Article ; Online: Solving Equations of Motion by Using Monte Carlo Metropolis: Novel Method Via Random Paths Sampling and the Maximum Caliber Principle.
2020 Volume 22, Issue 9
Abstract: A permanent challenge in physics and other disciplines is to solve Euler-Lagrange equations. Thereby, a beneficial investigation is to continue searching for new procedures to perform this task. A novel Monte Carlo Metropolis framework is presented for ... ...
Abstract | A permanent challenge in physics and other disciplines is to solve Euler-Lagrange equations. Thereby, a beneficial investigation is to continue searching for new procedures to perform this task. A novel Monte Carlo Metropolis framework is presented for solving the equations of motion in Lagrangian systems. The implementation lies in sampling the path space with a probability functional obtained by using the maximum caliber principle. Free particle and harmonic oscillator problems are numerically implemented by sampling the path space for a given action by using Monte Carlo simulations. The average path converges to the solution of the equation of motion from classical mechanics, analogously as a canonical system is sampled for a given energy by computing the average state, finding the least energy state. Thus, this procedure can be general enough to solve other differential equations in physics and a useful tool to calculate the time-dependent properties of dynamical systems in order to understand the non-equilibrium behavior of statistical mechanical systems. |
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Language | English |
Publishing date | 2020-08-21 |
Publishing country | Switzerland |
Document type | Journal Article |
ZDB-ID | 2014734-X |
ISSN | 1099-4300 ; 1099-4300 |
ISSN (online) | 1099-4300 |
ISSN | 1099-4300 |
DOI | 10.3390/e22090916 |
Database | MEDical Literature Analysis and Retrieval System OnLINE |
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