality of the theory, in that the renormalized coupling constant is identically zero.

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9

Raab, Benedikt, Thomas Srdinko, and Helmut Leeb. "Formulation of Model Defects Suitable for the Resonance Regime." EPJ Web of Conferences 211 (2019): 07006. http://dx.doi.org/10.1051/epjconf/201921107006.

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A method to account for model deficiencies in nuclear data evaluations in the resonance regime is proposed. The method follows the ideas of Schnabel and coworkers and relies on Gaussian processes with a novel problemadapted ansatz for the covariance matrix of model uncertainties extending the formalism to the energy region of resonances. The method was used to evaluate a set of schematic but realistic neutron reaction data generated by an R-matrix code and a well defined model defect. Using the extended ansatz for model defects the Bayesian evaluation successfully recovered the built-in model

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10

PERCUS, J. K. "INTERFACE STRUCTURE." International Journal of Modern Physics B 13, no. 05n06 (1999): 659–66. http://dx.doi.org/10.1142/s0217979299000552.

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Phase-separated fluids are analyzed from several viewpoints: local thermodynamic, in which all density correlations are ignored; mean field, which correctly treats those at medium range; and a modified Kac-Siegert form which only coarse-grains those at short range. The last form appears as an ensemble average over tail potential fields, and is treated variationally with a Gaussian ansatz. Application to a planar interface shows the anticipated surface softening as any confining field is removed, and in statistically homogeneous condensation, a form of the familiar level set description assumes

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11

BARAN, A., A. STASZCZAK, J. DOBACZEWSKI, and W. NAZAREWICZ. "COLLECTIVE INERTIA AND FISSION BARRIERS WITHIN THE SKYRME-HARTREE-FOCK THEORY." International Journal of Modern Physics E 16, no. 02 (2007): 443–51. http://dx.doi.org/10.1142/s0218301307005879.

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Spontaneous fission barriers, quadrupole inertia tensor, and zero-point quadrupole correlation energy are calculated for 252,256,258 Fm in the framework of the self-consistent Skyrme-Hartree-Fock+BCS theory. Two ways of computing collective inertia are employed: the Gaussian Overlap Approximation to the Generator Coordinate Method and cranking ansatz. The Skyrme results are compared with those of the Gogny-Hartree-Fock-Bogolyubov model.

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12

Wai, P. K. A., and K. Nakkeeran. "On the uniqueness of Gaussian ansatz parameters equations: generalized projection operator method." Physics Letters A 332, no. 3-4 (2004): 239–43. http://dx.doi.org/10.1016/j.physleta.2004.09.075.

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13

Iacob, Theodor-Felix, Marina Lute, and Felix Iacob. "A Numerical Approach for the Solution of Schrödinger Equation With Pseudo-Gaussian Potentials." Annals of West University of Timisoara - Physics 58, no. 1 (2015): 1–6. http://dx.doi.org/10.1515/awutp-2015-0201.

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Abstract The Schrödinger equation with pseudo-Gaussian potential is investigated. The pseudo-Gaussian potential can be written as an infinite power series. Technically, by an ansatz to the wave-functions, exact solutions can be found by analytic approach [12]. However, to calculate the solutions for each state, a condition that will stop the series has to be introduced. In this way the calculated energy values may suffer modifications by imposing the convergence of series. Our presentation, based on numerical methods, is to compare the results with those obtained in the analytic case and to de

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14

Dai, J., and R. V. Krems. "Quantum Gaussian process model of potential energy surface for a polyatomic molecule." Journal of Chemical Physics 156, no. 18 (2022): 184802. http://dx.doi.org/10.1063/5.0088821.

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With gates of a quantum computer designed to encode multi-dimensional vectors, projections of quantum computer states onto specific qubit states can produce kernels of reproducing kernel Hilbert spaces. We show that quantum kernels obtained with a fixed ansatz implementable on current quantum computers can be used for accurate regression models of global potential energy surfaces (PESs) for polyatomic molecules. To obtain accurate regression models, we apply Bayesian optimization to maximize marginal likelihood by varying the parameters of the quantum gates. This yields Gaussian process models

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15

Boulougouris, Georgios C. "Free energy calculations, enhanced by a gaussian ansatz, for the “chemical work” distribution." Journal of Computational Chemistry 35, no. 13 (2014): 1024–35. http://dx.doi.org/10.1002/jcc.23590.

