Relativistic Brownian motion: From a microscopic binary collision model to the Langevin equation

Abstract

The Langevin equation (LE) for the one-dimensional relativistic Brownian motion is derived from a microscopic collision model. The model assumes that a heavy point-like Brownian particle interacts with the lighter heat bath particles via elastic hard-core collisions. First, the commonly known, non-relativistic LE is deduced from this model, by taking into account the non-relativistic conservation laws for momentum and kinetic energy. Subsequently, this procedure is generalized to the relativistic case. There, it is found that the relativistic stochastic force is still $\gd$-correlated (white noise) but does \emph{no} longer correspond to a Gaussian white noise process. Explicit results for the friction and momentum-space diffusion coefficients are presented and discussed.

v2: Eqs. (17c) and (28) corrected; v3: discussion extended, Eqs. (33) added, thereby connection to earlier work clarified; v4: final version, accepted for publication in Phys. Rev. E

References in corpus (12)

• Brownian motors
• Heavy-Quark Probes of the Quark-Gluon Plasma at RHIC
• Fundamental Aspects of Quantum Brownian Motion
• On the Causality and Stability of the Relativistic Diffusion Equation
• Theory of the Relativistic Brownian Motion. The (1+1)-Dimensional Case
• Theory of Relativistic Brownian Motion: The (1+3)-Dimensional Case
• Causal Diffusion and the Survival of Charge Fluctuations in Nuclear Collisions
• Covariant Equilibrium Statistical Mechanics
• Diffusion and local deconfinement in relativistic systems
• Microscopic Derivation of Causal Diffusion Equation using Projection Operator Method
• MARKOV DIFFUSIONS IN COMOVING COORDINATES AND STOCHASTIC QUANTIZATION OF THE FREE RELATIVISTIC SPINLESS PARTICLE
• Brownian motion approach to the ideal gas of relativistic particles

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• Collisional behaviors of astrophysical collisionless plasmas
• Holographic Brownian Motion in Two Dimensional Rotating Fluid
• Persistent nonequilibrium effects in generalized Langevin dynamics of nonrelativistic and relativistic particles
• Relativistic stochastic mechanics II: Reduced Fokker-Planck equation in curved spacetime
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• The induced friction on a probe moving in a nonequilibrium medium
• Lorentz covariant physical Brownian motion: Classical and quantum
• A new look at Bell's inequalities and Nelson's theorem