Jump to ContentJump to Main Navigation

You are looking at 1-20 of 21 items

  • Keywords: thermodynamic limit x
Clear All Modify Search

View:

A Matter of Degree: Making Sense of Phase Structure

Laura Ruetsche

in Interpreting Quantum Theories

Published in print:
2011
Published Online:
September 2011
ISBN:
9780199535408
eISBN:
9780191728525
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199535408.003.0012
Subject:
Philosophy, Philosophy of Science

This chapter presents three reasons to take quantum statistical mechanics to the thermodynamic limit, where the number of systems considered becomes infinite, in the form of three phenomena that ... More


Stochastic Homogenization and Energy of Infinite Sets of Points

Xavier Blanc

in Analysis and Stochastics of Growth Processes and Interface Models

Published in print:
2008
Published Online:
September 2008
ISBN:
9780199239252
eISBN:
9780191716911
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199239252.003.0004
Subject:
Mathematics, Probability / Statistics, Analysis

This chapter presents, in a synthetic way, a series of recent works by X. Blanc, C. Le Bris, and P-L. Lions on homogenization of an elliptic partial differential equation under certain periodic or ... More


INTRODUCTION

Mathew Penrose

in Random Geometric Graphs

Published in print:
2003
Published Online:
September 2007
ISBN:
9780198506263
eISBN:
9780191707858
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198506263.003.0001
Subject:
Mathematics, Probability / Statistics

This introductory chapter contains a general discussion of both the historical and the applied background behind the study of random geometric graphs. A brief overview is presented, along with some ... More


Stability, existence and uniqueness

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/9780199556632.003.0003
Subject:
Physics, Theoretical, Computational, and Statistical Physics

This chapter develops the stability theory needed for the existence of the classical partition. This is extended to quantum stability with emphasis on the physically important case of nonrelativistic ... More


Classical statistical physics: One dimension

Jean Zinn-Justin

in Phase Transitions and Renormalization Group

Published in print:
2007
Published Online:
January 2010
ISBN:
9780199227198
eISBN:
9780191711107
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199227198.003.0004
Subject:
Physics, Theoretical, Computational, and Statistical Physics

This chapter, within the framework of classical statistical mechanics, discusses a family of models defined on one-dimensional lattices. It studies the simplest local examples: models that involve ... More


PERCOLATION AND THE LARGEST COMPONENT

Mathew Penrose

in Random Geometric Graphs

Published in print:
2003
Published Online:
September 2007
ISBN:
9780198506263
eISBN:
9780191707858
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198506263.003.0010
Subject:
Mathematics, Probability / Statistics

This chapter concerns the largest component of G(N(n),r) in the thermodynamic limit when the number of points N(n) is Poisson with parameter n and the underlying density is uniform on the unit ... More


THE LARGEST COMPONENT FOR A BINOMIAL PROCESS

Mathew Penrose

in Random Geometric Graphs

Published in print:
2003
Published Online:
September 2007
ISBN:
9780198506263
eISBN:
9780191707858
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198506263.003.0011
Subject:
Mathematics, Probability / Statistics

This chapter is mainly concerned with the largest component of G(n,r) in the thermodynamic limit (with a non-random number of points). In the subcritical case, the order of the largest component ... 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


ORDERING AND PARTITIONING PROBLEMS

Mathew Penrose

in Random Geometric Graphs

Published in print:
2003
Published Online:
September 2007
ISBN:
9780198506263
eISBN:
9780191707858
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198506263.003.0012
Subject:
Mathematics, Probability / Statistics

Given an ordering of the vertices of a graph, let the induced weight for an edge be the separation of its end-points in the ordering. Layout problems involve choosing the ordering to minimize a cost ... More


Introduction

Stephen J. Blundell and Katherine M. Blundell

in Concepts in Thermal Physics

Published in print:
2009
Published Online:
February 2010
ISBN:
9780199562091
eISBN:
9780191718236
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199562091.003.0001
Subject:
Physics, Particle Physics / Astrophysics / Cosmology

This introductory chapter explores the concept of large numbers, showing why large numbers appear in thermal physics and explaining how to handle them. Large numbers arise in thermal physics because ... More


