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Quantum noise and dissipation

J. C. Garrison and R. Y. Chiao

in Quantum Optics

Published in print:
2008
Published Online:
September 2008
ISBN:
9780198508861
eISBN:
9780191708640
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198508861.003.0015
Subject:
Physics, Atomic, Laser, and Optical Physics

Dissipation and noise are treated by dividing the world into the sample and the environment. For weak sample-environment coupling, the environment is modeled by one or more reservoirs, represented by ... More


Stochastic Differential Equations: Langevin, Fokker–Planck Equations

JEAN ZINN-JUSTIN

in Quantum Field Theory and Critical Phenomena

Published in print:
2002
Published Online:
January 2010
ISBN:
9780198509233
eISBN:
9780191708732
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198509233.003.0004
Subject:
Physics, Theoretical, Computational, and Statistical Physics

This chapter discusses Langevin equations, that is, stochastic differential equations related to diffusion processes, brownian motion, or random walk. From the Langevin equation, the Fokker–Planck ... More


Properties of Langevin and Fokker–Planck equations

Helmut Hofmann

in The Physics of Warm Nuclei: with Analogies to Mesoscopic Systems

Published in print:
2008
Published Online:
September 2008
ISBN:
9780198504016
eISBN:
9780191708480
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198504016.003.0025
Subject:
Physics, Nuclear and Plasma Physics

This chapter introduces Langevin- and Fokker-Planck equations by way of a heuristic approach to the physics of Brownian particles. Variances of physical quantities are defined and related to ... More


Stochastic Modeling and Analysis

Richard M. Murray

in Biomolecular Feedback Systems

Published in print:
2014
Published Online:
October 2017
ISBN:
9780691161532
eISBN:
9781400850501
Item type:
chapter
Publisher:
Princeton University Press
DOI:
10.23943/princeton/9780691161532.003.0004
Subject:
Biology, Biochemistry / Molecular Biology

This chapter explores stochastic behavior in biomolecular systems. It does so by first building on the preliminary discussion of stochastic modeling laid out in Chapter 2. The chapter reviews methods ... More


Implications of Langevin's theory

Daniel T. Gillespie and Effrosyni Seitaridou

in Simple Brownian Diffusion: An Introduction to the Standard Theoretical Models

Published in print:
2012
Published Online:
January 2013
ISBN:
9780199664504
eISBN:
9780191748516
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199664504.003.0009
Subject:
Physics, Soft Matter / Biological Physics

This chapter develops the major implications of the Langevin theory of diffusion. The chapter begins by deriving Langevin's formula for the mean-squared displacement of a solute molecule. That ... More


From Langevin Equation To Supersymmetry

JEAN ZINN-JUSTIN

in Quantum Field Theory and Critical Phenomena

Published in print:
2002
Published Online:
January 2010
ISBN:
9780198509233
eISBN:
9780191708732
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198509233.003.0017
Subject:
Physics, Theoretical, Computational, and Statistical Physics

A particular class of Langevin equations is of special interest: equations with gaussian noise, in which the drift force derives from a static action and is thus conservative (the corresponding ... More


Large-scale collective motion at finite thermal excitations

Helmut Hofmann

in The Physics of Warm Nuclei: with Analogies to Mesoscopic Systems

Published in print:
2008
Published Online:
September 2008
ISBN:
9780198504016
eISBN:
9780191708480
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198504016.003.0011
Subject:
Physics, Nuclear and Plasma Physics

This chapter uses a Kramers-Moyal expansion to derive from short time propagators transport equations of Fokker-Planck type for global motion. Because of the inherent non-linearities, the transport ... More


Diffusion in an external force field

Daniel T. Gillespie and Effrosyni Seitaridou

in Simple Brownian Diffusion: An Introduction to the Standard Theoretical Models

Published in print:
2012
Published Online:
January 2013
ISBN:
9780199664504
eISBN:
9780191748516
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199664504.003.0010
Subject:
Physics, Soft Matter / Biological Physics

This chapter considers what happens when diffusing solute molecules are subjected to an externally applied conservative force. The chapter starts by presenting the traditional derivation of the ... More


Langevin treatment of the Fokker–Planck process

Melvin Lax, Wei Cai, and Min Xu

in Random Processes in Physics and Finance

Published in print:
2006
Published Online:
January 2010
ISBN:
9780198567769
eISBN:
9780191718359
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198567769.003.0010
Subject:
Physics, Theoretical, Computational, and Statistical Physics

This chapter discusses the Langevin treatment of the Fokker–Planck process and diffusion. The form of Langevin equation used is different from the stochastic differential equation using Ito's ... More


Continuous Markov process theory

Daniel T. Gillespie and Effrosyni Seitaridou

in Simple Brownian Diffusion: An Introduction to the Standard Theoretical Models

Published in print:
2012
Published Online:
January 2013
ISBN:
9780199664504
eISBN:
9780191748516
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199664504.003.0007
Subject:
Physics, Soft Matter / Biological Physics

Three years after Einstein published his groundbreaking 1905 paper on diffusion, a different analysis was published by Paul Langevin. Although it was not clearly appreciated at the time, Langevin's ... More


Random Processes in Physics and Finance

Melvin Lax, Wei Cai, and Min Xu

Published in print:
2006
Published Online:
January 2010
ISBN:
9780198567769
eISBN:
9780191718359
Item type:
book
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198567769.001.0001
Subject:
Physics, Theoretical, Computational, and Statistical Physics

This book discusses random processes in physics, from basic probability theory to the Fokker-Planck process and Langevin equation for the Fokker Planck process and diffusion. It includes diverse ... More


Generalised Langevin Equation

Phil Attard

in Non-equilibrium Thermodynamics and Statistical Mechanics: Foundations and Applications

Published in print:
2012
Published Online:
January 2013
ISBN:
9780199662760
eISBN:
9780191745287
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199662760.003.0010
Subject:
Physics, Condensed Matter Physics / Materials

The generalised Langevin equation is derived in three ways: perturbation theory, linear response theory, and projector operator formalism. The perturbation theory derives the trajectory entropy for a ... More


STOCHASTIC EQUATIONS FROM A STATISTICAL MECHANICAL VIEWPOINT

Robert M. Mazo

in Brownian Motion: Fluctuations, Dynamics, and Applications

Published in print:
2008
Published Online:
January 2010
ISBN:
9780199556441
eISBN:
9780191705625
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199556441.003.0011
Subject:
Physics, Condensed Matter Physics / Materials

This chapter begins with a heuristic derivation of the Langevin equation using the Mori projection operator as the main tool. The random force and the friction constant are identified. A similar ... More


Dissipative Processes

STEPHEN M. BARNETT and PAUL M. RADMORE

in Methods in Theoretical Quantum Optics

Published in print:
2002
Published Online:
February 2010
ISBN:
9780198563617
eISBN:
9780191714245
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198563617.003.0005
Subject:
Physics, Theoretical, Computational, and Statistical Physics

This chapter treats dissipation arising from coupling to the environment. Problems treated include photoionization, spontaneous emission, and cavity damping. A short-time perturbative analysis leads ... More


Fluctuations, Dissipation, and Noise

Peter W. Milonni

in An Introduction to Quantum Optics and Quantum Fluctuations

Published in print:
2019
Published Online:
April 2019
ISBN:
9780199215614
eISBN:
9780191868689
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/oso/9780199215614.003.0006
Subject:
Physics, Atomic, Laser, and Optical Physics, Particle Physics / Astrophysics / Cosmology

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 ... More


REPRINT THE SURFACE STATISTICS OF A GRANULAR AGGREGATE

S. F. Edwards and D. R. Wilkinson

in Stealing the Gold: A celebration of the pioneering physics of Sam Edwards

Published in print:
2004
Published Online:
September 2007
ISBN:
9780198528531
eISBN:
9780191713415
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198528531.003.0022
Subject:
Physics, Theoretical, Computational, and Statistical Physics

This paper examines the problem of the surface fluctuations in a settled granular material. A simple model is given which describes the process by which a particle settles and comes to rest on the ... More


STOCHASTIC DIFFERENTIAL EQUATIONS AND INTEGRALS

Robert M. Mazo

in Brownian Motion: Fluctuations, Dynamics, and Applications

Published in print:
2008
Published Online:
January 2010
ISBN:
9780199556441
eISBN:
9780191705625
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199556441.003.0005
Subject:
Physics, Condensed Matter Physics / Materials

This chapter returns to a mathematical topic — that of stochastic differential equations and stochastic integrals — the meaning of which are essential for the interpretation of the Langevin equation ... More


Dynamic solvent effects, Kramers theory

Niels E. Henriksen and Flemming Y. Hansen

in Theories of Molecular Reaction Dynamics: The Microscopic Foundation of Chemical Kinetics

Published in print:
2008
Published Online:
January 2010
ISBN:
9780199203864
eISBN:
9780191708251
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199203864.003.0011
Subject:
Physics, Condensed Matter Physics / Materials

This chapter discusses dynamical solvent effects on the rate constants for chemical reactions in solution. The effect is described by stochastic dynamics, where the influence of the solvent on the ... More


Langevin's theory of diffusion

Daniel T. Gillespie and Effrosyni Seitaridou

in Simple Brownian Diffusion: An Introduction to the Standard Theoretical Models

Published in print:
2012
Published Online:
January 2013
ISBN:
9780199664504
eISBN:
9780191748516
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199664504.003.0008
Subject:
Physics, Soft Matter / Biological Physics

Although Einstein's theory of diffusion is adequate for many purposes, the previous chapters have shown that it is physically incorrect on small timescales. A theory of diffusion that has a firmer ... More


FLUCTUATIONS

HARRY SUHL

in Relaxation Processes in Micromagnetics

Published in print:
2007
Published Online:
January 2010
ISBN:
9780198528029
eISBN:
9780191713545
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198528029.003.0004
Subject:
Physics, Condensed Matter Physics / Materials

This chapter examines how the magnetization senses random fluctuations. Mathematical descriptions of stochastic processes of physical origin involve one or other of various incarnations of the ... More


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