scholarly journals A new algorithm derived from the view-point of the fluctuation-dissipation principle in the theory of KM2O-Langevin equations

1993 ◽  
Vol 22 (2) ◽  
pp. 199-209 ◽  
Author(s):  
Yasunori OKABE
Keyword(s):  
Langevin Equations ◽  
View Point ◽  
Fluctuation Dissipation

Fluctuations, Dissipation, and Noise

2019 ◽  
pp. 325-408
Author(s):  
Peter W. Milonni
Keyword(s):  
Brownian Motion ◽  
Noise Figure ◽  
Heat Bath ◽  
Radiation Reaction ◽  
Langevin Equations ◽  
Photon Statistics ◽  
Laser Linewidth ◽  
Homodyne Detection ◽  
Fluctuation Dissipation ◽  
Fundamental Laser

General concepts in the theory of fluctuations and dissipation are reviewed and applied to examples in quantum optics. Brownian motion, Fokker-Planck and Langevin equations, and the Wiener-Khintchine theorem are reviewed, followed by a derivation and discussion of the fluctuation-dissipation theorem. The general problem of an oscillator coupled to a heat bath is revisited, as is the nonrelativistic theory of radiation reaction. The general ideas about fluctuations and dissipation developed in the first part of the chapter are then applied to the theory of the fundamental laser linewidth, the photon statistics of linear amplifiers and attenuators, the noise figure, amplified spontaneous emission, and the quantum theory of the beam slitter and homodyne detection.

scholarly journals Energetics of Poisson–Kac Stochastic Processes Possessing Finite Propagation Velocity

2016 ◽  
Vol 41 (2) ◽  
Author(s):  
Antonio Brasiello ◽  
Massimiliano Giona ◽  
Silvestro Crescitelli
Keyword(s):  
Large Time ◽  
Coarse Grained ◽  
Langevin Equations ◽  
Stochastic Forcing ◽  
Stochastic Perturbations ◽  
Wiener Processes ◽  
Fluctuation Dissipation ◽  
Fluctuation Dissipation Theorem ◽  
Almost Everywhere ◽  
Large Time Limit

AbstractA local fluctuation–dissipation theorem for the power delivered by a stochastic forcing is derived for Ornstein–Uhlenbeck processes driven by smooth, i. e. almost everywhere (a. e.)-differentiable stochastic perturbations (Poisson–Kac processes). An analytic expression for the probability density function of the fluctuational power is obtained in the large time limit. As these processes converge, in the Kac limit, toward classical Langevin equations driven by Wiener processes, a coarse-grained analysis of the statistical properties of the fluctuational work is developed.

scholarly journals Relativistic Langevin Equation derived from a particle-bath Lagrangian

2021 ◽  
Author(s):  
Aleksandr Petrosyan ◽  
Alessio Zaccone
Keyword(s):  
Statistical Mechanics ◽  
Langevin Equation ◽  
Relativistic Correction ◽  
Analytical Approximation ◽  
Space Time ◽  
Langevin Equations ◽  
Generalized Langevin Equation ◽  
Time Translation ◽  
Fluctuation Dissipation ◽  
Wave Forms

Abstract We show how a relativistic Langevin equation can be derived from a Lorentz-covariant version of the Caldeira-Leggett particle-bath Lagrangian. In one of its limits, we identify the obtained equation with the Langevin equation used in contemporary extensions of statistical mechanics to the near-light-speed motion of a tagged particle in non-relativistic dissipative fluids. The proposed framework provides a more rigorous and first-principles form of the weakly-relativistic and partially-relativistic Langevin equations often quoted or postulated as ansatz in previous works. We then refine the aforementioned results to obtain a generalized Langevin equation valid for the case of both fully-relativistic particle and bath, using an analytical approximation obtained from numerics where the Fourier modes of the bath are systematically replaced with covariant plane-wave forms with a length-scale relativistic correction that depends on the space-time trajectory in a parabolic way. We discuss the implications of the apparent breaking of space-time translation and parity invariance, showing that these effects are not necessarily in contradiction with the assumptions of statistical mechanics. The intrinsically non-Markovian character of the fully relativistic generalised Langevin equation derived here, and of the associated fluctuation-dissipation theorem, is also discussed.

