Natural Fluctuations in Lasers

Klimontovich, Yu. L.; Kovalev, A. S.; Landa, P. S.

doi:10.1070/pu1972v015n01abeh004947

Cited by 36 publications

(50 citation statements)

References 41 publications

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“…Thereafter, KB method and BBGKY hierarchy, were used in deriving non-Markovian quantum equations for weakly coupled systems and neutral particle systems with very short interaction range [14], [15], [16], [17], [18]. In order to describe non-Markovian processes in a polarizable plasma Klimontovich [19] derived a set of equations for the particle distribution function and the electric field spectral function. But the equation for the spectral function was not solved, and the collision integral was obtained only in the averaged potential approximation.…”

Section: Introductionmentioning

confidence: 99%

Kinetic Theory of a Weakly-Nonideal Spatially Nonuniform Polarizable Plasma

Belyi

Kukharenko²,

Wallenborn

2002

Contrib. Plasma Phys.

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Section: Introductionmentioning

confidence: 99%

Kinetic Theory of a Weakly-Nonideal Spatially Nonuniform Polarizable Plasma

Belyi

Kukharenko²,

Wallenborn

2002

Contrib. Plasma Phys.

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“…Such nonrelativistic Langevin equations have been studied extensively in various contexts over the past decades (see, e.g., the reviews [78,112]). The list of successful applications covers a wide range of different areas including laser physics [112,113,449], optical lattices [450,451], plasma physics [452][453][454][455], high energy physics [315,316], biologically and chemically motivated population and reaction dynamics [456], active Brownian motion models [429,[457][458][459][460][461][462], or theoretical and experimental studies of excitation and transition phenomena in nonlinear systems [463][464][465][466].…”

Section: Remarks and Generalizationsmentioning

confidence: 99%

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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“…Later the KB method and the BBGKY hierarchy were used in deriving non-Marcovian quantum equations for weakly coupled systems and neutral particle systems with very short interaction range [4], [5], [6], [7], [8]. In order to describe non-Marcovian processes in a polarizable plasma, Klimontovich [9] derived a set of equations for the particle distribution function and the electric field spectral function. However, the equation for the spectral function was not solved, and the collision integral was obtained only in the averaged potential approximation.…”

Section: Introductionmentioning

confidence: 99%

Exchange Correlation of Particles and Quantum Collision Integral in a Non‐Ideal Plasma with Polarization

Belyi¹,

Kukharenko

2007

Contrib. Plasma Phys.

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Key words Plasma quantum kinetic equation, exchange scattering, quantum collision integral. PACS 52.25. Dg, 52.27.Aj, 52.20.Fs, 52.20.Hv Starting with the quantum BBGKY-hierarchy for the distribution functions, we have obtained the quantum non-Marcovian kinetic equation including the dynamical screening of the interaction potential, which exactly takes into account the exchange scattering in the plasma. The collision integral is expessed in terms of the Green function of the linearized Hartree -Fock equation.This quantum kinetic equation satisfies the law of total energy conservation with account of the polarization and exchange interaction.

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Natural Fluctuations in Lasers

Cited by 36 publications

References 41 publications

Kinetic Theory of a Weakly-Nonideal Spatially Nonuniform Polarizable Plasma

Kinetic Theory of a Weakly-Nonideal Spatially Nonuniform Polarizable Plasma

Relativistic Brownian motion

Exchange Correlation of Particles and Quantum Collision Integral in a Non‐Ideal Plasma with Polarization

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