Jump to ContentJump to Main Navigation

You are looking at 1-20 of 37 items

  • Keywords: Fokker–Planck equation x
Clear All Modify Search

View:

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


SINGLE CHAINS IN EXTERNAL FIELDS

Glenn H. Fredrickson

in The Equilibrium Theory of Inhomogeneous Polymers

Published in print:
2005
Published Online:
September 2007
ISBN:
9780198567295
eISBN:
9780191717956
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198567295.003.0003
Subject:
Physics, Condensed Matter Physics / Materials

This chapter examines the subject of polymers experiencing external potential fields that vary in space. The statistical mechanical problem is reduced to the solution of Fokker-Planck equations, and ... More


The master equation

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/9780198508861.003.0019
Subject:
Physics, Atomic, Laser, and Optical Physics

This chapter examines the evolution of an open system — the sample — with the quantum Liouville equation for the world density operator. The fundamental approximation is that the action of the sample ... More


Generalized Fokker–Planck equation

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/9780198567769.003.0008
Subject:
Physics, Theoretical, Computational, and Statistical Physics

Thermal noise and Gaussian noise sources combine to create a category of Markovian processes known as Fokker–Planck processes. This chapter discusses Fokker–Planck processes such as ... 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


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


Fokker–Planck Equations

Bryan J. Dalton, John Jeffers, and Stephen M. Barnett

in Phase Space Methods for Degenerate Quantum Gases

Published in print:
2014
Published Online:
April 2015
ISBN:
9780199562749
eISBN:
9780191747311
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199562749.003.0008
Subject:
Physics, Condensed Matter Physics / Materials, Atomic, Laser, and Optical Physics

This chapter deals with deriving Fokker–Planck equations (FPEs) that govern the behaviour of phase space distribution functions (normalised and unnormalised) for boson and fermion systems due to ... 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


IDEAL CHAIN MODELS

Glenn H. Fredrickson

in The Equilibrium Theory of Inhomogeneous Polymers

Published in print:
2005
Published Online:
September 2007
ISBN:
9780198567295
eISBN:
9780191717956
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198567295.003.0002
Subject:
Physics, Condensed Matter Physics / Materials

This chapter discusses elementary statistical mechanical models of ideal chains, i.e., polymers in isolation and not experiencing interactions with other polymers. Freely jointed and bead-spring ... 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


Classical Probability Theory and Stochastic Processes

Heinz-Peter Breuer and Francesco Petruccione

in The Theory of Open Quantum Systems

Published in print:
2007
Published Online:
January 2010
ISBN:
9780199213900
eISBN:
9780191706349
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199213900.003.01
Subject:
Physics, Theoretical, Computational, and Statistical Physics

This chapter contains a survey of classical probability theory and stochastic processes. It starts with a description of the fundamental concepts of probability space and Kolmogorov axioms. These ... 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


Langevin Equations

Bryan J. Dalton, John Jeffers, and Stephen M. Barnett

in Phase Space Methods for Degenerate Quantum Gases

Published in print:
2014
Published Online:
April 2015
ISBN:
9780199562749
eISBN:
9780191747311
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199562749.003.0009
Subject:
Physics, Condensed Matter Physics / Materials, Atomic, Laser, and Optical Physics

In this chapter, Langevin equations (or Ito stochastic differential equations, SDEs) are derived that are equivalent to Fokker–Planck equations for bosons and fermions. The approach involves ... More


Langevin Field Equations

Bryan J. Dalton, John Jeffers, and Stephen M. Barnett

in Phase Space Methods for Degenerate Quantum Gases

Published in print:
2014
Published Online:
April 2015
ISBN:
9780199562749
eISBN:
9780191747311
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199562749.003.0014
Subject:
Physics, Condensed Matter Physics / Materials, Atomic, Laser, and Optical Physics

In this chapter, Langevin field equations (or Ito stochastic field equations, SFEs) are derived that are equivalent to functional Fokker–Planck equations (FFPEs) for bosons and fermions. Phase space ... More


Phase Space Methods for Degenerate Quantum Gases

Bryan J. Dalton, John Jeffers, and Stephen M. Barnett

Published in print:
2014
Published Online:
April 2015
ISBN:
9780199562749
eISBN:
9780191747311
Item type:
book
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199562749.001.0001
Subject:
Physics, Condensed Matter Physics / Materials, Atomic, Laser, and Optical Physics

Recent experimental progress has enabled cold atomic gases to be studied at nanokelvin temperatures, creating new states of matter where quantum degeneracy occurs—Bose–Einstein condensates and ... More


THE SMOLUCHOWSKI EQUATION

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/9780199556441.003.0008
Subject:
Physics, Condensed Matter Physics / Materials

This chapter discusses the Smoluchowski equation, a configuration space description of a Brownian particle in a field of force. It begins with the Kramers–Klein equation, essentially the ... More


PATH INTEGRALS AND QUANTIZATION

Jean Zinn-Justin

in Path Integrals in Quantum Mechanics

Published in print:
2004
Published Online:
January 2010
ISBN:
9780198566748
eISBN:
9780191717994
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198566748.003.0005
Subject:
Physics, Particle Physics / Astrophysics / Cosmology, Theoretical, Computational, and Statistical Physics

This chapter constructs path integrals for general Hamiltonians with potentials linear in the velocities, like Hamiltonians of particles in a magnetic field. Two examples are considered: a quantum ... More


INTERACTING BROWNIAN PARTICLES

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/9780199556441.003.0017
Subject:
Physics, Condensed Matter Physics / Materials

This chapter studies the effect of the concentration of Brownian particles on Brownian motion. It starts from the multi-particle Fokker–Planck equation and the multi-particle Smoluchowski equation. ... More


Functional Fokker–Planck Equations

Bryan J. Dalton, John Jeffers, and Stephen M. Barnett

in Phase Space Methods for Degenerate Quantum Gases

Published in print:
2014
Published Online:
April 2015
ISBN:
9780199562749
eISBN:
9780191747311
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199562749.003.0013
Subject:
Physics, Condensed Matter Physics / Materials, Atomic, Laser, and Optical Physics

This chapter deals with deriving functional Fokker–Planck equations (FFPEs) that govern the behaviour of phase space distribution functionals (normalised and unnormalised) for boson and fermion ... 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


View: