A hybrid sinc-Galerkin/finite-difference method for the time-dependent Wigner equation

被引：2
|
作者：
Jiang, Haiyan [1 ]
Lu, Tiao [2 ]
Zhang, Weitong [3 ]
机构：
[1] Beijing Inst Technol, Sch Math & Stat, Beijing 100081, Peoples R China
[2] Peking Univ, Sch Math Sci, LMAM, CAPT,HEDPS, Beijing 100871, Peoples R China
[3] Peking Univ, Sch Math Sci, Beijing 100871, Peoples R China
来源：
JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS | 2022年 / 409卷
基金：
中国国家自然科学基金;
关键词：
Wigner equation; Finite difference method; Sinc-Galerkin method; Quantum tunneling; PARITY-DECOMPOSITION; SELF-CONSISTENT; SIMULATION;
D O I：
10.1016/j.cam.2022.114152
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
The Wigner equation is a remarkable tool to model complex problems of quantum physics in phase space. The main objective of this paper is to propose a new hybrid algorithm for the time-dependent Wigner equation. This scheme is based on sinc-Galerkin and finite difference approximations and is moderately simple but highly efficient. Error estimation, stability, and convergence are also investigated concretely. Numerical experiments validate the theoretical results and present the reliability and efficiency of the proposed algorithm to simulate quantum effects. (C) 2022 Elsevier B.V. All rights reserved.
引用
收藏
页数：12
相关论文
共 50 条
  • [41] FINITE-DIFFERENCE METHODS FOR TIME-DEPENDENT, LINEAR-DIFFERENTIAL ALGEBRAIC EQUATIONS
    RABIER, PJ
    RHEINBOLDT, WC
    APPLIED MATHEMATICS LETTERS, 1994, 7 (02) : 29 - 34
  • [42] ASSESSMENT OF QUALITY OF SELECTED FINITE-DIFFERENCE SCHEMES FOR TIME-DEPENDENT COMPRESSIBLE FLOWS
    SRINIVAS, K
    GURURAJA, J
    PRASAD, KK
    JOURNAL OF COMPUTATIONAL PHYSICS, 1976, 20 (02) : 140 - 159
  • [43] TIME-DEPENDENT WAVE ENVELOPE FINITE-DIFFERENCE ANALYSIS OF SOUND-PROPAGATION
    BAUMEISTER, KJ
    AIAA JOURNAL, 1986, 24 (01) : 32 - 38
  • [44] Hybrid Nodal Integral/Finite Element Method for Time-Dependent Convection Diffusion Equation
    Namala, Sundar
    Uddin, Rizwan
    JOURNAL OF NUCLEAR ENGINEERING AND RADIATION SCIENCE, 2022, 8 (02):
  • [45] CURVILINEAR FINITE-DIFFERENCE METHOD FOR BIHARMONIC EQUATION
    LAU, PCM
    INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, 1979, 14 (06) : 791 - 812
  • [46] Observing Quantum Dynamics in Real Time: An Excel-Ready Finite-Difference Algorithm for Solving the Time-Dependent Schrodinger Equation
    Rossman, Taylor A.
    Parks, Zachary P.
    Messina, Michael
    JOURNAL OF CHEMICAL EDUCATION, 2020, 97 (04) : 1026 - 1034
  • [47] Numerical Simulation of the Time-Dependent Mild-Slope Equation by the Generalized Finite Difference Method
    Zhang, Ting
    Lin, Zhen-Huan
    Lin, Chuan
    Liang, Lin
    Fan, Chia-Ming
    PURE AND APPLIED GEOPHYSICS, 2021, 178 (11) : 4401 - 4424
  • [48] Numerical Simulation of the Time-Dependent Mild-Slope Equation by the Generalized Finite Difference Method
    Ting Zhang
    Zhen-Huan Lin
    Chuan Lin
    Lin Liang
    Chia-Ming Fan
    Pure and Applied Geophysics, 2021, 178 : 4401 - 4424
  • [49] Analysis of photonic crystals using the hybrid finite-element/finite-difference time domain technique based on the discontinuous Galerkin method
    Zhu, Bao
    Chen, Jiefu
    Zhong, Wanxie
    Liu, Qing Huo
    INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, 2012, 92 (05) : 495 - 506
  • [50] Hybrid finite-difference thermal lattice Boltzmann equation
    Lallemand, P
    Luo, LS
    INTERNATIONAL JOURNAL OF MODERN PHYSICS B, 2003, 17 (1-2): : 41 - 47
12345