Relativistic Brownian motion and the spectrum of thermal radiation

Ben-Ya'acov, Uri

doi:10.1103/physrevd.23.1441

Cited by 18 publications

(19 citation statements)

References 5 publications

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“…34-36 in Feynman and Hibbs [389]. 16 Relativistic Fokker-Planck-type equations also played a role in the debate about whether or not the black body radiation spectrum is compatible with Jüttner's relativistic equilibrium distribution [191,[413][414][415][416]. 17 A main reason for the lively interest in relativistic FPEs at that time was the prospect of building plasma fusion reactors.…”

Section: Structure Of the Reviewmentioning

confidence: 99%

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Relativistic Brownian motion

2009

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a b s t r a c tOver the past one hundred years, Brownian motion theory has contributed substantially to our understanding of various microscopic phenomena. Originally proposed as a phenomenological paradigm for atomistic matter interactions, the theory has since evolved into a broad and vivid research area, with an ever increasing number of applications in biology, chemistry, finance, and physics. The mathematical description of stochastic processes has led to new approaches in other fields, culminating in the path integral formulation of modern quantum theory. Stimulated by experimental progress in high energy physics and astrophysics, the unification of relativistic and stochastic concepts has re-attracted considerable interest during the past decade. Focusing on the framework of special relativity, we review, here, recent progress in the phenomenological description of relativistic diffusion processes. After a brief historical overview, we will summarize basic concepts from the Langevin theory of nonrelativistic Brownian motions and discuss relevant aspects of relativistic equilibrium thermostatistics. The introductory parts are followed by a detailed discussion of relativistic Langevin equations in phase space. We address the choice of time parameters, discretization rules, relativistic fluctuationdissipation theorems, and Lorentz transformations of stochastic differential equations. The general theory is illustrated through analytical and numerical results for the diffusion of free relativistic Brownian particles. Subsequently, we discuss how Langevin-type equations can be obtained as approximations to microscopic models. The final part of the article is dedicated to relativistic diffusion processes in Minkowski spacetime. Since the velocities of relativistic particles are bounded by the speed of light, nontrivial relativistic Markov processes in spacetime do not exist; i.e., relativistic generalizations of the nonrelativistic diffusion equation and its Gaussian solutions must necessarily be non-Markovian. We compare different proposals that were made in the literature and discuss their respective benefits and drawbacks. The review concludes with a summary of open questions, which may serve as a starting point for future investigations and extensions of the theory.

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Section: Structure Of the Reviewmentioning

confidence: 99%

“…The remainder of this section addresses the latter problem, which has attracted considerable interest over the past decades [16,21,[90][91][92][93][94][95][96]415,428,430,443]. Langevin equations provide an approximate stochastic description of the 'exact' microscopic dynamics.…”

Section: Microscopic Modelsmentioning

confidence: 99%

Relativistic Brownian motion

2009

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“…The implementation of the Brownian motion concept [1][2][3][4][5][6] into special relativity [7,8] represents a longstanding issue in mathematical and statistical physics (classical references are [9][10][11]; more recent contributions include [12][13][14][15][16][17][18][19][20][21][22]; for a kinetic theory approach, see Refs. [23][24][25]).…”

Section: Introductionmentioning

confidence: 99%

One-dimensional non-relativistic and relativistic Brownian motions: a microscopic collision model

Dunkel

Hänggi

2007

Physica A: Statistical Mechanics and its Applications

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We study a simple microscopic model for the one-dimensional stochastic motion of a (non-)relativistic Brownian particle, embedded into a heat bath consisting of (non-)relativistic particles. The stationary momentum distributions are identified self-consistently (for both Brownian and heat bath particles) by means of two coupled integral criteria. The latter follow directly from the kinematic conservation laws for the microscopic collision processes, provided one additionally assumes probabilistic independence of the initial momenta. It is shown that, in the non-relativistic case, the integral criteria do correctly identify the Maxwellian momentum distributions as stationary (invariant) solutions. Subsequently, we apply the same criteria to the relativistic case. Surprisingly, we find here that the stationary momentum distributions differ slightly from the standard Ju¨ttner distribution by an additional prefactor proportional to the inverse relativistic kinetic energy. r

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“…Since then, they have become cornerstones for our understanding of a wide range of physical processes [8,9,10,11,12]. This fact notwithstanding, the unification of both concepts poses a theoretical challenge still nowadays (classical references are [13,14,15,16,17,18]; recent contributions include [19,20,21,22,23,24,25,26,27,28,29,30,31]; potential applications in high-energy physics and astrophysics are considered in [32,33,34,35,36,37]). The relatively slow progress in this field can be attributed to the severe difficulties that arise when one tries to describe N -body systems in a relativistically consistent manner [38,39].…”

Section: Introductionmentioning

confidence: 99%

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

Dunkel

Hänggi

2006

Phys. Rev. E

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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 δ-correlated (white noise) but does no longer correspond to a Gaussian white noise process. Explicit results for the friction and momentum-space diffusion coefficients are presented and elucidated.

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Relativistic Brownian motion and the spectrum of thermal radiation

Cited by 18 publications

References 5 publications

Relativistic Brownian motion

Relativistic Brownian motion

One-dimensional non-relativistic and relativistic Brownian motions: a microscopic collision model

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

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