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16

Aydogmus, Fatma. "Numeric Solutions of Dirac–Gursey Spinor Field Equation Under External Gaussian White Noise." Fluctuation and Noise Letters 15, no. 02 (2016): 1650018. http://dx.doi.org/10.1142/s0219477516500188.

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In this paper, we consider the Dirac-Gursey spinor field equation that has particle-like solutions derived classical field equations so-called instantons, formed by using Heisenberg ansatz, under the effect of an additional Gaussian white noise term. Our purpose is to understand how the behavior of spinor-type excited instantons in four dimensions can be affected by noise. Thus, we simulate the phase portraits and Poincaré sections of the obtained system numerically both with and without noise. Recurrence plots are also given for more detailed information regarding the system.

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17

Spychala, Kai J., Zeeshan H. Amber, Lukas M. Eng, and Michael Ruesing. "Modeling nonlinear optical interactions of focused beams in bulk crystals and thin films: A phenomenological approach." Journal of Applied Physics 133, no. 12 (2023): 123105. http://dx.doi.org/10.1063/5.0136252.

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Coherent nonlinear optical [Formula: see text]-spectroscopy is a frequently used tool in modern material science as it is sensitive to many different local observables, which comprise, among others, crystal symmetry and vibrational properties. The richness in information, however, may come with challenges in data interpretation, as one has to disentangle the many different effects like multiple reflections, phase jumps at interfaces, or the influence of the Guoy-phase. In order to facilitate interpretation, the work presented here proposes an easy-to-use semi-analytical modeling Ansatz, which

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18

Rusin, Rahmi, Rudy Kusdiantara, and Hadi Susanto. "Variational approximations using Gaussian ansatz, false instability, and its remedy in nonlinear Schrödinger lattices." Journal of Physics A: Mathematical and Theoretical 51, no. 47 (2018): 475202. http://dx.doi.org/10.1088/1751-8121/aae4be.

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19

Wang, Hui, and Tian-Tian Zhang. "Stability analysis, solition solutions and Gaussian solitons of the generalized nonlinear Schrödinger equation with higher order terms." International Journal of Numerical Methods for Heat & Fluid Flow 29, no. 3 (2019): 878–89. http://dx.doi.org/10.1108/hff-08-2018-0448.

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Purpose The purpose of this paper is to study stability analysis, solition solutions and Gaussian solitons of the generalized nonlinear Schrödinger equation with higher order terms, which can be used to describe the propagation properties of optical soliton solutions. Design/methodology/approach The authors apply the ansatz method and the Hamiltonian system technique to find its bright, dark and Gaussian wave solitons and analyze its modulation instability analysis and stability analysis solution. Findings The results imply that the generalized nonlinear Schrödinger equation has bright, dark a

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20

Barna, Imre F., Gabriella Bognár, Mohammed Guedda, László Mátyás, and Krisztián Hriczó. "ANALYTIC SELF-SIMILAR SOLUTIONS OF THE KARDAR-PARISI-ZHANG INTERFACE GROWING EQUATION WITH VARIOUS NOISE TERMS." Mathematical Modelling and Analysis 25, no. 2 (2020): 241–56. http://dx.doi.org/10.3846/mma.2020.10459.

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The one-dimensional Kardar-Parisi-Zhang dynamic interface growth equation with the self-similar ansatz is analyzed. As a new feature additional analytic terms are added. From the mathematical point of view, these can be considered as various noise distribution functions. Six different cases were investigated among others Gaussian, Lorentzian, white or even pink noise. Analytic solutions are evaluated and analyzed for all cases. All results are expressible with various special functions like Kummer, Heun, Whittaker or error functions showing a very rich mathematical structure with some common g

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21

YAMAGUCHI, SATOSHI. "BUBBLING GEOMETRIES FOR HALF-BPS WILSON LINES." International Journal of Modern Physics A 22, no. 07 (2007): 1353–74. http://dx.doi.org/10.1142/s0217751x07035070.

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We consider the supergravity backgrounds that correspond to supersymmetric Wilson line operators in the context of AdS/CFT correspondence. We study the gravitino and dilatino conditions of the IIB supergravity under the appropriate ansatz, and obtain some necessary conditions for a supergravity background that preserves the same symmetry as the supersymmetric Wilson lines. The supergravity solutions are characterized by continuous version of Maya diagrams. This diagram is related to the eigenvalue distribution of the Gaussian matrix model. We also consider the similar backgrounds of the 11-dim

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22

Leone, Lorenzo, Salvatore F. E. Oliviero, Lukasz Cincio, and M. Cerezo. "On the practical usefulness of the Hardware Efficient Ansatz." Quantum 8 (July 3, 2024): 1395. http://dx.doi.org/10.22331/q-2024-07-03-1395.

