Stealing the Gold A Celebration of the Pioneering Physics of Sam Edwards

, by Goldbart, Paul M.; Goldenfeld, Nigel; Sherrington, David

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ISBN: 9780198528531 | 0198528531
Cover: Hardcover
Copyright: 2/10/2005

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Over the course of nearly half a century, Sam Edwards has led the field of condensed matter physics into new directions, ranging from the electronic and statistical properties of disordered materials to the mechanical properties of granular materials. Along the way, he has provided seminal contributions to fluid mechanics, polymer science, surface science and statistical mechanics. This volume celebrates the immense scope of his influence by presenting a collection of original articles by recognized leaders in theoretical physics, including two Nobel Laureates and a Fields Medalist, which describe the genesis, evolution and future prospects of the various sub-fields of condensed matter theory, along with reprints of a selection of Edwards' seminal papers that helped give birth to the subject. Stealing the Gold, Edwards' favorite caricature of the relationship between theoretical physicists and Nature, will be of singular interest to graduate students looking for an overview of some of the most exciting areas of theoretical physics, as well as to researchers in condensed matter physics looking for a comprehensive, broad and uniquely incisive snapshot of their subject at the dawn of the 21st century.

Papers of Sir Sam Edwards reprinted, with permission, in this volume

Contributing Authors

xiii

Foreword

(2)

P.-G. de Gennes

Preface

(156)

1 Reprint: A new method for the evaluation of electric conductivity in metals

S.F. Edwards

(13)

2 Impurity diagrammatics and the physics of disordered metals

D. Khmelnitskii

(7)

References

(2)

3 Reprint: The statistical dynamics of homogeneous turbulence

S.F. Edwards

(36)

4 Sam Edwards and the turbulence theory

(20)

K.R. Sreenivasan and G.L. Eyink

4.1 Introduction

(1)

4.2 Contributions of Edwards

(6)

4.3 The white-noise passive scalar model

(4)

4.4 Navier-Stokes turbulence

(2)

4.5 Conclusion

(1)

References

(6)

5 Reprint: The statistical mechanics of polymers with excluded volume

S.F. Edwards

(13)

6 The entry of field theory into polymer science

(9)

R.C. Ball

6.1 Background

(1)

6.2 The new polymer theory, and excluded volume

100

(1)

6.3 Polymer solutions

101

(1)

6.4 Mathematical aspects

102

(2)

6.5 Future directions

104

(2)

References

106

(2)

7 Reprint: The theory of polymer solutions at intermediate concentration

S.F. Edwards

108

(17)

8 The coarse grained approach in polymer physics

125

(19)

Y. Oono and T. Ohta

8.1 Introduction

125

(1)

8.2 Edwards model and cutoff

125

(2)

8.3 Edwards goes beyond dilute solutions

127

(4)

8.4 Semidilute solutions

131

(3)

8.5 Block copolymer melts

134

(5)

8.6 Some reflections on models

139

(3)

References

142

(2)

9 Reprint: Statistical mechanics with topological constraints: II

S.F. Edwards

144

(15)

10 Notes on 'Statistical mechanics with topological constraints: I & II'

159

(5)

E. Witten

References

162

(2)

11 Reprint: Theory of spin glasses

S.F. Edwards and P.W. Anderson

164

(11)

12 Remarks on the Edwards-Anderson paper

175

(4)

P.W. Anderson

References

177

(2)

13 Edwards-Anderson: Opening up the world of complexity

179

(13)

D. Sherrington

13.1 Introduction

179

(2)

13.2 Edwards-Anderson spin glass and beyond

181

(7)

13.2.1 Edwards-Anderson

181

(1)

13.2.2 Exactly soluble model

181

(2)

13.2.3 Beyond spin glasses

183

(2)

13.2.4 Dynamics

185

(2)

13.2.5 Edwards-Anderson again

187

(1)

13.2.6 Mathematics

188

(1)

13.3 Concluding Remarks

188

(1)

References

189

(3)

14 The overlap in glassy systems

192

(20)

G. Parisi

14.1 Introduction

192

(1)

14.2 The original definition of the overlap

193

(5)

14.2.1 Only one state

193

(2)

14.2.2 Many states

195

(2)

14.2.3 A soluble model

197

(1)

14.3 The thermodynamic definition of the overlap

198

(1)

14.4 The two susceptibilities

199

(3)

14.5 Virtual probabilities

202

(5)

14.5.1 General considerations

202

(1)

14.5.2 A first attempt

202

(1)

14.5.3 Generalized susceptibilities

203

(2)

14.5.4 Local overlap

205

(2)

14.6 Fluctuation-dissipation relations

207

(2)

14.6.1 The global fluctuation-dissipation relations

207

(1)

14.6.2 The local fluctuation-dissipation relations

208

(1)

14.7 Conclusions

209

(1)

References

210

(2)

15 Theory of random solid states

212

(25)

M. Mézard

15.1 A few landmarks

212

(9)

15.1.1 Structural glasses

212

(2)

15.1.2 From rubber to spin glass and proteins

214

(2)

15.1.3 Networks of interacting individuals: global equilibrium

216

(3)

15.1.4 Networks of interacting individuals: dynamics

219

(2)

15.2 Tools and concepts

221

(8)

15.2.1 Statistical description

221

(2)

