scholarly journals Upside/Downside statistical mechanics of nonequilibrium Brownian motion. I. Distributions, moments, and correlation functions of a free particle

2018 ◽  
Vol 148 (4) ◽  
pp. 044101 ◽  
Author(s):  
Galen T. Craven ◽  
Abraham Nitzan
Keyword(s):  
Brownian Motion ◽  
Statistical Mechanics ◽  
Correlation Functions ◽  
Free Particle

scholarly journals A path integral approach to the Langevin equation

2015 ◽  
Vol 30 (07) ◽  
pp. 1550028 ◽  
Author(s):  
Ashok K. Das ◽  
Sudhakar Panda ◽  
J. R. L. Santos
Keyword(s):  
Brownian Motion ◽  
Path Integral ◽  
Langevin Equation ◽  
Correlation Functions ◽  
Free Particle ◽  
Transition Amplitude ◽  
Planck Equation ◽  
Markovian Process ◽  
Integral Approach ◽  
Generalized Langevin Equation

We study the Langevin equation with both a white noise and a colored noise. We construct the Lagrangian as well as the Hamiltonian for the generalized Langevin equation which leads naturally to a path integral description from first principles. This derivation clarifies the meaning of the additional fields introduced by Martin, Siggia and Rose in their functional formalism. We show that the transition amplitude, in this case, is the generating functional for correlation functions. We work out explicitly the correlation functions for the Markovian process of the Brownian motion of a free particle as well as for that of the non-Markovian process of the Brownian motion of a harmonic oscillator (Uhlenbeck–Ornstein model). The path integral description also leads to a simple derivation of the Fokker–Planck equation for the generalized Langevin equation.

scholarly journals SYMMETRY REDUCTION OF BROWNIAN MOTION AND QUANTUM CALOGERO–MOSER MODELS

2012 ◽  
Vol 13 (01) ◽  
pp. 1250007
Author(s):  
SIMON HOCHGERNER
Keyword(s):  
Brownian Motion ◽  
Schrödinger Equation ◽  
Jacobi Equation ◽  
Schrodinger Equation ◽  
Free Particle ◽  
Symmetry Reduction ◽  
Reduction Scheme ◽  
Polar Actions ◽  
Stochastic Setting ◽  
Hamilton Jacobi Equation

Let Q be a Riemannian G-manifold. This paper is concerned with the symmetry reduction of Brownian motion in Q and ramifications thereof in a Hamiltonian context. Specializing to the case of polar actions, we discuss various versions of the stochastic Hamilton–Jacobi equation associated to the symmetry reduction of Brownian motion and observe some similarities to the Schrödinger equation of the quantum–free particle reduction as described by Feher and Pusztai [10]. As an application we use this reduction scheme to derive examples of quantum Calogero–Moser systems from a stochastic setting.

Brownian Motion

2018 ◽  
pp. 1-24
Author(s):  
Giovanni Zocchi
Keyword(s):  
Brownian Motion ◽  
Statistical Mechanics ◽  
Concentration Gradient ◽  
Nonequilibrium Statistical Mechanics ◽  
Thermal Fluctuations ◽  
Nonequilibrium System ◽  
Individual Particle ◽  
Equilibrium Concept ◽  
Self Diffusion ◽  
Main Ideas

This chapter provides an introduction to the main ideas of Brownian motion. Brownian motion connects equilibrium and nonequilibrium statistical mechanics. It connects diffusion—a nonequilibrium phenomenon—with thermal fluctuations—an equilibrium concept. More precisely, diffusion with a net flow of particles, driven by a concentration gradient, pertains to a nonequilibrium system, since there is a net current. Without a concentration gradient, the system is macroscopically in equilibrium, but each individual particle undergoes self-diffusion just the same. In this sense, Brownian motion is at the border of equilibrium and nonequilibrium statistical mechanics.

From Brownian Motion to Bending Beams

2021 ◽  
pp. 84-98
Author(s):  
Robert W. Batterman
Keyword(s):  
Brownian Motion ◽  
Correlation Function ◽  
Correlation Functions ◽  
Materials Science ◽  
Prima Facie ◽  
Representative Volume ◽  
Representative Volume Elements ◽  
Hydrodynamic Correlation

This chapter argues that the hydrodynamic, correlation function methodology discussed in “fluid” contexts is really the same methodology employed in materials science to determine effective values for quantities like conductivity, elasticity, stiffness. Thus, Einstein’s arguments discussed in the previous chapter have a bearing on what prima facie appear to be completely different problems. The mesoscale approach using representative volume elements and correlation functions to describe the important features of those representative volume elements is presented in some detail.

scholarly journals Entropic Approach to the Detection of Crucial Events

Entropy ◽  
2019 ◽  
Vol 21 (2) ◽  
pp. 178 ◽  
Author(s):  
Garland Culbreth ◽  
Bruce West ◽  
Paolo Grigolini
Keyword(s):  
Brownian Motion ◽  
Fractional Brownian Motion ◽  
Anomalous Diffusion ◽  
Correlation Functions ◽  
Joint Action ◽  
Clear Distinction ◽  
Aging Effects ◽  
Recent Advances ◽  
The Brain

In this paper, we establish a clear distinction between two processes yielding anomalous diffusion and 1 / f noise. The first process is called Stationary Fractional Brownian Motion (SFBM) and is characterized by the use of stationary correlation functions. The second process rests on the action of crucial events generating ergodicity breakdown and aging effects. We refer to the latter as Aging Fractional Brownian Motion (AFBM). To settle the confusion between these different forms of Fractional Brownian Motion (FBM) we use an entropic approach properly updated to incorporate the recent advances of biology and psychology sciences on cognition. We show that although the joint action of crucial and non-crucial events may have the effect of making the crucial events virtually invisible, the entropic approach allows us to detect their action. The results of this paper lead us to the conclusion that the communication between the heart and the brain is accomplished by AFBM processes.

Statistical mechanics of holonomic systems as a Brownian motion on smooth manifolds

2015 ◽  
Vol 528 (5) ◽  
pp. 381-393 ◽  
Author(s):  
Fabio Manca ◽  
Pierre-Michel Déjardin ◽  
Stefano Giordano
Keyword(s):  
Brownian Motion ◽  
Statistical Mechanics ◽  
Smooth Manifolds ◽  
Holonomic Systems
Sign in / Sign up

Export Citation Format

Share Document