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Variational Quantum Algorithms (VQAs) and Quantum Machine Learning (QML) models train a parametrized quantum circuit to solve a given learning task. The success of these algorithms greatly hinges on appropriately choosing an ansatz for the quantum circuit. Perhaps one of the most famous ansatzes is the one-dimensional layered Hardware Efficient Ansatz (HEA), which seeks to minimize the effect of hardware noise by using native gates and connectives. The use of this HEA has generated a certain ambivalence arising from the fact that while it suffers from barren plateaus at long depths, it can als

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23

Putra, Gusrian, Hanifah Septaningtiyas, Elsa Nabila, and Lisa Arianti Br Tarigan. "Analisis Kestabilan Solusi Soliton pada Persamaan Schrodinger Nonlinier Diskrit Nonlokal." Indonesian Journal of Applied Mathematics 2, no. 1 (2022): 17. http://dx.doi.org/10.35472/indojam.v2i1.730.

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In this paper, the Nonlocal Discrete Nonlinear Schrodinger (DNLS) equation that interpolates the Nonlocal Ablowitz-Ladik DNLS and the Nonlocal Cubic DNLS equations and its stability are studied in detail. The solution of the Nonlocal SNLD equation is a soliton wave in the form of a Gaussian ansatz obtained using the method of Variational Approximation (VA). The stability of the solution is also analyzed using the VA. These semi-analytical results are then compared to numerical results. The soliton and its stability obtained via VA is concluded to be having a fairly good conformity with numeric

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24

ANTONOV, D. V. "AN EXACT SOLUTION OF THE LOOP EQUATION IN STRONG TURBULENCE." Modern Physics Letters A 11, no. 39n40 (1996): 3113–18. http://dx.doi.org/10.1142/s021773239600309x.

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The Hamilton–Jacobi equation for the loop effective action in strong turbulence with Gaussian random forces1,2 is solved by making use of the smearing procedure for the loop space functional Laplacian, proposed in Ref. 3. The solution obtained satisfies tensor- or scalar area law ansatz and depends on the initial data and the potential term in the loop Hamiltonian, averaged over loops. In the lowest order in the viscosity this average may be eliminated, and the solution is given by a certain linear combination of the initial data and the potential term and their functional derivatives.

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25

Nse Biyoghe, S., Th B. Ekogo, and A. B. Moubissi. "Collective variable analysis of the nonlinear Schrödinger equation for soliton molecules in fibers." Journal of Nonlinear Optical Physics & Materials 26, no. 02 (2017): 1750023. http://dx.doi.org/10.1142/s0218863517500230.

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We present a description of soliton molecules in terms of its collective variables namely temporal separation between two consecutive pulses, peak-power of each pulse, center-of-mass, chirp, frequency and phase of the whole molecule. Assuming the Hermite–Gaussian ansatz to represent the temporal profile of the molecule, we derive a set of six differential equations for the evolution of the collective variables in the limit of the bare or variational approximation. Then we perform numerical experiments to confirm the ability of the proposed approach for two-soliton molecule propagating along a

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26

Ruban, V. P. "Gaussian variational ansatz in the problem of anomalous sea waves: Comparison with direct numerical simulation." Journal of Experimental and Theoretical Physics 120, no. 5 (2015): 925–32. http://dx.doi.org/10.1134/s1063776115050179.

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27

Sattary Nikkhoo, Negin, and Mohammad Reza Shojaei. "Electromagnetic and gravitational form factors by using the modified Gaussian ansatz for Hq(x,t)." Nuclear Physics A 969 (January 2018): 138–50. http://dx.doi.org/10.1016/j.nuclphysa.2017.09.010.

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28

Mardonov, Shukhrat N., and Bobomurat J. Ahmedov. "Rabi Frequency Management of Collapsing Quasi-Two-Dimensional Bose-Einstein Condensates with Pseudospin-1/2." Particles 5, no. 2 (2022): 135–45. http://dx.doi.org/10.3390/particles5020012.

