Defects and Geometry in Condensed Matter Physics

Defects and Geometry in Condensed Matter Physics

by David R. Nelson
     
 

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ISBN-10: 0521004004

ISBN-13: 9780521004008

Pub. Date: 04/28/2010

Publisher: Cambridge University Press

Defects and geometrical patterns embedded in orderly arrays of atoms and molecules explain important everyday phenomena such as why soap is slippery, why steel is strong, and how a liquid crystal display device works. An understanding of how to pin vortex defects in superconductors is essential for applications such as magnetic levitation and improved magnetic

Overview

Defects and geometrical patterns embedded in orderly arrays of atoms and molecules explain important everyday phenomena such as why soap is slippery, why steel is strong, and how a liquid crystal display device works. An understanding of how to pin vortex defects in superconductors is essential for applications such as magnetic levitation and improved magnetic resonance imaging devised for medical diagnosis. This book discusses the crucial role played by defects and geometry in disrupting order in solids, superconductors, superfluids, liquid crystals and polymers.

Product Details

ISBN-13:
9780521004008
Publisher:
Cambridge University Press
Publication date:
04/28/2010
Edition description:
New Edition
Pages:
392
Product dimensions:
6.85(w) x 9.72(h) x 0.79(d)

Table of Contents

Preface to the bookxi
Acknowledgementsxiii
1Fluctuations, renormalization and universality1
1.1Fluctuations and universality in condensed matter physics2
1.2The universal Prandtl number in two-dimensional hydrodynamics5
1.3The universal Poisson ratio in fluctuating polymerized membranes8
1.4Defect-mediated phase transitions and hydrodynamic theories12
1.5The contents of this book18
Appendix ARenormalization21
Appendix BThe self-dual point of Ising spins in two dimensions26
References28
2Defect-mediated phase transitions30
Preface30
2.1Introduction31
2.2The XY model and superfluidity in two dimensions41
2.3Dynamic scaling and third sound in helium films60
2.4Statistical mechanics of two-dimensional melting68
2.5Melting dynamics91
2.6Anisotropic melting99
2.7Line singularities in three dimensions106
References117
3Order, frustration and two-dimensional glass124
Preface124
3.1Introduction126
3.2Order and frustration in quenched binary arrays129
3.3Order and frustration in spaces of incommensurate curvature136
References144
4The structure and statistical mechanics of three-dimensional glass146
Preface146
4.1A physical picture147
4.2The model free energy154
References163
5The statistical mechanics of crumpled membranes165
Preface165
5.1Flat surfaces166
5.2Crumpled membranes170
5.3Normal-normal correlations in liquid membranes179
5.4Tethered surfaces with bending energy181
5.5Defects and hexatic order in membranes186
References191
6Defects in superfluids, superconductors and membranes194
Preface194
6.1Introduction195
6.2Two-dimensional superfluids and superconductors198
6.3Defects in membranes and monolayers217
Appendix ASuperfluid density and momentum correlations238
References241
7Vortex-line fluctuations in superconductors from elementary quantum mechanics245
Preface245
7.1Introduction246
7.2Correlated pinning and quantum bound states249
7.3Flux melting and the quantum harmonic oscillator258
7.4Vortex entanglement in the liquid phase261
Appendix AThe transfer-matrix representation of the partition function266
Appendix BVortex probability distributions267
References269
8Correlations and transport in vortex liquids271
Preface271
8.1Introduction272
8.2Statistical mechanics of flexible lines285
8.3Correlations in flux liquids with weak disorder301
8.4Dynamics near the irreversibility line311
References316
9Statistical mechanics of directed polymers322
Preface322
9.1Introduction323
9.2One polymer in a nematic solvent327
9.3A model of polymer nematics332
9.4Mapping onto boson quantum mechanics335
9.5Correlations in polymer nematics with soft broken symmetry341
9.6The hydrodynamic treatment of line liquids344
9.7Defects in hexagonal columnar crystals347
References361
Index365

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