Interpreting QM∞: Some Options

Laura Ruetsche

in Interpreting Quantum Theories

Published in print:
2011
Published Online:
September 2011
ISBN:
9780199535408
eISBN:
9780191728525
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199535408.003.0006
Subject:
Philosophy, Philosophy of Science

This chapter catalogs interpretative responses to the breakdown of unitary equivalence in QM∞. These range from ‘Hilbert Space Conservatism’ to ‘Algebraic Imperialism’. Maintaining the ordinary ... More


Thermodynamics of a Trapped 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/9780198758884.003.0013
Subject:
Physics, Condensed Matter Physics / Materials

This chapter is devoted to the thermodynamic behaviour of an interacting trapped Bose gas. It developes the Hartree–Fock theory for nonuniform interacting Bose gases at low temperatures, and ... More


Beyond the Stone–von Neumann Theorem

Laura Ruetsche

in Interpreting Quantum Theories

Published in print:
2011
Published Online:
September 2011
ISBN:
9780199535408
eISBN:
9780191728525
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199535408.003.0003
Subject:
Philosophy, Philosophy of Science

This chapter catalogs circumstances under which the reassuring uniqueness results presented in Chapter 2 break down. The Stone-von Neumann theorem presupposes a continuity condition; with that ... More


Dipolar Systems

A. Campa, T. Dauxois, D. Fanelli, and S. Ruffo

in Physics of Long-Range Interacting Systems

Published in print:
2014
Published Online:
October 2014
ISBN:
9780199581931
eISBN:
9780191787140
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199581931.003.0015
Subject:
Physics, Theoretical, Computational, and Statistical Physics

This chapter is devoted to studying systems with magnetic dipolar interactions. After a general introduction, the origin of the so called demagnetized field arising in the interior of magnetized ... More


Bethe Ansatz for the Anisotropic Heisenberg Quantum Spin Chain

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/9780199678839.003.0014
Subject:
Physics, Theoretical, Computational, and Statistical Physics, Condensed Matter Physics / Materials

This chapter verifies the conjecture for the wave function, the Bethe ansatz wave function, of the anisotropic Heisenberg quantum spin chain by examining first the cases for one, two, and three spin ... More


Quantum Long-Range Systems

A. Campa, T. Dauxois, D. Fanelli, and S. Ruffo

in Physics of Long-Range Interacting Systems

Published in print:
2014
Published Online:
October 2014
ISBN:
9780199581931
eISBN:
9780191787140
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199581931.003.0006
Subject:
Physics, Theoretical, Computational, and Statistical Physics

This chapter opens with the notion of stable interaction in quantum systems, somewhat different from classical systems. It is shown that an unstable classical system can become stable when treated ... More


Interpreting Extraordinary QM

Laura Ruetsche

in Interpreting Quantum Theories

Published in print:
2011
Published Online:
September 2011
ISBN:
9780199535408
eISBN:
9780191728525
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199535408.003.0008
Subject:
Philosophy, Philosophy of Science

This chapter argues that, due to the circumstances described in Chapter 7, techniques developed for interpreting ordinary QM lack straightforward extension to the interpretation of QM∞. These ... More


Abstraction and Idealisation: Understanding via Models

Margaret Morrison

in Reconstructing Reality: Models, Mathematics, and Simulations

Published in print:
2015
Published Online:
January 2015
ISBN:
9780199380275
eISBN:
9780199380299
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199380275.003.0002
Subject:
Philosophy, Philosophy of Science, General

It is commonly thought that the greater the degree of abstraction used in describing phenomena, the less understanding we have with respect to their concrete features. As a result, it is often ... More


QM∞

Laura Ruetsche

in Physical Theory: Method and Interpretation

Published in print:
2014
Published Online:
October 2014
ISBN:
9780195145649
eISBN:
9780199396740
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780195145649.003.0009
Subject:
Philosophy, Philosophy of Science, General

When quantum theory is applied to systems with an infinite number of degrees of freedom, wholly new interpretative issues arise. This is due to the fact that such theories have physically ... More


The Ideal Bose Gas in the Harmonic Trap

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/9780198758884.003.0010
Subject:
Physics, Condensed Matter Physics / Materials

This chapter describes the main properties of the ideal Bose gas confined by a harmonic potential. It calculates the temperature dependence of the condensate density and identify the value of the ... More


View: