scholarly journals Fluctuation-dissipation relation for nonlinear Langevin equations

2011 ◽  
Vol 83 (4) ◽  
Author(s):  
V. Kumaran
Keyword(s):  
Langevin Equations ◽  
Fluctuation Dissipation ◽  
Nonlinear Langevin Equations

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.

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