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The collapse of quasi-two-dimensional pseudospin-1/2 Bose-Einstein condensate of attracting atoms with intra- and cross-spin interaction is studied in the presence of the Rabi coupling. The condensate dynamics is presented as a function of the self-interaction and Rabi frequency. The evolution of two components of the condensate by using the Gross-Pitaevskii equations is investigated. The initial Gaussian ansatz for two-component wave functions is selected for the better interpretation of the numerical results. The intra-spin-coupling modifies the critical number of atoms causing the collapse

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29

DE AVELLAR, MARCIO G. B., and J. E. HORVATH. "EXACT AND QUASI-EXACT MODELS OF STRANGE STARS." International Journal of Modern Physics D 19, no. 12 (2010): 1937–55. http://dx.doi.org/10.1142/s0218271810018128.

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We construct and compare in this work a variety of simple models for strange stars, namely, hypothetical self-bound objects made of a cold stable version of the quark-gluon plasma. Exact, quasi-exact and numerical models are examined to find the most economical description for these objects. A simple and successful parametrization of them is given in terms of the central density, and the differences among the models are explicitly shown and discussed. In particular, we present a model starting with a Gaussian ansatz for the density profile that provides a very accurate and almost complete anal

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30

Piela, Lucjan. "Search for the Most Stable Structures on Potential Energy Surfaces." Collection of Czechoslovak Chemical Communications 63, no. 9 (1998): 1368–80. http://dx.doi.org/10.1135/cccc19981368.

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Smoothing techniques for global optimization in search for the most stable structures (clusters or conformers) have been a novel possibility for the last decade. The techniques turned out to be related to a variety of fundamental laws: Fick's diffusion equation, time-dependent and time-independent Schrodinger equations, Smoluchowski dynamics equation, Bloch equation of canonical ensemble evolution with temperature, Gibbs free-energy principle. The progress indicator of global optimization in those methods takes different physical meanings: time, imaginary time, Planck constant, or the inverse

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31

Çakmak, Burak, Yue M. Lu, and Manfred Opper. "Analysis of random sequential message passing algorithms for approximate inference." Journal of Statistical Mechanics: Theory and Experiment 2022, no. 7 (2022): 073401. http://dx.doi.org/10.1088/1742-5468/ac764a.

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Abstract We analyze the dynamics of a random sequential message passing algorithm for approximate inference with large Gaussian latent variable models in a student–teacher scenario. To model nontrivial dependencies between the latent variables, we assume random covariance matrices drawn from rotation invariant ensembles. Moreover, we consider a model mismatching setting, where the teacher model and the one used by the student may be different. By means of dynamical functional approach, we obtain exact dynamical mean-field equations characterizing the dynamics of the inference algorithm. We als

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32

Song, Yu-Kun. "Azimuthal Asymmetries for eA/eN Semi-Inclusive DIS and Its Nuclear Dependence." International Journal of Modern Physics: Conference Series 40 (January 2016): 1660036. http://dx.doi.org/10.1142/s2010194516600363.

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We applied collinear expansion to the semi-inclusive deeply inelastic lepton-nucleon (nucleus) scattering process [Formula: see text] with both polarized beam and polarized target up to twist-3, and unpolarized process up to twist-4. The differential cross section and azimuthal asymmetries are expressed in terms of gauge invariant twist-3 and twist-4 TMD parton distribution/correlation functions. Measurements of such azimuthal asymmetries provide methods to study different spin and transverse momentum aspects of the partonic structure of nucleon. We further study the nuclear dependence of azim

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33

Prestipino, Santi, Alessandro Sergi, Ezio Bruno, and Paolo V. Giaquinta. "A variational mean-field study of clusterization in a zero-temperature system of soft-core bosons." EPJ Web of Conferences 230 (2020): 00008. http://dx.doi.org/10.1051/epjconf/202023000008.

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We work out the ground-state diagram of weakly-repulsive penetrable bosons, using mean-field theory with a Gaussian ansatz on the single-particle wave function. Upon compression, the fluid transforms into a cluster supersolid, whose structure is characterized for various choices of the embedding space. In Euclidean space, the stable crystals are those with the most compact structure, i.e., triangular and fcc in two and three dimensions, respectively. For particles confined in a spherical surface, as the sphere radius increases we observe a sequence of transitions between different cluster phas

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34

Kadam, Guru Prakash. "Transport properties of hadronic matter in magnetic field." Modern Physics Letters A 30, no. 10 (2015): 1550031. http://dx.doi.org/10.1142/s0217732315500315.

