Comparison of Dynamic Diffusion with an Explicit Difference Scheme for the Schroedinger Equation

V. Kukushkin; Y. I. Ozhigov

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Comparison of Dynamic Diffusion with an Explicit Difference Scheme for the Schroedinger Equation

机译：Schrodinger方程的动态扩散与显式差分格式的比较

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We represent the method of dynamic diffusion for the approximate solution of Schrodinger's equation with decoherence and describe a swarm simulation as a proof of concept. Decoherence occurs as the divergence of the exact solution for the dynamics of the diffusion swarm, which arises when the total number of real particles grows. The method of dynamic diffusion cannot be reduced to the solution of differential equations, in contrast to Bohm's quantum hydrodynamics; hence, direct computer simulation is the mandatory next step. We compare the dynamic diffusion with the explicit finite differences scheme for the Schrodinger equation for some standard one-dimension cases.

机译：我们用退相干来表示薛定inger方程近似解的动态扩散方法，并描述了群体仿真作为概念证明。退相干发生在扩散群动力学的精确解的发散处，当真实粒子总数增长时会出现退相干。与波姆的量子流体力学相反，动态扩散的方法不能简化为微分方程的求解。因此，直接的计算机模拟是必不可少的下一步。对于某些标准一维情况，我们将动态扩散与Schrodinger方程的显式有限差分方案进行了比较。

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《Complex Systems》 |2013年第4期|423-450|共28页
作者
V. Kukushkin; Y. I. Ozhigov;
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Moscow State University of M. V. Lomonosov Institute of Physics and Technology RAS;

Moscow State University of M. V. Lomonosov Institute of Physics and Technology RAS;

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1. Numerical stability of explicit Runge-Kutta finite-difference schemes for the nonlinear Schroedinger equation [J] . R.M. Caplan, R. Carretero-Gonzalez Applied numerical mathematics . 2013,第sepa期

机译：非线性Schroedinger方程显式Runge-Kutta有限差分格式的数值稳定性
2. L~2-DISSIPATIVITY CRITERIA FOR LINEARIZED EXPLICIT FINITE DIFFERENCE SCHEMES FOR REGULARIZATION OF ONE-DIMENSIONAL GAS DYNAMICS EQUATIONS [J] . T. A. Lomonosov Journal of Mathematical Sciences . 2020,第4期

机译：线性一维气体动力学方程正则化的线性有限差分格式的L〜2耗散准则
3. L-2-dissipativity of the linearized explicit finite-difference scheme with a kinetic regularization for 2D and 3D gas dynamics system of equations [J] . Zlotnik Alexander, Lomonosov Timofey Applied mathematics letters . 2020,第期

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4. A New Exponential-Type Explicit Difference Scheme For Convection-Diffusion Equation [C] . Qinghua Feng International Conference on Numerical Analysis and Applied Mathematics . 2008

机译：对流扩散方程的一种新的指数型显式差分方案
5. Development of a Generalized Finite Difference Scheme for Convection-Diffusion Equation. [D] . He, Shixin. 2014

机译：对流扩散方程的广义有限差分格式的发展。
6. Stability Analysis of the Explicit Difference Scheme for Richards Equation [O] . Fengnan Liu, Yasuhide Fukumoto, Xiaopeng Zhao 2020

机译：理查兹方程明确差分方案的稳定性分析
7. Comparizon of dynamic diffusion with explicit difference scheme for Shredinger equation [O] . Kukushkin, V., Ozhigov, Y. I. 2011

机译：动态扩散与显式差分格式的比较 shredinger方程
8. Construction of stable explicit finite-difference schemes for Schroedinger type differential equations [R] . Mickens, Ronald E. 1989

机译：schroedinger型微分方程稳定显式有限差分格式的构造

Comparison of Dynamic Diffusion with an Explicit Difference Scheme for the Schroedinger Equation

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