15.2.2 Physics without symmetry: equilibrium

223

(1)

15.2.3 Replicas

224

(3)

15.2.4 Physics without symmetry: dynamics

227

(2)

15.2.5 Simulations

229

(1)

15.3 Directions

229

(6)

15.3.1 Physical glasses

230

(1)

15.3.2 Random systems

231

(1)

15.3.3 The unreasonable inefficiency of mathematics

232

(1)

15.3.4 Consilience

233

(2)

References

235

(2)

16 Reprint: The theory of rubber elasticity

R.T. Deam and S.F. Edwards

237

(38)

17 Sam Edwards and the statistical mechanics of rubber

275

(25)

P.M. Goldbart and N. Goldenfeld

17.1 Introduction

275

(5)

17.2 Edwards' formulation of the statistical mechanics of vulcanized macromolecular systems

280

(7)

17.2.1 Idealized model

280

(2)

17.2.2 Quenched disorder: treating the cross-links statistically

282

(1)

17.2.3 Handling the quenched disorder via replicas

282

(2)

17.2.4 Modelling the statistics of the cross-links

284

(2)

17.2.5 Effective pure theory of coupled replicas

286

(1)

17.3 Predictions of the Deam-Edwards theory

287

(1)

17.4 Nature of the vulcanization transition

288

(3)

17.5 The emergent amorphous solid state

291

(4)

17.5.1 Microscopic character

291

(2)

17.5.2 Macroscopic character

293

(1)

17.5.3 Goldstone fluctuations; low dimensions

294

(1)

17.6 Ongoing directions: Dynamics at the liquid to solid transition

295

(1)

17.7 Concluding remarks

296

(1)

References

297

(3)

18 Reprint: Dynamics of concentrated polymer systems Part 2.-Molecular motion under flow

M. Doi and S.F. Edwards

300

(18)

19 The Doi-Edwards theory

318

(10)

W.W. Graessley and T.C.B. McLeish

References

326

(2)

20 Reprint: The surface statistics of a granular aggregate

S.F. Edwards and D.R. Wilkinson

328

(16)

21 The surface statistics of a growing aggregate

344

(19)

M. Kardar

21.1 The Edwards-Wilkinson equation

344

(3)

21.1.1 Derivation

344

(1)

21.1.2 Results

345

(1)

21.1.3 Numerical simulations

346

(1)

21.2 The Kardar-Parisi-Zhang equation

347

(5)

21.2.1 Derivation

347

(2)

21.2.2 Scaling behaviour in one dimension

349

(1)

21.2.3 Conservative growth

350

(1)

21.2.4 Experiments

351

(1)

21.3 Directed paths in random media

352

(7)

21.3.1 The Cole-Hopf transformation

352

(2)

21.3.2 Directed polymers

354

(1)

21.3.3 The replica approach

355

(2)

21.3.4 Many directed polymers

357

(2)

21.4 Perspectives

359

(2)

21.4.1 Sequence alignment

359

(1)

21.4.2 Textural growth

360

(1)

References

361

(2)

22 Reprint: Theory of powders

S.F. Edwards and R.B.S. Oakeshott

363

(12)

23 Building a thermodynamics on sand

375

(16)

J. Kurchan

23.1 Introduction

375

(2)

23.2 Compact granular matter is an athermal glass. 'Granularizing' simple glass models

377

(1)

23.3 The assumption

378

(1)

23.4 Caveat I. Flat distributions are not generic out of equilibrium

378

(1)

23.5 Caveat II. Convection currents, shear bands, inhomogeneities, insufficient relaxation

379

(1)

23.6 Encouraging news from the analytic front

380

(11)

23.6.1 Closure approximations

380

(3)

23.6.2 The athermal situation

383

(1)

23.6.3 Intrinsic limitations of the approach

384

(1)

23.7 Towards realistic models and experiment

384

(1)

23.7.1 Effective temperatures

385

(1)

23.7.2 Tests of the flat measure hypothesis

385

(1)

23.8 Inherent structures

386

(1)

23.9 Counter-examples

387

(1)

23.10 Conclusions

388

(1)

References

388

(3)

24 Reprint: The transmission of stress in an aggregate

S.F. Edwards and R.B.S. Oakeshott

391

(6)

25 Granular media: Three seminal ideas of Sir Sam

397

(20)

J.-P. Bouchaud and M. E. Cates

25.1 Introduction

397

(2)

25.2 Statistical mechanics of granular matter

399

(4)

25.2.1 Force chains and arching granular assemblies

399

(1)

25.2.2 Marginal coordination of granular packings

400

(1)

25.2.3 Thermodynamics without temperature: the Edwards ensemble

401

(2)

25.3 Some related developments

403

(8)

25.3.1 The discrete scalar model

404

(2)

25.3.2 Continuum closure schemes for granular stresses

406

(4)

25.3.3 Slow compaction and dynamics

410

(1)

25.4 Concluding remarks

411

(1)

References

412

(5)

Chapters on the Edwardsian approach to research

417

(20)

26 The case for Edwardsian research in solid mechanics: A sermon

419

(9)

J.S. Langer

References

426

(2)

27 A scientist for all seasons

428

(9)

G. Allen

Editors' acknowledgements

437

(2)

Index

439

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Stealing the Gold A Celebration of the Pioneering Physics of Sam Edwards

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