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The Hartree–Fock approximation

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/9780198504016.003.0020
Subject:
Physics, Nuclear and Plasma Physics

This chapter formulates the Hartree-Fock approximation with density matrices, and discusses the properties of the Hartree-Fock equations together with the energy functional for the ground state ... More


Classical Ensembles: Grand and Otherwise

Robert H. Swendsen

in An Introduction to Statistical Mechanics and Thermodynamics

Published in print:
2012
Published Online:
December 2013
ISBN:
9780199646944
eISBN:
9780191775123
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199646944.003.0020
Subject:
Physics, Condensed Matter Physics / Materials

This chapter introduces the grand canonical ensemble and demonstrates how to calculate the grand canonical partition function for a classical ideal gas. One purpose of the introduction of the grand ... More


Basic principles

Barry M. McCoy

in Advanced Statistical Mechanics

Published in print:
2009
Published Online:
February 2010
ISBN:
9780199556632
eISBN:
9780191723278
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199556632.003.0001
Subject:
Physics, Theoretical, Computational, and Statistical Physics

This chapter reviews the basic results of thermodynamics. It derives the basic formulas of the canonical and grand canonical ensemble from the microcanonical ensemble. It defines the concept of a ... More


Ideal Quantum Gases

Robert H. Swendsen

in An Introduction to Statistical Mechanics and Thermodynamics

Published in print:
2012
Published Online:
December 2013
ISBN:
9780199646944
eISBN:
9780191775123
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199646944.003.0026
Subject:
Physics, Condensed Matter Physics / Materials

This chapter develops the basic equations that will be used to analyse the Fermi-Dirac and Bose-Einstein gases. The representation of many-particle states in terms of products of single-particle ... More


Thermodynamic Limit

Jochen Rau

in Statistical Physics and Thermodynamics: An Introduction to Key Concepts

Published in print:
2017
Published Online:
November 2017
ISBN:
9780199595068
eISBN:
9780191844300
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/oso/9780199595068.003.0005
Subject:
Physics, Theoretical, Computational, and Statistical Physics

When one describes systems which are homogeneous, stable, and macroscopic in size, it no longer matters whether macroscopic data are given as sharp constraints or as expectation values. This is the ... More


Monte Carlo methods

Michael P. Allen and Dominic J. Tildesley

in Computer Simulation of Liquids: Second Edition

Published in print:
2017
Published Online:
November 2017
ISBN:
9780198803195
eISBN:
9780191841439
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/oso/9780198803195.003.0004
Subject:
Physics, Theoretical, Computational, and Statistical Physics, Soft Matter / Biological Physics

The estimation of integrals by Monte Carlo sampling is introduced through a simple example. The chapter then explains importance sampling, and the use of the Metropolis and Barker forms of the ... More


Quantum Mechanical Ensemble Averages and Statistical Thermodynamics

Norman J. Morgenstern Horing

in Quantum Statistical Field Theory: An Introduction to Schwinger's Variational Method with Green's Function Nanoapplications, Graphene and Superconductivity

Published in print:
2017
Published Online:
January 2018
ISBN:
9780198791942
eISBN:
9780191834165
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/oso/9780198791942.003.0006
Subject:
Physics, Theoretical, Computational, and Statistical Physics

Chapter 6 introduces quantum-mechanical ensemble theory by proving the asymptotic equivalence of the quantum-mechanical, microcanonical ensemble average with the quantum grand canonical ensemble ... More


Thermodynamic Green’s Functions and Spectral Structure

Norman J. Morgenstern Horing

in Quantum Statistical Field Theory: An Introduction to Schwinger's Variational Method with Green's Function Nanoapplications, Graphene and Superconductivity

Published in print:
2017
Published Online:
January 2018
ISBN:
9780198791942
eISBN:
9780191834165
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/oso/9780198791942.003.0007
Subject:
Physics, Theoretical, Computational, and Statistical Physics

Multiparticle thermodynamic Green’s functions, defined in terms of grand canonical ensemble averages of time-ordered products of creation and annihilation operators, are interpreted as tracing the ... More


The Ideal Bose Gas

Lev Pitaevskii and Sandro Stringari

in Bose-Einstein Condensation and Superfluidity

Published in print:
2016
Published Online:
March 2016
ISBN:
9780198758884
eISBN:
9780191818721
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198758884.003.0003
Subject:
Physics, Condensed Matter Physics / Materials

This chapter describes the mechanism of Bose–Einstein condensation in the simplest ideal Bose gas case. An explicit expression for the critical temperature is derived in the analytically soluble case ... More


Equilibrium Statistical Mechanics

Hans-Peter Eckle

in Models of Quantum Matter: A First Course on Integrability and the Bethe Ansatz

Published in print:
2019
Published Online:
September 2019
ISBN:
9780199678839
eISBN:
9780191878589
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/oso/9780199678839.003.0004
Subject:
Physics, Theoretical, Computational, and Statistical Physics, Condensed Matter Physics / Materials

Chapter 4 reviews the basic notions of equilibrium statistical mechanics and begins with its fundamental postulate and outlines the structure of the theory using the most important of the various ... More


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