24小时热门版块排行榜

返回列表

【奖励】本帖被评价18次，作者pkusiyuan增加金币 14.4 个

pkusiyuan

银虫 (正式写手)

应助: 0 (幼儿园)
金币: 15204.9
帖子: 773
在线: 130小时
虫号: 3451204

[资源] Statistical Physics of Liquids at Freezing and Beyond

Preface page xiii
Acknowledgements xvi
1 Statistical physics of liquids 1
1.1 Basic statistical mechanics 3
1.1.1 Thermodynamic functions 3
1.1.2 The classical N-particle system 6
1.1.3 The BBGKY hierarchy equations 7
1.1.4 The Boltzmann equation 9
1.2 Equilibrium properties 11
1.2.1 The Gibbs H-theorem 12
1.2.2 The equilibrium ensembles 14
1.2.3 The static structure factor 19
1.2.4 Integral equations for g(r) 24
1.3 Time correlation functions 36
1.3.1 The density correlation function 38
1.3.2 The self-correlation function 41
1.3.3 The linear response function 47
1.4 Brownian motion 50
1.4.1 The Langevin equation 50
1.4.2 The Stokes–Einstein relation 53
Appendix to Chapter 1 55
A1.1 The Gibbs inequality 55
A1.2 The force–force correlation 55
A1.3 Brownian motion 56
A1.3.1 The noise correlation 56
A1.3.2 Evaluation of the integrals 57
2 The freezing transition 58
2.1 The density-functional approach 58
2.1.1 A thermodynamic extremum principle 60
vii
viii Contents
2.1.2 An approximate free-energy functional 64
2.1.3 The Ramakrishnan–Yussouff model 68
2.2 Weighted density functionals 72
2.2.1 The modified weighted-density approximation 75
2.2.2 Gaussian density profiles 76
2.2.3 The hard-sphere system 78
2.3 Fundamental measure theory 85
2.3.1 Density-independent weight functions 86
2.3.2 The free-energy functional 88
2.4 Applications to other systems 90
2.4.1 Long-range interaction potentials 91
2.4.2 The solid–liquid interface 99
Appendix to Chapter 2 105
A2.1 Correlation functions for the inhomogeneous solid 105
A2.2 The Ramakrishnan–Yussouff model 106
A2.3 The weighted-density-functional approximation 109
A2.4 The modified weighted-density-functional approximation 113
A2.5 The Gaussian density profiles and phonon model 115
3 Crystal nucleation 117
3.1 Classical nucleation theory 117
3.1.1 The free-energy barrier 118
3.1.2 The nucleation rate 121
3.1.3 Heterogeneous nucleation 129
3.2 A simple nonclassical model 131
3.2.1 The critical nucleus 133
3.2.2 The free-energy barrier 134
3.3 The density-functional approach 137
3.3.1 The square-gradient approximation 137
3.3.2 The critical nucleus 141
3.3.3 The weighted-density-functional approach 145
3.4 Computer-simulation studies 150
3.4.1 Comparisons with CNT predictions 152
3.4.2 The structure of the nucleus 155
Appendix to Chapter 3 160
A3.1 The schematic model for nucleation 160
A3.1.1 Critical nucleus 160
A3.1.2 The free-energy barrier 161
A3.2 The excess free energy in the DFT model 162
4 The supercooled liquid 164
4.1 The liquid–glass transition 164
4.1.1 Characteristic temperatures of the glassy state 165
Contents ix
4.1.2 The free-volume model 170
4.1.3 Self-diffusion and the Stokes–Einstein relation 171
4.2 Glass formation vs. crystallization 175
4.2.1 The minimum cooling rate 176
4.2.2 The kinetic spinodal and the Kauzmann paradox 177
4.3 The landscape paradigm 181
4.3.1 The potential-energy landscape 182
4.3.2 The free-energy landscape 188
4.4 Dynamical heterogeneities 192
4.4.1 Computer-simulation results 193
4.4.2 Dynamic length scales 198
5 Dynamics of collective modes 204
5.1 Conservation laws and dissipation 205
5.1.1 The microscopic balance equations 205
5.1.2 Euler equations of hydrodynamics 207
5.1.3 Dissipative equations of hydrodynamics 209
5.1.4 Tagged-particle dynamics 211
5.1.5 Two-component systems 212
5.2 Hydrodynamic correlation functions 215
5.2.1 Self-diffusion 217
5.2.2 Transport coefficients 218
5.3 Linear fluctuating hydrodynamics 225
5.3.1 The generalized Langevin equation 225
5.3.2 The liquid-state dynamics 236
5.4 Hydrodynamics of a solid 246
Appendix to Chapter 5 260
A5.1 The microscopic-balance equations 260
A5.1.1 The Euler equations 263
A5.1.2 The entropy-production rate 264
