Ginzburg–Landau Theory of Condensates: Thermodynamics, Dynamics and Formation of Topological Matter

Front matter
Copyright
Contents
Preface
1 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
	1.4 Bibliographic Notes
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
		2.4 More Complicated Symmetry Breaking Patterns
		2.5 Bibliographic Notes
	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
		3.4 Bibliographic Notes
	*4 Topological Characterization of Solitons
		4.1 Type I Solitons: Core as a Topological Defect
		4.2 Coreless (Type II) Topological Solitons
		4.3 Generalizations
		4.4 Bibliographical Notes
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
		5.4 Bibliographic Notes
	6 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
		6.4 Bibliographic Notes
	7 Structure and Magnetization of the Vortex Lattice within London Approximation
		7.1 Formation of the Vortex Lattice
		7.2 Symmetry and Thermodynamics of Vortex Lattice
		7.3 Sparse and Intermediate Density Vortex Lattice
		7.4 Bibliographic Notes
	*8 Structure and Magnetization of the Vortex Lattice within Abrikosov Approximation
		8.1 Dense Topological Matter 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 Hc2
		8.5 Bibliographic Notes
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 Linear Stability Analysis and Linear Waves
		9.2 Waves in Homogeneous Condensates
		9.3 Bibliographic Notes
	10 Stability and the Excitation Spectrum of the Single Soliton and the Vortex Lattice
		10.1 Spectrum of Excitations of a Single Topological Soliton
		*10.2 The Vortex Lattice Magnetophonons at Intermediate Densities
		*10.3 Dense Lattice and Supersoft Goldstone Modes
		10.4 Bibliographic Notes
	11 Forces on Solitons, Pinning, and Elasticity of the Vortex Matter
		11.1 External Force on a Single Soliton
		11.2 Elastic Moduli of the Vortex Lattice
		11.3 Elasticity of Fields within the Abrikosov Approximation
		11.4 Bibliographic Notes
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
		12.3 Bibliographic Notes
	13 Solitary Waves
		13.1 Solitary Waves in the GL Model
		13.2 Viscosity of the Moving Vortex
		13.3 Bibliographic Notes
	*14 Viscous Flow of the Abrikosov Flux Lattice
		14.1 Time-Dependent GL Equations in the Presence of an Electromagnetic Field
		14.2 Structure and I-V Characteristics of the Dense Moving Lattice
		14.3 The Resistivity of the Flux Flow State
		14.4 Bibliographic Notes
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
		15.5 Bibliographic Notes
	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
		16.4 Bibliographic Notes
	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
		17.4 Bibliographic Notes
Appendix
	A.1 Abrikosov Quasimomentum Functions Averages
	A.2 Calculation of Gaussian Integrals
	A.3 Sparse Matrices and Their Determinants
Index