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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


From random walk to critical dynamics

Jean Zinn-Justin

in From Random Walks to Random Matrices

Published in print:
2019
Published Online:
August 2019
ISBN:
9780198787754
eISBN:
9780191829840
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/oso/9780198787754.003.0022
Subject:
Physics, Theoretical, Computational, and Statistical Physics

Chapter 22 studies stochastic dynamical equations, consistent with the detailed balance condition, which are generalized Langevin equations which describe a wide range of phenomena from Brownian ... More


Energy and Entropy

Manfred Eigen

in From Strange Simplicity to Complex Familiarity: A Treatise on Matter, Information, Life and Thought

Published in print:
2013
Published Online:
May 2013
ISBN:
9780198570219
eISBN:
9780191748974
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198570219.003.0002
Subject:
Physics, History of Physics

Sensorily perceptible material structures are made up of many atoms or molecules which, at the temperatures of our biosphere, are in wild – free or oscillatory – motion. “Wild” means that velocities ... More


The Einstein A and B coefficients

Geoffrey Brooker

in Essays in Physics: Thirty-two thoughtful essays on topics in undergraduate-level physics

Published in print:
2021
Published Online:
September 2021
ISBN:
9780198857242
eISBN:
9780191890284
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/oso/9780198857242.003.0019
Subject:
Physics, Condensed Matter Physics / Materials, Theoretical, Computational, and Statistical Physics

The Einstein A and B coefficients for atom–photon reactions are defined: they describe absorption, stimulated emission, and spontaneous emission. We calculate B and consequently find A by the ... More


Markov Chain Monte Carlo sampling of graphs

A.C.C. Coolen, A. Annibale, and E.S. Roberts

in Generating Random Networks and Graphs

Published in print:
2017
Published Online:
May 2017
ISBN:
9780198709893
eISBN:
9780191780172
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/oso/9780198709893.003.0006
Subject:
Physics, Theoretical, Computational, and Statistical Physics

This chapter looks at Markov Chain Monte Carlo techniques to generate hard- and soft-constrained exponential random graph ensembles. The essence is to define a Markov chain based on ergodic ... More


Kinematical Theory of Scattering

Andrew T. Boothroyd

in Principles of Neutron Scattering from Condensed Matter

Published in print:
2020
Published Online:
October 2020
ISBN:
9780198862314
eISBN:
9780191895081
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/oso/9780198862314.003.0003
Subject:
Physics, Atomic, Laser, and Optical Physics, Condensed Matter Physics / Materials

The chapter introduces the kinematical theory of scattering, which is based on the Born approximation. It is shown that the neutron scattering response function can be written as the time Fourier ... More


Understanding entropy

Andrew M. Steane

in Thermodynamics: A complete undergraduate course

Published in print:
2016
Published Online:
January 2017
ISBN:
9780198788560
eISBN:
9780191830426
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198788560.003.0009
Subject:
Physics, Theoretical, Computational, and Statistical Physics

Entropy is described and discussed from numerous perspectives. First we present example calculations of entropy changes, and the role of entropy in heat engines and heat conduction. Then the ... More


Rate Law and Mechanism

Robert B. Jordan

in Reaction Mechanisms of Inorganic and Organometallic Systems

Published in print:
2007
Published Online:
November 2020
ISBN:
9780195301007
eISBN:
9780197562406
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/oso/9780195301007.003.0004
Subject:
Chemistry, Inorganic Chemistry

Once the experimental rate law has been established, the next step is to formulate a mechanism that is consistent with the rate law. The rate law will not uniquely define the mechanism but will ... More


Approximate theories

Gert D. Billing (ed.)

in The Quantum Classical Theory

Published in print:
2003
Published Online:
November 2020
ISBN:
9780195146196
eISBN:
9780197561836
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/oso/9780195146196.003.0007
Subject:
Chemistry, Quantum and Theoretical Chemistry

Many calculations of rates or cross sections will have to be carried out using reliable approximate theories, simply because the number of systems and the number of detailed rate constants needed ... More


Optical Electromagnetics II

Michael E. Thomas

in Optical Propagation in Linear Media: Atmospheric Gases and Particles, Solid State Components, and Water

Published in print:
2006
Published Online:
November 2020
ISBN:
9780195091618
eISBN:
9780197560679
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/oso/9780195091618.003.0006
Subject:
Earth Sciences and Geography, Atmospheric Sciences

In this chapter the same basic topics are addressed as in the previous chapter, but now in the presence of matter. This greatly complicates the description of optical propagation and continues to ... More


Spectroscopy

Abraham Nitzan

in Chemical Dynamics in Condensed Phases: Relaxation, Transfer and Reactions in Condensed Molecular Systems

Published in print:
2006
Published Online:
November 2020
ISBN:
9780198529798
eISBN:
9780191916649
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/oso/9780198529798.003.0025
Subject:
Chemistry, Physical Chemistry

The interaction of light with matter provides some of the most important tools for studying structure and dynamics on the microscopic scale. Atomic and molecular spectroscopy in the low pressure ... More


Electron Transfer Processes

Abraham Nitzan

in Chemical Dynamics in Condensed Phases: Relaxation, Transfer and Reactions in Condensed Molecular Systems

Published in print:
2006
Published Online:
November 2020
ISBN:
9780198529798
eISBN:
9780191916649
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/oso/9780198529798.003.0023
Subject:
Chemistry, Physical Chemistry

Electron transfer processes are at the core of all oxidation–reduction reactions, including those associated with electrochemistry and corrosion. Photoelectrochemistry and solar energy conversion, ... More


Time Correlation Functions

Abraham Nitzan

in Chemical Dynamics in Condensed Phases: Relaxation, Transfer and Reactions in Condensed Molecular Systems

Published in print:
2006
Published Online:
November 2020
ISBN:
9780198529798
eISBN:
9780191916649
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/oso/9780198529798.003.0012
Subject:
Chemistry, Physical Chemistry

In the previous chapter we have seen how spatial correlation functions express useful structural information about our system. This chapter focuses on time correlation functions that, as will be ... More


The Spin–Boson Model

Abraham Nitzan

in Chemical Dynamics in Condensed Phases: Relaxation, Transfer and Reactions in Condensed Molecular Systems

Published in print:
2006
Published Online:
November 2020
ISBN:
9780198529798
eISBN:
9780191916649
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/oso/9780198529798.003.0018
Subject:
Chemistry, Physical Chemistry

In a generic quantum mechanical description of a molecule interacting with its thermal environment, the molecule is represented as a few level system (in the simplest description just two, for ... More


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