Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

Progress of Theoretical Physics

On the Quantum Mechanics-like Description of the Theories of the Brownian Motion and Quantum Statistical Mechanics

Nobuhiko Saitô, Mikio Namiki

Published Aug 1, 1956• 29 citations
Publisher

Abstract

Analogies among the theories of Brownian motion, quantum mechanics and quantum statistics are pointed out from various aspects. Along this line of thought quantum mechanics-like descriptions of Brownian motion and quantum statistics are presented.
DOI
10.1143/ptp.16.71

Related papers

On the Quantum Mechanics-like Description of the Theories of the Brownian Motion and Quantum Statistical Mecahnics

N. Saitô, M. Namiki

1. In the following Table A should read B. 2. From dimension-analytical oint of view, it may be convenient to rewrite eqs. (3.3) and (3.5) as fol

Progress of Theoretical Physics•Mar 1, 1957•0 citations

Brownian Motion and Quantum Mechanics

Roumen Tsekov

A theoretical parallel between the classical Brownian motion and quantum mechanics is explored via two stochastic sources. It is shown that, in contrast to the classical Langevin force, quantum mechanics is driven by turbulent velocity fluctuations with diffusive behavior. In the case of simultaneous action of the thermal and quantum noises, the quantum Brownian motion is described as well.

arXiv:1902.05930•Fluctuation and Noise Letters•Nov 19, 2019•6 citations

Quantum Mechanics as a Theory of Relativistic Brownian Motion

Yu. A. Rylov

Abstract It is shown that non‐relativistic quantum mechanics can be treated as a kind of relativistic statistical theory which describes a random motion of a classical particle. The theory is relativistic in the sense that for the description of the particle behaviour the relativistic notion of the state is used. This is very important because a statistics is a state calculus and the result depends on the definition of the notion of state.

Annalen der Physik•Jan 1, 1971•20 citations

Dynamical Theories of Brownian Motion

EDWARD B. NELSON

These notes are based on a course of lectures given by Professor Nelson at Princeton during the spring term of 1966. The subject of Brownian motion has long been of interest in mathematical probability. In these lectures, Professor Nelson traces the history of earlier work in Brownian motion, both the mathematical theory, and the natural phenomenon with its physical interpretations. He continues through recent dynamical theories of Brownian motion, and concludes with a discussion of the relevance of these theories to quantum field theory and quantum statistical mechanics.

Princeton University Press eBooks•Oct 6, 2020•1,121 citations

Brownian Motion: The Quantum Perspective

Vacchini, B

We briefly go through the problem of the quantum description of Brownian motion, concentrating on recent results about the connection between dynamics of the particle and dynamic structure factor of the medium.

•Jan 1, 2001•3 citations

AN OVERVIEW OF THE APPLICATION OF THE LANGEVIN EQUATION TO THE DESCRIPTION OF BROWNIAN AND QUANTUM MOTIONS OF A PARTICLE

Kh. Namsrai, YA. HULREE, N. Njamtseren

A simple scheme of unified description of different physical phenomena by using the Langevin type equations is reviewed. Within this approach much attention is being paid to the study of Brownian and quantum motions. Stochastic equations with a white noise term give all characteristics of the Brownian motion. Some generalization of the Langevin type equations allows us to obtain nonlinear equations of particles' motion, which are formally equivalent to the Schrödinger equation. Thus, we establish Nelson's stochastic mechanics on the basis of the Langevin equation.

International Journal of Modern Physics A•May 10, 1992•3 citations
These notes are based on a course of lectures given by Professor Nelson at Princeton during the spring term of 1966. The subject of Brownian motion has long been of interest in mathematical probability. In these lectures, Professor Nelson traces the history of earlier work in Brownian motion, both the mathematical theory, and the natural phenomenon with its physical interpretations. He continues through recent dynamical theories of Brownian motion, and concludes with a discussion of the relevance of these theories to quantum field theory and quantum statistical mechanics.
A simple scheme of unified description of different physical phenomena by using the Langevin type equations is reviewed. Within this approach much attention is being paid to the study of Brownian and quantum motions. Stochastic equations with a white noise term give all characteristics of the Brownian motion. Some generalization of the Langevin type equations allows us to obtain nonlinear equations of particles' motion, which are formally equivalent to the Schrödinger equation. Thus, we establish Nelson's stochastic mechanics on the basis of the Langevin equation.