## 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