导语

  

内容提要

  

    由巴鲁赫·儒森斯坦、李定平编著的《量子凝聚体及其拓扑物态的Ginzbury-Landau理论(英文版)》从Ginzburg－Landau理论出发，讨论了电磁场中的第二类超导体的热力学。运用对于刻画正常相变线的参数的展开，导出了Abrikosov磁通格子解。本书在细节上确定了磁场中的涡旋物质的相图。在存在介观尺度显著热涨落的情况下，涡旋晶体融化成涡旋液体。运用最低朗道能级近似，本书给出了热涨落的定量理论，这使得确定融化线、融化中的不连续现象以及涡旋液态的一些重要性质成为可能。在存在淬致无序的情况下，涡旋物质会获得某些玻璃样的性质。本书还运用“replica”方法研究了不可逆线和涡旋玻璃态的静态性质。本书详细介绍了大部分解析方法。各种定量和定性的结果都和第二类超导体的实验结果做了对比。

Introduction and Overview
    1.1  Major phenomena, concepts and their historical development
    1.2  Solitons and topological matter
    1.3  How to use this book
Part I  Ordered Phases of Condensed Matter Disrupted by Topological Defects
  2  The Phenomenological (Landau) Description of the Ordered Condensed Matter from Magnets to Bose Condensates
    2.1  Energetics of the spontaneous ordering
    2.2  How do inhomogeneities, fluctuations and external fields affect the condensate?
    2.3  The order parameter field equations and their boundary conditions
  3  Simplest Topological Defects
    3.1  Domain wall in the Ising universality class
    3.2  Characteristic scales and dimensionless form of the field equations
    3.3  Single vortex in a 2D XY magnet or superconductor
  *4  Topological Defects and Their Classification
    4.1  Topological analysis of the vortex and homotopy group
    4.2  Coreless (type II) topological solitons
Part II  Structure of the Topological Matter Created by Gauge Field
  5  Repulsion between Solitons and Viable Vortex Matter Created by a Gauge Field
    5.1  Interactions between the φ4 vortices, difficulty to create the soliton matter
    5.2  The order parameter coupled to a gauge field
    5.3  Two homogeneous phases of a superconductor under magnetic field and their excitations
  6  Finite Energy of Abrikosov Vortices Created by the Magnetic Field
    6.1  Negative Gibbs energy of the normal-superconducting interface in type II superconductors
    6.2  London approximation in gauge theories
    6.3  Abrikosov vortex solution
  7  Structure and Magnetization of the Vortex Lattice within London Approximation
    7.1  Multi-vortex configurations within London approximation and formation of the vortex lattice
    7.2  Vortex lattice
    7.3  Sparse and intermediate density vortex lattice, a >> ζ
  *8  Structure and Magnetization of the Vortex Lattice within Abrikosov Approximation
    8.1  Dense topological matter a << A and the lowest Landau level approximation
    8.2  Digression: symmetry in a gauge field
    8.3  Energy and magnetization of a lattice structure and current distribution in an LLL configuration
    8.4  The bifurcation point perturbation theory at He2
Part III  Excitation Modes of Condensate: Elasticity and Stability of the Topological Matter
  9  Linear Stability Analysis of the Homogeneous States
    9.1  General idea of the linear stability analysis and the linear waves
    9.2  Waves in homogeneous condensates
  10  Stability and the Excitation Spectrum of the Single Soliton and the
  Vortex Lattice
    10.1  Spectrum of excitations of single topological soliton
  *  10.2  The vortex lattice magneto-phonons at intermediate densities
  *  10.3  Dense lattice and supersoft Goldstone modes
  11  Forces on Solitons, Pinning and Elasticity of the Vortex Matter
    11.1  External force on a single soliton and pinning
    11.2  Elastic moduli of the vortex lattice
    11.3  Elasticity of fields within Abrikosov approximation
Part IV  Dynamics of Condensates and Solitary Waves
  12  Dynamics of the Order Parameter Field
    12.1  General type A dynamics
    12.2  The relaxation time and dissipation
  13  Solitary Waves
    13.1  Solitary waves in GL model
    13.2  Viscosity of the moving vortex
  *14  Viscous Flow of the Abrikosov Flux Lattice
    14.1  Time dependent GL equations in the presence of electromagnetic field
    14.2  Structure and I-V characteristics of the dense moving lattice
    14.3  The resistivity of the flux flow state
Part V  Thermal Fluctuations
  15  Statistical Physics of Mesoscopic Degrees of Freedom
    15.1  Statistical theory of thermal fluctuations of a point-like object.
    15.2  Thermal fluctuations of an extended object described by the path integral
    15.3  Mesoscopic thermal fluctuations of the order parameter field
    15.4  Gaussian fluctuations effects in a homogeneous condensate: activation of harmonic excitations
  16  The Landau-Wilson Approach to Statistical Physics of the Interacting Field Fluctuations
    16.1  Perturbative approach to the "interacting" thermal fluctuations in the disordered phase
    16.2  Perturbation theory in the broken symmetry phase
    *16.3  Beyond perturbation theory: gaussian variational approximation ~
  17  Thermal Fluctuations in the Vortex Matter
    17.1  Elastic theory of the vortex lattice softening and melting
    17.2  Thermal fluctuations of the order parameter and magnetic field in GL theory
    *17.3  Basic properties of the vortex liquid and the melting line at high magnetic fields
Appendix
  1  Abrikosov quasi-momentum functions averages
  2  Calculation of gaussian integrals
  3  Sparse matrices and their determinants
General References