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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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