A5.2 The second fluctuation–dissipation relation 269
6 Nonlinear fluctuating hydrodynamics 271
6.1 Nonlinear Langevin equations 271
6.1.1 Coupling of collective modes 271
6.1.2 Nonlinear Langevin equations 274
6.2 The compressible liquid 287
6.2.1 The one-component fluid 287
6.2.2 The nonlinear diffusion equation 293
6.2.3 A two-component fluid 295
6.2.4 The solid state 300
6.3 Stochastic balance equations 303
6.3.1 Smoluchowski dynamics 303
x Contents
6.3.2 Fokker–Planck dynamics 308
Appendix to Chapter 6 310
A6.1 The coarse-grained free energy 310
7 Renormalization of the dynamics 318
7.1 The Martin–Siggia–Rose theory 319
7.1.1 The MSR action functional 320
7.2 The compressible liquid 327
7.2.1 MSR theory for a compressible liquid 328
7.2.2 Correlation and response functions 330
7.3 Renormalization 334
7.3.1 Fluctuation–dissipation relations 335
7.3.2 Nonperturbative results 339
7.3.3 One-loop renormalization 343
Appendix to Chapter 7 348
A7.1 The Jacobian of MSR fields 350
A7.2 The MSR field theory 351
A7.3 Invariance of the MSR action 355
A7.4 The memory-function approach 357
A7.4.1 The projection-operator method 358
A7.4.2 The mode-coupling approximation 361
8 The ergodic–nonergodic transition 363
8.1 Mode-coupling theory 363
8.1.1 The schematic model 365
8.1.2 Effects of structure on dynamics 369
8.1.3 Tagged-particle dynamics 376
8.1.4 Dynamical heterogeneities and MCT 383
8.1.5 Linking DFT with MCT 388
8.1.6 Dynamic density-functional theory 391
8.2 Evidence from experiments 400
8.2.1 Testing with schematic MCT 400
8.2.2 Glass transition in colloids 406
8.2.3 Molecular-dynamics simulations 407
8.2.4 Discussion 409
8.3 Ergodicity-restoring mechanisms 411
8.3.1 Ergodic behavior in the NFH model 412
8.3.2 The hydrodynamic limit 414
8.3.3 Numerical solution of NFH equations 417
8.4 Spin-glass models 419
8.4.1 The p-spin interaction model 420
8.4.2 MCT and mean-field theories 426
Contents xi
Appendix to Chapter 8 430
A8.1 Calculation of the spring constant 430
A8.2 Field-theoretic treatment of the DDFT model 432
A8.3 The one-loop result for ˆv ˆv(0, 0) 442
9 The nonequilibrium dynamics 443
9.1 The nonequilibrium state 443
9.1.1 A generalized fluctuation–dissipation relation 443
9.1.2 Computer-simulation studies 444
9.2 The effective temperature 449
9.2.1 The phenomenological approach 451
9.2.2 A simple thermometer 451
9.3 A mean-field model 456
9.3.1 The mode-coupling approximation 459
9.3.2 The FDT regime 460
9.3.3 The aging regime 465
9.3.4 Quasi-ergodic behavior 469
9.4 Glassy aging dynamics 471
9.4.1 Thermalization 471
9.4.2 Aging dynamics: experiments 473
Appendix to Chapter 9 479
A9.1 The energy of the oscillator 479
A9.2 Evaluation of integrals 481
A9.2.1 Integral IR for the FDT solution 481
A9.2.2 Integrals for the aging solution 482
10 The thermodynamic transition scenario 486
10.1 The entropy crisis 486
10.1.1 The Adam–Gibbs theory 487
10.1.2 Dynamics near TK 488
10.2 First-order transitions 490
10.2.1 Metastable aperiodic structures 491
10.2.2 Random first-order transition theory 494
10.3 Self-generated disorder 498
10.3.1 Effective potential and overlap functions 498
10.3.2 A model calculation 501
10.4 Spontaneous breaking of ergodicity 505
10.4.1 The replica method for self-generated disorder 507
10.4.2 Free energy of the Replicated liquid 509
10.4.3 An example: The φ4 model 514
10.5 The amorphous solid 519
10.5.1 The Mézard–Parisi model 522
xii Contents
Appendix to Chapter 10 531
A10.1 Matrix identity 531
A10.2 Matrix identity II 532
A10.3 Computation of the vibrational contribution Iv 533
A10.4 Computation of Tr lnM∗ 536
References 540
Index 558

回复此楼

» 本帖附件资源列表

欢迎监督和反馈：小木虫仅提供交流平台，不对该内容负责。
本内容由用户自主发布，如果其内容涉及到知识产权问题，其责任在于用户本人，如对版权有异议，请联系邮箱：xiaomuchong@tal.com
附件 1 : Statistical_Physics_of_Liquids_at_Freezing_and_Beyond_-_Shankar_Prasad_Das_-_(_Cambridge_University_Press_-_2011_-_pp.586).pdf

2015-09-16 11:16:48, 4.24 M