Critical Dynamics ：A Field Theory Approach to Equilibrium and Non-Equilibrium Scaling Behavior

Publication subTitle ：A Field Theory Approach to Equilibrium and Non-Equilibrium Scaling Behavior

Author： Uwe C. Täuber

Publisher： Cambridge University Press‎

Publication year： 2014

E-ISBN: 9781139698481

P-ISBN(Paperback): 9780521842235

Subject： O414.21 statistical theory

Keyword：物理学

Language： ENG

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Critical Dynamics

Description

Introducing a unified framework for describing and understanding complex interacting systems common in physics, chemistry, biology, ecology, and the social sciences, this comprehensive overview of dynamic critical phenomena covers the description of systems at thermal equilibrium, quantum systems, and non-equilibrium systems. Powerful mathematical techniques for dealing with complex dynamic systems are carefully introduced, including field-theoretic tools and the perturbative dynamical renormalization group approach, rapidly building up a mathematical toolbox of relevant skills. Heuristic and qualitative arguments outlining the essential theory behind each type of system are introduced at the start of each chapter, alongside real-world numerical and experimental data, firmly linking new mathematical techniques to their practical applications. Each chapter is supported by carefully tailored problems for solution, and comprehensive suggestions for further reading, making this an excellent introduction to critical dynamics for graduate students and researchers across many disciplines within physical and life sciences.

Chapter

Part I Near-equilibrium critical dynamics

Introduction

1 Equilibrium critical phenomena

1.1 Mean-field theory

1.2 Landau–Ginzburg theory

1.3 Scaling theory

1.4 Momentum shell renormalization group

1.5 Appendix: Functional derivatives and integration

Problems

2 Stochastic dynamics

2.1 Dynamic response and correlation functions

2.2 Stochastic processes

2.3 Three examples

2.4 Langevin equations

Problems

3 Dynamic scaling

3.1 Dynamic scaling hypothesis

3.2 Continuum theory: relaxational models

3.3 Conserved quantities and reversible mode couplings

Problems

4 Dynamic perturbation theory

4.1 Response field formalism

4.2 Relaxational dynamics: systematic perturbation theory

4.3 Feynman diagrams

4.4 Vertex functions

4.5 Appendix: discretization, Jacobian, and response loops

Problems

5 Dynamic renormalization group

5.1 Primitive divergences and scaling dimensions

5.2 Renormalization via dimensional regularization

5.3 Renormalization group and dimensional expansion

5.4 Broken rotational symmetry and Goldstone modes

5.5 Appendix: integrals in dimensional regularization

Problems

6 Hydrodynamic modes and reversible mode couplings

6.1 Coupling to a conserved scalar field

6.2 Reversible mode couplings in isotropic ferromagnets

6.3 The O(n)-symmetric Sasvári–Schwabl–Szépfalusy model

6.4 Critical dynamics of binary fluids

Problems

7 Phase transitions in quantum systems

7.1 Coherent-state path integrals

7.2 Boson superfluids

7.3 Quantum critical phenomena

7.4 Quantum antiferromagnets

7.5 Appendix: Matsubara frequency sums

Problems

Part II Scale invariance in non-equilibrium systems

Introduction

8 Non-equilibrium critical dynamics

8.1 Non-equilibrium critical relaxation and 'aging'

8.2 Coarsening and phase ordering

8.3 Effects of violating the detailed balance conditions

8.4 Non-equilibrium work and fluctuation theorems

8.5 Appendix: general Gaussian fluctuations

Problems

9 Reaction-diffusion systems

9.1 Rate equations and scaling theory

9.2 Field theory for stochastic interacting particle systems

9.3 Diffusion-limited annihilation: depletion zones

9.4 Pair annihilation of distinct particle species

9.5 Fluctuation effects in two-species binary reactions

Problems

10 Active to absorbing state transitions

10.1 The directed percolation universality class

10.2 DP variants and other percolation processes

10.3 Branching and annihilating random walks

Problems

11 Driven diffusive systems and growing interfaces

11.1 Driven diffusive systems

11.2 Critical dynamics of driven Ising lattice gases

11.3 Driven interfaces and the KPZ equation

11.4 Renormalization group analysis of the KPZ equation

Problems

Index

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