Langevin equations for quasi-linear wave particle interaction

Castejón, F.; Eguilior, Sonsoles

doi:10.1088/0741-3335/45/2/307

Cited by 13 publications

(8 citation statements)

References 25 publications

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“…A complementary approach towards relativistic stochastic processes in phase space starts from Langevin equations [11][12][13][14][15]17,18,20,21,[24][25][26]31,32,[391][392][393][394][395]. Stochastic differential equations of the Langevin type yield explicit sample trajectories for the stochastic motion of a relativistic Brownian particle.…”

Section: Relativistic Markov Processes In Phase Spacementioning

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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Section: Relativistic Markov Processes In Phase Spacementioning

confidence: 99%

Relativistic Brownian motion

2009

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“…To track the electrons trajectories on their relaxation paths, a natural and convenient method consists in solving the Langevin equations [1,24,25]. Besides providing a clear insight in the dynamics underlying the relaxation process [26], they can be used to compute the response function χ.…”

Section: Langevin Equationsmentioning

confidence: 99%

Theory of synergy between electron cyclotron and lower hybrid waves

Dümont

Giruzzi

2004

Physics of Plasmas

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A theoretical study of the improvement of the Electron Cyclotron Current Drive (ECCD) efficiency in regimes where most of the current is driven by Lower Hybrid (LH) waves is presented. A perturbation technique is employed to solve the adjoint equation and derive the response function including both collisional and LH effects in the limit where the former dominate. An alternative treatment of the problem, involving a numerical solution of the Langevin equations is proposed to gain insight into the current drive mechanism and confirm the obtained results. The existence of a cross-effect between the two waves is demonstrated and the conditions for the synergy, i.e. significant enhancement of the ECCD efficiency in the presence of LH power, are identified.

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“…HLE for resonant optical systems are often nonlinear in operators, which makes them difficult for solving analytically. Several methods of solving HLE are proposed [3,[20][21][22][23][24][25].…”

Section: Introductionmentioning

confidence: 99%

Perturbation approach in Heisenberg equations for lasers

Protsenko,

Uskov

2022

Preprint

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Nonlinear Heisenberg-Langevin equations are solved analytically by operator Fourier-expansion for the laser in the LED regime. Fluctuations of populations of lasing levels are taken into account as perturbations. Spectra of operator products are calculated as convolutions, preserving Bose commutations for the lasing field operators. It is found that fluctuations of population significantly affect spontaneous and stimulated emissions into the lasing mode, increase the radiation rate, the number of lasing photons and broad the spectrum of a bad cavity thresholdless and the superradiant lasers. The method can be applied to various resonant systems in quantum optics.

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Langevin equations for quasi-linear wave particle interaction

Cited by 13 publications

References 25 publications

Relativistic Brownian motion

Relativistic Brownian motion

Theory of synergy between electron cyclotron and lower hybrid waves

Perturbation approach in Heisenberg equations for lasers

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