scholarly journals QUANTUM-LIOUVILLE AND LANGEVIN EQUATIONS FOR GRAVITATIONAL RADIATION DAMPING

2002 ◽  
Vol 17 (26) ◽  
pp. 3729-3736 ◽  
Author(s):  
Z. HABA ◽  
H. KLEINERT
Keyword(s):  
Master Equation ◽  
Path Integral ◽  
Langevin Equation ◽  
Gravitational Radiation ◽  
Heat Bath ◽  
Radiation Damping ◽  
Langevin Equations ◽  
Quantum Object ◽  
Dense Stars

From a forward–backward path integral, we derive a master equation for the emission and absorption of gravitons by a massive quantum object in a heat bath of gravitons. Such an equation could describe the collapse phenomena of dense stars. We also present a useful approximate Langevin equation for such a system.

scholarly journals Fokker–Planck representations of non-Markov Langevin equations: application to delayed systems

2019 ◽  
Vol 377 (2153) ◽  
pp. 20180131 ◽  
Author(s):  
Luca Giuggioli ◽  
Zohar Neu
Keyword(s):  
Langevin Equation ◽  
Complex Dynamics ◽  
Probability Distributions ◽  
Delay Systems ◽  
Langevin Equations ◽  
Delayed Systems ◽  
Temporal Features ◽  
Fokker Planck Equations ◽  
Random Fluctuations ◽  
Fokker Planck

Noise and time delays, or history-dependent processes, play an integral part in many natural and man-made systems. The resulting interplay between random fluctuations and time non-locality are essential features of the emerging complex dynamics in non-Markov systems. While stochastic differential equations in the form of Langevin equations with additive noise for such systems exist, the corresponding probabilistic formalism is yet to be developed. Here we introduce such a framework via an infinite hierarchy of coupled Fokker–Planck equations for the n -time probability distribution. When the non-Markov Langevin equation is linear, we show how the hierarchy can be truncated at n  = 2 by converting the time non-local Langevin equation to a time-local one with additive coloured noise. We compare the resulting Fokker–Planck equations to an earlier version, solve them analytically and analyse the temporal features of the probability distributions that would allow to distinguish between Markov and non-Markov features. This article is part of the theme issue ‘Nonlinear dynamics of delay systems’.

scholarly journals Quantum analysis of sub harmonic generation with two-mode coherent light

2021 ◽  
Vol 4 (1) ◽  
pp. 026-030
Author(s):  
Getahun Alemayehu ◽  
Dagnew Habtamu
Keyword(s):  
Master Equation ◽  
Harmonic Generation ◽  
Langevin Equation ◽  
Photon Number ◽  
Photon Statistics ◽  
Coherent Light ◽  
Quantum Analysis ◽  
Quadrature Squeezing ◽  
Mean And Variance ◽  
Quadrature Variance

In this work the statistical and squeezing properties of light-driven by sub-harmonic generation with two-mode coherent light are studied. With interaction Hamiltonian of both two-mode coherent and sub harmonic generation, we have driven master equation of system under consideration. From the master equation, the solution of the C-number Langevin equation is derived. It helps us to solve quadrature variance, quadrature squeezing, mean, and variance of photon number for light produced by sub-harmonic generation with the two-mode coherent light state. And the result shows that; the squeezing occurs in plus quadrature with the maximum squeezing of 87%. The photon statistics of the system under consideration is subpoissonian in which both mean & variance are increasing as kappa increase.

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 THE STOCHASTIC QUANTIZATION METHOD IN PHASE SPACE AND A NEW GAUGE FIXING PROCEDURE

1994 ◽  
Vol 09 (30) ◽  
pp. 2803-2815
Author(s):  
RIUJI MOCHIZUKI
Keyword(s):  
Phase Space ◽  
Path Integral ◽  
Equilibrium Solution ◽  
Planck Equation ◽  
Langevin Equations ◽  
Stochastic Quantization ◽  
Quantization Method ◽  
Canonical Variables ◽  
Gauge Fixing ◽  
Integral Distribution

We study the stochastic quantization of the system with first class constraints in phase space. Though the Langevin equations of the canonical variables are defined without ordinary gauge fixing procedure, gauge fixing conditions are automatically selected and introduced by imposing stochastic consistency conditions upon the first class constraints. Then the equilibrium solution of the Fokker–Planck equation is identical to the corresponding path-integral distribution.

QUANTUM STOCHASTIC EQUATIONS FOR A NON-LINEAR DAMPED OSCILLATOR

1993 ◽  
Vol 07 (09) ◽  
pp. 623-631 ◽  
Author(s):  
T. SAITO ◽  
T. ARIMITSU
Keyword(s):  
Master Equation ◽  
Conventional Treatment ◽  
Random Force ◽  
Quantum Systems ◽  
Langevin Equations ◽  
Unified Framework ◽  
Thermo Field Dynamics ◽  
Non Linear ◽  
Damping Theory ◽  
Damped Oscillator

A unified framework of stochastic differential equations for quantum systems, formulated within Non-Equilibrium Thermo Field Dynamics (NETFD), is applied to a model of non-linear damped oscillator. The quantum stochastic Liouville equation and the quantum Langevin equations (both of Ito and Stratonovich type), which are consistent with the corresponding master equation, are written down explicitly in the case of a non-conventional treatment. This solves Kubo's third problem: how one can obtain the correlations of random force operators for the Langevin equation compatible with the master equation derived by the non-conventional treatment of the damping theory.

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