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ОбложкаTäuber U.C. Critical dynamics: a field theory approach to equilibrium and non-equilibrium scaling behavior. - Cambridge; New York: Cambridge university press, 2014. - xvi, 511 p.: ill. - Incl. bibl. ref. - Ind.: p.499-511. - ISBN 978-0-521-84223-5
Шифр: (И/В31-T24) 02
 

Место хранения: 02 | Отделение ГПНТБ СО РАН | Новосибирск

Оглавление / Contents
 
Preface ........................................................ xi

Part I  Near-equilibrium critical dynamics
Introduction .................................................... 3
1  Equilibrium critical phenomena ............................... 5
   1.1  Mean-field theory ....................................... 6
   1.2  Landau-Ginzburg theory ................................. 16
   1.3  Scaling theory ......................................... 23
   1.4  Momentum shell renormalization group ................... 28
   1.5  Appendix: Functional derivatives and integration ....... 39
   Problems .................................................... 41
2  Stochastic dynamics ......................................... 45
   2.1  Dynamic response and correlation functions ............. 46
   2.2  Stochastic processes ................................... 56
   2.3  Three examples ......................................... 67
   2.4  Langevin equations ..................................... 77
   Problems .................................................... 92
3  Dynamic scaling ............................................. 96
   3.1  Dynamic scaling hypothesis ............................. 97
   3.2  Continuum theory:relaxational models .................. 101
   3.3  Conserved quantities and reversible mode couplings .... 112
   Problems ................................................... 126
4  Dynamic perturbation theory ................................ 130
   4.1  Response field formalism .............................. 131
   4.2  Relaxational dynamics: systematic perturbation
        theory ................................................ 135
   4.3  Feynman diagrams ...................................... 142
   4.4  Vertex functions ...................................... 153
   4.5  Appendix: discretization, Jacobian, and response
        loops ................................................. 167
   Problems ................................................... 168
5  Dynamic renormalization group .............................. 171
   5.1  Primitive divergences and scaling dimensions .......... 172
   5.2  Renormalization via dimensional regularization ........ 177
   5.3  Renormalization group and dimensional expansion ....... 185
   5.4  Broken rotational symmetry and Goldstone modes ........ 193
   5.5  Appendix: integrals in dimensional regularization ..... 202
   Problems ................................................... 204
6  Hydrodynamic modes and reversible mode couplings ........... 207
   6.1  Coupling to a conserved scalar field .................. 208
   6.2  Reversible mode couplings in isotropic ferromagnets ... 217
   6.3  The O(n)-symmetric Sasvári-Schwabl-Szépfalusy model ... 226
   6.4  Critical dynamics of binary fluids .................... 238
   Problems ................................................... 246
7  Phase transitions in quantum systems ....................... 251
   7.1  Coherent-state path integrals ......................... 252
   7.2  Boson superfluids ..................................... 266
   7.3  Quantum critical phenomena ............................ 283
   7.4  Quantum antiferromagnets .............................. 290
   7.5  Appendix: Matsubara frequency sums .................... 301
   Problems ................................................... 301
Part II Scale invariance in non-equilibrium systems
Introduction .................................................. 307
8  Non-equilibrium critical dynamics .......................... 309
   8.1  Non-equilibrium critical relaxation and 'aging' ....... 310
   8.2  Coarsening and phase ordering ......................... 319
   8.3  Effects of violating the detailed balance conditions .. 329
   8.4  Non-equilibrium work and fluctuation theorems ......... 336
   8.5  Appendix: general Gaussian fluctuations ............... 339
   Problems ................................................... 341
9  Reaction-diffusion systems ................................. 345
   9.1  Rate equations and scaling theory ..................... 346
   9.2  Field theory for stochastic interacting particle
        systems ............................................... 355
   9.3  Diffusion-limited annihilation: depletion zones ....... 367
   9.4  Pair annihilation of distinct particle species ........ 376
   9.5  Fluctuation effects in two-species binary reactions ... 382
   Problems ................................................... 394
10 Active to absorbing state transitions ...................... 400
   10.1 The directed percolation universality class ........... 401
   10.2 DP variants and other percolation processes ........... 412
   10.3 Branching and annihilating random walks ............... 426
   Problems ................................................... 437
11 Driven diffusive systems and growing interfaces ............ 443
   11.1 Driven diffusive systems .............................. 444
   11.2 Critical dynamics of driven Ising lattice gases ....... 456
   11.3 Driven interfaces and the KPZ equation ................ 469
   11.4 Renormalization group analysis of the KPZ equation .... 479

Problems ...................................................... 492
Index ......................................................... 499

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