论相对论布朗运动

IF 0.5 Q4 MATHEMATICS, INTERDISCIPLINARY APPLICATIONS

P-Adic Numbers Ultrametric Analysis and Applications Pub Date : 2024-05-06 DOI:10.1134/s207004662402002x

E. A. Kurianovich, A. I. Mikhailov, I. V. Volovich

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引用次数: 0

摘要

摘要用路径积分法考虑了速度的有界性，将相对论随机过程视为布朗运动。尝试建立维纳度量的相对论类似物，作为有限差分近似的弱极限。提出了相对论布朗运动过程中粒子转换概率的计算公式。用三种不同的方法进行了计算，结果完全相同。在此过程中，还获得了 N-1 维单位立方体某些部分和截面体积的精确公式和渐近公式。它们可以有独立的值。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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On the Theory of Relativistic Brownian Motion

Abstract

The approach to the theory of a relativistic random process is considered by the path integral method as Brownian motion taking into account the boundedness of speed. An attempt was made to build a relativistic analogue of the Wiener measure as a weak limit of finite-difference approximations. A formula has been proposed for calculating the probability particle transition during relativistic Brownian motion. Calculations were carried out by three different methods with identical results. Along the way, exact and asymptotic formulas for the volume of some parts and sections of an N-1-dimensional unit cube were obtained. They can have independent value.

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来源期刊

P-Adic Numbers Ultrametric Analysis and Applications MATHEMATICS, INTERDISCIPLINARY APPLICATIONS-

CiteScore

1.10

自引率

20.00%

发文量

期刊介绍： This is a new international interdisciplinary journal which contains original articles, short communications, and reviews on progress in various areas of pure and applied mathematics related with p-adic, adelic and ultrametric methods, including: mathematical physics, quantum theory, string theory, cosmology, nanoscience, life sciences; mathematical analysis, number theory, algebraic geometry, non-Archimedean and non-commutative geometry, theory of finite fields and rings, representation theory, functional analysis and graph theory; classical and quantum information, computer science, cryptography, image analysis, cognitive models, neural networks and bioinformatics; complex systems, dynamical systems, stochastic processes, hierarchy structures, modeling, control theory, economics and sociology; mesoscopic and nano systems, disordered and chaotic systems, spin glasses, macromolecules, molecular dynamics, biopolymers, genomics and biology; and other related fields.