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We study the effect of magnetic field on the transport properties like shear and bulk viscosities of hot and dense hadronic matter within hadron resonance gas model. We estimate the bulk viscosity using low energy theorems for bilocal correlators of the energy–momentum tensor generalized to finite temperature, density and magnetic field. We use Gaussian ansatz for the spectral function at low frequency. We estimate shear viscosity coefficient using molecular kinetic theory. We find that vacuum contribution due to finite magnetic field dominates the bulk viscosity (ζ) for the temperatures up to

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35

ABOBAKER, ABDOSLLAM M., A. B. MOUBISSI, TH B. EKOGO, and K. NAKKEERAN. "ANALYTICAL SOLUTIONS FOR THE VARIATIONAL EQUATIONS DERIVED FOR THE NONLINEAR SCHRÖDINGER EQUATION: DISPERSION-MANAGED FIBER SYSTEM." Journal of Nonlinear Optical Physics & Materials 17, no. 03 (2008): 285–97. http://dx.doi.org/10.1142/s0218863508004226.

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We consider the nonlinear Schrödinger equation which governs the pulse propagation in dispersion-managed (DM) optical fiber transmission systems. Using a generalized form of ansatz function for the shape of the pulse, we derive the variational equations. For a particular case of DM fiber systems when the Hamiltonian is zero, we solve the variational equations analytically and obtain the expressions for the pulse energy, amplitude, width and chirp. Finally for Gaussian and hyperbolic secant shaped pulses, we show through numerical simulations that the analytically calculated energy (for the giv

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36

Campa, Alessandro. "The study of the dynamics of the order parameter of coupled oscillators in the Ott–Antonsen scheme for generic frequency distributions." Chaos: An Interdisciplinary Journal of Nonlinear Science 32, no. 8 (2022): 083104. http://dx.doi.org/10.1063/5.0093577.

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The Ott–Antonsen ansatz shows that, for certain classes of distribution of the natural frequencies in systems of [Formula: see text] globally coupled Kuramoto oscillators, the dynamics of the order parameter, in the limit [Formula: see text], evolves, under suitable initial conditions, in a manifold of low dimension. This is not possible when the frequency distribution, continued in the complex plane, has an essential singularity at infinity; this is the case, for example, of a Gaussian distribution. In this work, we propose a simple approximation scheme that allows one to extend also to this

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37

Convy, Ian, William Huggins, Haoran Liao, and K. Birgitta Whaley. "Mutual information scaling for tensor network machine learning." Machine Learning: Science and Technology 3, no. 1 (2022): 015017. http://dx.doi.org/10.1088/2632-2153/ac44a9.

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Abstract Tensor networks have emerged as promising tools for machine learning, inspired by their widespread use as variational ansatze in quantum many-body physics. It is well known that the success of a given tensor network ansatz depends in part on how well it can reproduce the underlying entanglement structure of the target state, with different network designs favoring different scaling patterns. We demonstrate here how a related correlation analysis can be applied to tensor network machine learning, and explore whether classical data possess correlation scaling patterns similar to those f

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38

De, Bitan, Piotr Sierant, and Jakub Zakrzewski. "On intermediate statistics across many-body localization transition." Journal of Physics A: Mathematical and Theoretical 55, no. 1 (2021): 014001. http://dx.doi.org/10.1088/1751-8121/ac39cd.

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Abstract The level statistics in the transition between delocalized and localized phases of many body interacting systems is considered. We recall the joint probability distribution for eigenvalues resulting from the statistical mechanics for energy level dynamics as introduced by Pechukas and Yukawa. The resulting single parameter analytic distribution is probed numerically via Monte Carlo method. The resulting higher order spacing ratios are compared with data coming from different quantum many body systems. It is found that this Pechukas–Yukawa distribution compares favorably with β–Gaussia

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Seo, Sambu, and Klaus Obermayer. "Soft Learning Vector Quantization." Neural Computation 15, no. 7 (2003): 1589–604. http://dx.doi.org/10.1162/089976603321891819.

