scholarly journals The Development of a Parallel Algorithm and Program for Solving the Stationary Many-Body Schrodinger Equation by the Monte Carlo Method on the Example of S States of Atomic Systems

2018 ◽  
Vol 136 ◽  
pp. 154-163
Author(s):  
A.A. Danshin
Keyword(s):  
Monte Carlo ◽  
Monte Carlo Method ◽  
Schrödinger Equation ◽  
Parallel Algorithm ◽  
Schrodinger Equation ◽  
Many Body ◽  
Atomic Systems ◽  
The Monte Carlo Method ◽  
S States

A quantum method for dynamic nonlinear programming technique using Schrödinger equation and Monte Carlo approach

2018 ◽  
Vol 32 (30) ◽  
pp. 1850374 ◽  
Author(s):  
Amandeep Kaur ◽  
Satnam Kaur ◽  
Gaurav Dhiman
Keyword(s):  
Monte Carlo ◽  
Quantum Computing ◽  
Nonlinear Programming ◽  
Monte Carlo Method ◽  
Schrödinger Equation ◽  
Nonlinear Problem ◽  
Schrodinger Equation ◽  
Programming Technique ◽  
Quantum Method ◽  
Speed Up

The power of quantum computing may allow for solving the problems which are not practically feasible on classical computers and suggest a considerable speed up to the best known classical approaches. In this paper, we present the contemporary quantum behaved approach which is based on Schrödinger equation and Monte Carlo method. The three basic steps of proposed technique are also mathematically modeled and discussed for effective movement of particles. The performance of the proposed approach is tested for solving the dynamic nonlinear problem. Experimental results reveal the supremacy of proposed approach for solving the nonlinear problem as compared to other approaches.

scholarly journals Ring statistics in disordered solids: a parallel algorithm for clusters with hundred thousands of atoms

2017 ◽  
pp. 447-454
Author(s):  
Ф.В. Григорьев ◽  
В.Б. Сулимов ◽  
А.В. Тихонравов
Keyword(s):  
Monte Carlo ◽  
Distribution Function ◽  
Monte Carlo Method ◽  
Parallel Algorithm ◽  
Structural Elements ◽  
Disordered Solids ◽  
The Monte Carlo Method

Кольца, состоящие из различного числа атомов, являются основным структурным элементом во многих неупорядоченных веществах. В настоящей статье представлен параллельный алгоритм получения приближенной функции распределения колец по числу атомов, основанный на методе Монте-Карло. Алгоритм применен к кластерам диоксида кремния, содержащим до миллиона атомов. Исследована эффективность алгоритма, как функция числа используемых вычислительных ядер, вплоть до 1024. The rings consisting of various number of atoms are basic structural elements in many disordered solids. In this paper, a parallel algorithm for calculating an approximate ring distribution function by the number of atoms is proposed. The algorithm is based on the Monte Carlo method and is applied to SiO$_2$ clusters consisting of up to $10^6$ atoms. The efficiency of the algorithm is studied using up to 1024 computational cores.

A NONADIABATIC QUANTUM MECHANICAL MONTE CARLO METHOD

2002 ◽  
Vol 13 (07) ◽  
pp. 909-915
Author(s):  
A. M. MAZZONE
Keyword(s):  
Monte Carlo ◽  
Monte Carlo Method ◽  
Schrödinger Equation ◽  
Ground State ◽  
Schrodinger Equation ◽  
Efficient Solution ◽  
Time Dependent ◽  
Quantum Mechanical ◽  
Classical Dynamics ◽  
Hartree Fock

The problem addressed by this study is an efficient solution of the multi-particle time-dependent Schrödinger equation to be used under nonadiabatic conditions. To this purpose a solution combining classical dynamics for the nuclei and a quantum mechanical Monte Carlo method for the electrons is suggested as a practically feasible approach. As a show-case example, the method is applied to the evaluation of the ground state of H, He, H2 and H3 whose energy and structure is also obtained from stationary Hartree–Fock calculations.

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