scholarly journals Effective one-component model of binary mixture: molecular arrest induced by the spatially correlated stochastic dynamics

2019 ◽  
Vol 9 (1) ◽  
Author(s):  
M. Majka ◽  
P. F. Góra
Keyword(s):  
Binary Mixtures ◽  
Soft Matter ◽  
Stochastic Dynamics ◽  
Component Model ◽  
Langevin Equations ◽  
Correlated Noise ◽  
Spatially Correlated ◽  
Fluctuation Dissipation ◽  
The Difference ◽  
Spatially Correlated Noise

AbstractSpatially correlated noise (SCN), i.e. the thermal noise that affects neighbouring particles in a similar manner, is ubiquitous in soft matter systems. In this work, we apply the over-damped SCN-driven Langevin equations as an effective, one-component model of the dynamics in dense binary mixtures. We derive the thermodynamically consistent fluctuation-dissipation relation for SCN to show that it predicts the molecular arrest resembling the glass transition, i.e. the critical slow-down of dynamics in the disordered phases. We show that the mechanism of singular dissipation is embedded in the dissipation matrix, accompanying SCN. We are also able to identify the characteristic length of collective dissipation, which diverges at critical packing. This novel physical quantity conveniently describes the difference between the ergodic and non-ergodic dynamics. The model is fully analytically solvable, one-dimensional and admits arbitrary interactions between the particles. It qualitatively reproduces several different modes of arrested disorder encountered in binary mixtures, including e.g. the re-entrant arrest. The model can be effectively compared to the mode coupling theory.

Non-Markovian dynamics of dust charge fluctuations in dusty plasmas

2014 ◽  
Vol 80 (3) ◽  
pp. 465-476 ◽  
Author(s):  
H. Asgari ◽  
S. V. Muniandy ◽  
Amir Ghalee
Keyword(s):  
Correlation Function ◽  
Langevin Equation ◽  
Dusty Plasmas ◽  
Langevin Equations ◽  
Transient Time ◽  
Charge Fluctuations ◽  
Dust Charge ◽  
Fluctuation Dissipation ◽  
Dust Charge Fluctuations ◽  
Markovian Systems

Dust charge fluctuates even in steady-state uniform plasma due to the discrete nature of the charge carriers and can be described using standard Langevin equation. In this work, two possible approaches in order to introduce the memory effect in dust charging dynamics are proposed. The first part of the paper provides the generalization form of the fluctuation-dissipation relation for non-Markovian systems based on generalized Langevin equations to determine the amplitudes of the dust charge fluctuations for two different kinds of colored noises under the assumption that the fluctuation-dissipation relation is valid. In the second part of the paper, aiming for dusty plasma system out of equilibrium, the fractionalized Langevin equation is used to derive the temporal two-point correlation function of grain charge fluctuations which is shown to be non-stationary due to the dependence on both times and not the time difference. The correlation function is used to derive the amplitude of fluctuations for early transient time.

scholarly journals Data-driven parameterization of the generalized Langevin equation

2016 ◽  
Vol 113 (50) ◽  
pp. 14183-14188 ◽  
Author(s):  
Huan Lei ◽  
Nathan A. Baker ◽  
Xiantao Li
Keyword(s):  
Explicit Memory ◽  
Random Noise ◽  
Data Driven ◽  
Langevin Equations ◽  
Generalized Langevin Equation ◽  
Memory Kernel ◽  
Laplace Domain ◽  
Fluctuation Dissipation ◽  
Data Driven Approach ◽  
Generalized Langevin Equations

We present a data-driven approach to determine the memory kernel and random noise in generalized Langevin equations. To facilitate practical implementations, we parameterize the kernel function in the Laplace domain by a rational function, with coefficients directly linked to the equilibrium statistics of the coarse-grain variables. We show that such an approximation can be constructed to arbitrarily high order and the resulting generalized Langevin dynamics can be embedded in an extended stochastic model without explicit memory. We demonstrate how to introduce the stochastic noise so that the second fluctuation-dissipation theorem is exactly satisfied. Results from several numerical tests are presented to demonstrate the effectiveness of the proposed method.

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