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REPRINT THE STATISTICAL DYNAMICS OF HOMOGENEOUS TURBULENCE

S. F. Edwards

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/9780198528531.003.0005
Subject:
Physics, Theoretical, Computational, and Statistical Physics

This chapter presents a paper which examines the problem of steady homogeneous isotropic turbulence under idealized conditions, allowing the for the exact form of the correlation functions to be ... 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


Transport and evolution of classical and quantum ensembles

Sandip Tiwari

in Semiconductor Physics: Principles, Theory and Nanoscale

Published in print:
2020
Published Online:
November 2020
ISBN:
9780198759867
eISBN:
9780191820830
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/oso/9780198759867.003.0008
Subject:
Physics, Condensed Matter Physics / Materials

This chapter explores the evolution of an ensemble of electrons under stimulus, classically and quantum-mechanically. The classical Liouville description is derived, and then reformed to the quantum ... More


STATISTICAL MECHANICS

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/9780199556441.003.0010
Subject:
Physics, Condensed Matter Physics / Materials

This chapter begins by reviewing the definitions and properties of N particle molecular distribution functions and the Liouville equation, which governs their evolution in time. Zwanzig projection ... More


Distribution functions

Rodrigo Soto

in Kinetic Theory and Transport Phenomena

Published in print:
2016
Published Online:
June 2016
ISBN:
9780198716051
eISBN:
9780191824401
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198716051.003.0002
Subject:
Physics, Theoretical, Computational, and Statistical Physics

The concepts that were advanced in Chapter 1 are defined formally here for classical systems described by Hamilton equations. The need for a statistical description of the system dynamics is ... More


A Sturm-Liouville Equation: The Time-Independent One-Dimensional Schrödinger Equation

John A. Adam

in Rays, Waves, and Scattering: Topics in Classical Mathematical Physics

Published in print:
2017
Published Online:
May 2018
ISBN:
9780691148373
eISBN:
9781400885404
Item type:
chapter
Publisher:
Princeton University Press
DOI:
10.23943/princeton/9780691148373.003.0023
Subject:
Mathematics, Applied Mathematics

This chapter examines the mathematical properties of the time-independent one-dimensional Schrödinger equation as they relate to Sturm-Liouville problems. The regular Sturm-Liouville theory was ... More


Quantization of cavity modes

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/9780198508861.003.0003
Subject:
Physics, Atomic, Laser, and Optical Physics

This chapter begins with a normal-mode analysis of the classical electromagnetic field in an ideal cavity. The resulting expression for the electromagnetic energy has the same form as the energy of a ... More


The Quantum Mechanical Density Operator And Its Time Evolution: Quantum Dynamics Using The Quantum Liouville Equation

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/9780198529798.003.0016
Subject:
Chemistry, Physical Chemistry

The starting point of the classical description of motion is the Newton equations that yield a phase space trajectory (rN (t), pN (t)) for a given initial condition (rN (0), pN (0)). Alternatively ... More


Special functions

Chun Wa Wong

in Introduction to Mathematical Physics: Methods & Concepts

Published in print:
2013
Published Online:
May 2013
ISBN:
9780199641390
eISBN:
9780191747786
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199641390.003.0007
Subject:
Physics, Theoretical, Computational, and Statistical Physics

Special functions are advanced functions frequently used in science and engineering. The properties of Legendre, Hermite, Laguerre, Chebyshev and spherical harmonics polynomials and Bessel functions ... More


Quantum description of nuclear ensembles

Paul T. Callaghan

in Translational Dynamics and Magnetic Resonance: Principles of Pulsed Gradient Spin Echo NMR

Published in print:
2011
Published Online:
December 2013
ISBN:
9780199556984
eISBN:
9780191774928
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199556984.003.0003
Subject:
Physics, Condensed Matter Physics / Materials, Nuclear and Plasma Physics

This chapter outlines the quantum ideas that underpin magnetic resonance and explains their link to classical physics. It discusses some of the essential concepts governing the quantum behaviour of ... More


Micro, kinetic and fluid descriptions—Hierarchy of plasma descriptions

Abraham Bers

in Plasma Physics and Fusion Plasma Electrodynamics

Published in print:
2016
Published Online:
November 2016
ISBN:
9780199295784
eISBN:
9780191749063
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199295784.003.0023
Subject:
Physics, Nuclear and Plasma Physics, Particle Physics / Astrophysics / Cosmology

This chapter describes the hierarchical development of classical plasma dynamic model equations. In any macroscopic physical system containing many individual particles, there are basically three ... More


Kinetic theory

Nathalie Deruelle and Jean-Philippe Uzan

in Relativity in Modern Physics

Published in print:
2018
Published Online:
October 2018
ISBN:
9780198786399
eISBN:
9780191828669
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/oso/9780198786399.003.0010
Subject:
Physics, Particle Physics / Astrophysics / Cosmology

This chapter covers the equations governing the evolution of particle distribution and relates the macroscopic thermodynamical quantities to the distribution function. The motion of N particles is ... More


The Dissipation Bracket

Antony N. Beris and Brian J. Edwards

in Thermodynamics of Flowing Systems: with Internal Microstructure

Published in print:
1994
Published Online:
November 2020
ISBN:
9780195076943
eISBN:
9780197560341
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/oso/9780195076943.003.0011
Subject:
Chemistry, Thermochemistry and Chemical Thermodynamics

In the opening chapters of the book, we saw how a variety of conservative phenomena could be described through the Poisson bracket of classical physics. As already mentioned, the majority of ... More


Statistical Mechanics: The Basics

Wayne C. Myrvold

in Beyond Chance and Credence: A Theory of Hybrid Probabilities

Published in print:
2021
Published Online:
February 2021
ISBN:
9780198865094
eISBN:
9780191897481
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/oso/9780198865094.003.0007
Subject:
Philosophy, Logic/Philosophy of Mathematics

This chapter introduces the reader to the basics of statistical mechanics. Gibbsian and neo-Boltzmannian approaches are outlined. It includes a statistical-mechanical analogue of the second law of ... More


Non-Equilibrium Statistical Mechanics

Adrian F. Tuck

in Atmospheric Turbulence: a molecular dynamics perspective

Published in print:
2008
Published Online:
November 2020
ISBN:
9780199236534
eISBN:
9780191917462
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/oso/9780199236534.003.0010
Subject:
Earth Sciences and Geography, Atmospheric Sciences

The Earth’s atmosphere is far from equilibrium; it is constantly in motion from the combined effects of gravity and planetary rotation, is constantly absorbing and ... More


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