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Learning vector quantization (LVQ) is a popular class of adaptive nearest prototype classifiers for multiclass classification, but learning algorithms from this family have so far been proposed on heuristic grounds. Here, we take a more principled approach and derive two variants of LVQ using a gaussian mixture ansatz. We propose an objective function based on a likelihood ratio and derive a learning rule using gradient descent. The new approach provides a way to extend the algorithms of the LVQ family to different distance measure and allows for the design of “soft” LVQ algorithms. Benchmark

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Singh, Sudhir, R. Sakthivel, M. Inc, A. Yusuf, and K. Murugesan. "Dynamics of optical solitons and conservation laws of a new (2+1)-dimensional integrable nonlinear evolution equation in deep water oceanic waves." Modern Physics Letters B 34, no. 05 (2020): 2050068. http://dx.doi.org/10.1142/s0217984920500682.

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An integrable extension of the famous Schrödinger equation in (2[Formula: see text]+[Formula: see text]1) dimension, named Kundu–Mukherjee–Naskar (KMN) equation, governing the evolution of ion-acoustic wave in magnetized plasma and oceanic rogue waves is considered, and dark/black as well as gray optical soliton solutions are constructed by using a complex envelope ansatz approach with appropriate conditions for the existence of solitons. Also, a new class of combined gray and black optical soliton solutions is obtained by applying Chupin Liu’s theorem, and it is found to be anti-dark solitons

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Wang, Guoming, Sukin Sim, and Peter D. Johnson. "State Preparation Boosters for Early Fault-Tolerant Quantum Computation." Quantum 6 (October 6, 2022): 829. http://dx.doi.org/10.22331/q-2022-10-06-829.

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Quantum computing is believed to be particularly useful for the simulation of chemistry and materials, among the various applications. In recent years, there have been significant advancements in the development of near-term quantum algorithms for quantum simulation, including VQE and many of its variants. However, for such algorithms to be useful, they need to overcome several critical barriers including the inability to prepare high-quality approximations of the ground state. Current challenges to state preparation, including barren plateaus and the high-dimensionality of the optimization la

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Lasar, Christian, and Thorsten Klüner. "Explicitly correlated orbital optimized contracted pair correlation methods: Foundations and applications." Journal of Theoretical and Computational Chemistry 17, no. 04 (2018): 1850024. http://dx.doi.org/10.1142/s0219633618500244.

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Pair correlation methods are able to achieve highly accurate solutions for chemical problems. Unfortunately, their applicability is generally restricted to medium-sized molecules due to storage requirements and computational costs. These restrictions can be partly overcome by local correlation methods. These methods use physical and mathematical criteria to decide which interactions are of such a long range that they do not have to be computed and saved. In our new ansatz, we define an alternative way towards local correlation. The range of interactions is strictly bound to the decay of integr

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Sarkar, Mrinal, and Shamik Gupta. "Synchronization in the Kuramoto model in presence of stochastic resetting." Chaos: An Interdisciplinary Journal of Nonlinear Science 32, no. 7 (2022): 073109. http://dx.doi.org/10.1063/5.0090861.

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What happens when the paradigmatic Kuramoto model involving interacting oscillators of distributed natural frequencies and showing spontaneous collective synchronization in the stationary state is subject to random and repeated interruptions of its dynamics with a reset to the initial condition? While resetting to a synchronized state, it may happen between two successive resets that the system desynchronizes, which depends on the duration of the random time interval between the two resets. Here, we unveil how such a protocol of stochastic resetting dramatically modifies the phase diagram of t

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Jahn, A., M. Gluza, F. Pastawski, and J. Eisert. "Holography and criticality in matchgate tensor networks." Science Advances 5, no. 8 (2019): eaaw0092. http://dx.doi.org/10.1126/sciadv.aaw0092.

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The AdS/CFT correspondence conjectures a holographic duality between gravity in a bulk space and a critical quantum field theory on its boundary. Tensor networks have come to provide toy models to understand these bulk-boundary correspondences, shedding light on connections between geometry and entanglement. We introduce a versatile and efficient framework for studying tensor networks, extending previous tools for Gaussian matchgate tensors in 1 + 1 dimensions. Using regular bulk tilings, we show that the critical Ising theory can be realized on the boundary of both flat and hyperbolic bulk la

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MENGESHA, ELIAS, and SHASHANK BHATNAGAR. "RADIATIVE DECAYS OF EQUAL MASS VECTOR MESONS IN A BETHE–SALPETER EQUATION FRAMEWORK." International Journal of Modern Physics E 21, no. 10 (2012): 1250084. http://dx.doi.org/10.1142/s021830131250084x.

