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Defects and Geometry in Condensed Matter Physics - David R. Nelson

Defects and Geometry in Condensed Matter Physics

Paperback Published: 7th May 2002
ISBN: 9780521004008
Number Of Pages: 392

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Thermally excited defects such as vortices, disclinations, dislocations, vacancies and interstitials play a key role in the physics of crystals, superfluids, superconductors, liquid crystals and polymer arrays. Geometrical aspects of statistical mechanics become particularly important when thermal fluctuations entangle or crumple extended line-like or surface-like objects in three dimensions. In the case of entangled vortices above the first-order flux lattice melting transition in high temperature superconductors, the lines themselves are defects. A variety of low temperature theories combined with renormalization group ideas are used to describe the delicate interplay between defects, statistical mechanics and geometry characteristic of these problems in condensed matter physics. David Nelson provides a coherent and pedagogic graduate level introduction to the field of defects and geometry.

Industry Reviews

'For 25 years, David Nelson has made major contributions to the study of how condensed matter systems as solids, liquid crystals, superfluids, and polymer solutions and melts. His dominance in the field has been reinforced by his excellent surveys in the proceedings of summer schools, workshops, and conferences from 1983 to 1996. The book provides an admirable overview of Nelson's achievements and of their relation to other work.' Physics Today
"The book provides an admirable overview of Nelson's achievements and of their relation to other works." Physics Today
"This book exposes the common grounds of several apparently disconnected problems of actual relevance in condensed matter theory. This is an ambitious goal that the book accomplishes quite successfully.... The book by Dr. Nelson will be welcomed by the scientific community, and it is certainly a necessary item in the library of any condensed matter physicist working on this and related areas." Journal of Statistical Physics
"...his excellent surveys in the proceedings of summer schools, workshops, and conferences from 1983 to 1996. Defects and Geometry in Condensed Matter Physics is primarily a compilation (of Nelson's surveys)....It is valuable to have all these contributions collected in one volume." Physics Today

Preface to the bookp. xi
Acknowledgementsp. xiii
Fluctuations, renormalization and universalityp. 1
Fluctuations and universality in condensed matter physicsp. 2
The universal Prandtl number in two-dimensional hydrodynamicsp. 5
The universal Poisson ratio in fluctuating polymerized membranesp. 8
Defect-mediated phase transitions and hydrodynamic theoriesp. 12
The contents of this bookp. 18
Renormalizationp. 21
The self-dual point of Ising spins in two dimensionsp. 26
Referencesp. 28
Defect-mediated phase transitionsp. 30
Prefacep. 30
Introductionp. 31
The XY model and superfluidity in two dimensionsp. 41
Dynamic scaling and third sound in helium filmsp. 60
Statistical mechanics of two-dimensional meltingp. 68
Melting dynamicsp. 91
Anisotropic meltingp. 99
Line singularities in three dimensionsp. 106
Referencesp. 117
Order, frustration and two-dimensional glassp. 124
Prefacep. 124
Introductionp. 126
Order and frustration in quenched binary arraysp. 129
Order and frustration in spaces of incommensurate curvaturep. 136
Referencesp. 144
The structure and statistical mechanics of three-dimensional glassp. 146
Prefacep. 146
A physical picturep. 147
The model free energyp. 154
Referencesp. 163
The statistical mechanics of crumpled membranesp. 165
Prefacep. 165
Flat surfacesp. 166
Crumpled membranesp. 170
Normal-normal correlations in liquid membranesp. 179
Tethered surfaces with bending energyp. 181
Defects and hexatic order in membranesp. 186
Referencesp. 191
Defects in superfluids, superconductors and membranesp. 194
Prefacep. 194
Introductionp. 195
Two-dimensional superfluids and superconductorsp. 198
Defects in membranes and monolayersp. 217
Superfluid density and momentum correlationsp. 238
Referencesp. 241
Vortex-line fluctuations in superconductors from elementary quantum mechanicsp. 245
Prefacep. 245
Introductionp. 246
Correlated pinning and quantum bound statesp. 249
Flux melting and the quantum harmonic oscillatorp. 258
Vortex entanglement in the liquid phasep. 261
The transfer-matrix representation of the partition functionp. 266
Vortex probability distributionsp. 267
Referencesp. 269
Correlations and transport in vortex liquidsp. 271
Prefacep. 271
Introductionp. 272
Statistical mechanics of flexible linesp. 285
Correlations in flux liquids with weak disorderp. 301
Dynamics near the irreversibility linep. 311
Referencesp. 316
Statistical mechanics of directed polymersp. 322
Prefacep. 322
Introductionp. 323
One polymer in a nematic solventp. 327
A model of polymer nematicsp. 332
Mapping onto boson quantum mechanicsp. 335
Correlations in polymer nematics with soft broken symmetryp. 341
The hydrodynamic treatment of line liquidsp. 344
Defects in hexagonal columnar crystalsp. 347
Referencesp. 361
Indexp. 365
Table of Contents provided by Syndetics. All Rights Reserved.

ISBN: 9780521004008
ISBN-10: 0521004004
Audience: Professional
Format: Paperback
Language: English
Number Of Pages: 392
Published: 7th May 2002
Publisher: Cambridge University Press
Country of Publication: GB
Dimensions (cm): 24.7 x 17.6  x 2.0
Weight (kg): 0.82