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In this work, we have employed Bethe–Salpeter equation (BSE) under Covariant Instantaneous Ansatz (CIA) to study radiative decays of light vector mesons through the process: h→h'γ, taking h and h' as equal mass light vector and pseudoscalar mesons, respectively. The decay widths calculated for these processes are in reasonable agreement with data. The motivation for this work was our intention to resolve the problems involved in calculations of triangle quark-loop diagrams which appear in processes such as radiative meson decays, meson form factors, strong decays of mesons, etc., in BSE under

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EMRAN, M. S., and J. SCHUMACHER. "Fine-scale statistics of temperature and its derivatives in convective turbulence." Journal of Fluid Mechanics 611 (September 25, 2008): 13–34. http://dx.doi.org/10.1017/s0022112008002954.

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We study the fine-scale statistics of temperature and its derivatives in turbulent Rayleigh–Bénard convection. Direct numerical simulations are carried out in a cylindrical cell with unit aspect ratio filled with a fluid with Prandtl number equal to 0.7 for Rayleigh numbers between 107 and 109. The probability density function of the temperature or its fluctuations is found to be always non-Gaussian. The asymmetry and strength of deviations from the Gaussian distribution are quantified as a function of the cell height. The deviations of the temperature fluctuations from the local isotropy, as

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Manzhos, Sergei, and Manabu Ihara. "Advanced Machine Learning Methods for Learning from Sparse Data in High-Dimensional Spaces: A Perspective on Uses in the Upstream of Development of Novel Energy Technologies." Physchem 2, no. 2 (2022): 72–95. http://dx.doi.org/10.3390/physchem2020006.

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Machine learning (ML) has found increasing use in physical sciences, including research on energy conversion and storage technologies, in particular, so-called sustainable technologies. While often ML is used to directly optimize the parameters or phenomena of interest in the space of features, in this perspective, we focus on using ML to construct objects and methods that help in or enable the modeling of the underlying phenomena. We highlight the need for machine learning from very sparse and unevenly distributed numeric data in multidimensional spaces in these applications. After a brief in

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BOONSERM, PETARPA, and MATT VISSER. "BUCHDAHL-LIKE TRANSFORMATIONS FOR PERFECT FLUID SPHERES." International Journal of Modern Physics D 17, no. 01 (2008): 135–63. http://dx.doi.org/10.1142/s0218271808011912.

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In two previous articles [Phys. Rev. D71 (2005) 124307 (gr-qc/0503007) and Phys. Rev. D76 (2006) 0440241 (gr-qc/0607001)] we have discussed several "algorithmic" techniques that permit one (in a purely mechanical way) to generate large classes of general-relativistic static perfect fluid spheres. Working in Schwarzschild curvature coordinates, we used these algorithmic ideas to prove several "solution-generating theorems" of varying levels of complexity. In the present article we consider the situation in other coordinate systems. In particular, in general diagonal coordinates we shall general

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Barna, Imre Ferenc, and László Mátyás. "Diffusion Cascades and Mutually Coupled Diffusion Processes." Mathematics 12, no. 20 (2024): 3298. http://dx.doi.org/10.3390/math12203298.

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In this paper, we define and investigate a system of coupled regular diffusion equations in which each concentration acts as a driving term in the next diffusion equation. Such systems can be understood as a kind of cascade process which appear in different fields of physics like diffusion and reaction processes or turbulence. As a solution, we apply the time-dependent self-similar Ansatz method, the obtained solutions can be expressed as the product of a Gaussian and a Kummer’s function. This model physically means that the first diffusion works as a catalyst in the second diffusion system. T

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Mamis, K. I., G. A. Athanassoulis, and Z. G. Kapelonis. "A systematic path to non-Markovian dynamics: new response probability density function evolution equations under Gaussian coloured noise excitation." Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 475, no. 2226 (2019): 20180837. http://dx.doi.org/10.1098/rspa.2018.0837.

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Determining evolution equations governing the probability density function (pdf) of non-Markovian responses to random differential equations (RDEs) excited by coloured noise, is an important issue arising in various problems of stochastic dynamics, advanced statistical physics and uncertainty quantification of macroscopic systems. In the present work, such equations are derived for a scalar, nonlinear RDE under additive coloured Gaussian noise excitation, through the stochastic Liouville equation. The latter is an exact, yet non-closed equation, involving averages over the time history of the

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