Ginzburg-Landau theory of condensates: thermodynamics, dynamics, and formation of topological matter
Ginzburg-Landau theory is an important tool in condensed matter physics research, describing the ordered phases of condensed matter, including the dynamics, elasticity, and thermodynamics of the condensed configurations. In this systematic introduction to Ginzberg-Landau theory, both common and topo...
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2022
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| Zusammenfassung: | Ginzburg-Landau theory is an important tool in condensed matter physics research, describing the ordered phases of condensed matter, including the dynamics, elasticity, and thermodynamics of the condensed configurations. In this systematic introduction to Ginzberg-Landau theory, both common and topological excitations are considered on the same footing (including their thermodynamics and dynamical phenomena). The role of the topological versus energetic considerations is made clear. Required mathematics (symmetry, including lattice translation, topology, and perturbative techniques) are introduced as needed. The results are illustrated using arguably the most fascinating class of such systems, high Tc superconductors subject to magnetic field. This book is an important reference for both researchers and graduate students working in condensed matter physics or can act as a textbook for those taking advanced courses on these topics |
| Beschreibung: | The phenomenological (Landau) description of the ordered condensed matter from magnets to Bose condensates -- Simplest topological defects -- Topological defects and their classification -- Repulsion between solitons and viable vortex matter created by a Gauge field -- Abrikosov vortices created by the magnetic field -- Structure and magnetization of the vortex lattice within London approximation -- Structure and magnetization of the vortex lattice within Abrikosov approximation -- Linear stability analysis of the homogeneous states -- Stability and the excitation spectrum of the single soliton and the vortex lattice -- Forces on solitons, pinning and elasticity of the vortex matter -- Dynamics of the order parameter field -- Solitary waves -- Viscous flow of the Abrikosov flux lattice -- Statistical physics of mesoscopic degrees of freedom -- The Landau-Wilson approach to statistical physics of the interacting field fluctuations -- Thermal fluctuations in the vortex matter |
| Beschreibung: | x, 344 Seiten Illustrationen, Diagramme |
| ISBN: | 9781108836852 |
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| 500 | |a The phenomenological (Landau) description of the ordered condensed matter from magnets to Bose condensates -- Simplest topological defects -- Topological defects and their classification -- Repulsion between solitons and viable vortex matter created by a Gauge field -- Abrikosov vortices created by the magnetic field -- Structure and magnetization of the vortex lattice within London approximation -- Structure and magnetization of the vortex lattice within Abrikosov approximation -- Linear stability analysis of the homogeneous states -- Stability and the excitation spectrum of the single soliton and the vortex lattice -- Forces on solitons, pinning and elasticity of the vortex matter -- Dynamics of the order parameter field -- Solitary waves -- Viscous flow of the Abrikosov flux lattice -- Statistical physics of mesoscopic degrees of freedom -- The Landau-Wilson approach to statistical physics of the interacting field fluctuations -- Thermal fluctuations in the vortex matter | ||
| 520 | |a Ginzburg-Landau theory is an important tool in condensed matter physics research, describing the ordered phases of condensed matter, including the dynamics, elasticity, and thermodynamics of the condensed configurations. In this systematic introduction to Ginzberg-Landau theory, both common and topological excitations are considered on the same footing (including their thermodynamics and dynamical phenomena). The role of the topological versus energetic considerations is made clear. Required mathematics (symmetry, including lattice translation, topology, and perturbative techniques) are introduced as needed. The results are illustrated using arguably the most fascinating class of such systems, high Tc superconductors subject to magnetic field. This book is an important reference for both researchers and graduate students working in condensed matter physics or can act as a textbook for those taking advanced courses on these topics | ||
| 650 | 4 | |a Condensed matter | |
| 650 | 4 | |a Vortex-motion | |
| 650 | 4 | |a Superconductivity | |
| 650 | 4 | |a Topological defects (Physics) | |
| 650 | 4 | |a Phase transformations (Statistical physics) | |
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| 999 | |a oai:aleph.bib-bvb.de:BVB01-033580867 | ||
Datensatz im Suchindex
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| adam_text | Contents Preface 1 page ix 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 1 1 17 28 36 Part I Ordered Phases of Condensed Matter Disrupted by Topological Defects 37 2 3 The Phenomenological (Landau) Description of the Ordered Condensed Matter from Magnets to Bose Condensates 39 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 BreakingPatterns 2.5 Bibliographic Notes Simplest Topological Defects 3.1 Domain Wall in the IsingUniversality 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 Characterizationof Solitons 4.1 Type I Solitons: Core as aTopological Defect 39 47 52 59 66 67 67 75 78 83 84 84 v
Contents vi 4.2 4.3 4.4 Part II Coreless (Type II) Topological Solitons Generalizations Bibliographical Notes 90 95 100 Structure of the Topological Matter Created by Gauge Field 101 Repulsion between Solitons and Viable Vortex Matter Created by a Gauge Field 5.1 Interactions between the ф4 Vortices, Difficulty to 5 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 7 *8 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 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 103 104 109 116 120 122 122 128 132 141 142 142 147 151 159 Structure and Magnetization of the Vortex Lattice within Abrikosov Approximation 160 8.1 Dense Topological Matter and the Lowest Landau-Level Approximation 160 8.2 Digression: Symmetry in a Gauge Field 164 8.3 Energy and Magnetization of a Lattice Structure and Current Distribution in an LLL Configuration 171 8.4 The Bifurcation Point Perturbation Theory at HC2 176 8.5 Bibliographic Notes 180 Part III Excitation Modes of Condensate: Elasticity and Stability of the Topological Matter 183 9 Linear Stability Analysis of the Homogeneous States
185
Contents 9.1 9.2 9.3 General Idea of Linear Stability Analysis and Linear Waves Waves in Homogeneous Condensates Bibliographic Notes vii 185 188 194 10 Stability and the Excitation Spectrum of the Single Soliton and the Vortex Lattice 195 10.1 Spectrum of Excitations of a Single Topological Soliton 195 *10. 2 The Vortex Lattice Magnetophonons at Intermediate Densities *10. 3 Dense Lattice and Supersoft Goldstone Modes 206 10.4 Bibliographic Notes 211 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 212 212 220 224 228 229 12 Dynamics of the Order Parameter Field 12.1 General Type A Dynamics 12.2 The Relaxation Time and Dissipation 12.3 Bibliographic Notes 231 231 234 239 13 240 240 247 249 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 15 Thermal Fluctuations 250 250 257 262 266 267 Statistical Physics of Mesoscopic Degrees of Freedom 269 15.1 Statistical Theory of Thermal Fluctuations of a Point-Like Object 269 15.2 Thermal Fluctuations of an Extended Object Described by the Path Integral 279 15.3 Mesoscopic
Thermal Fluctuations of the Order Parameter Field 289 199
Contents viii 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 293 298 300 300 310 315 318 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 319 319 Appendix A.l Abrikosov Quasimomentum Functions Averages A.2 Calculation of Gaussian Integrals A.3 Sparse Matrices and Their Determinants 335 335 338 340 Index 324 330 334 342
|
| adam_txt |
Contents Preface 1 page ix 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 1 1 17 28 36 Part I Ordered Phases of Condensed Matter Disrupted by Topological Defects 37 2 3 The Phenomenological (Landau) Description of the Ordered Condensed Matter from Magnets to Bose Condensates 39 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 BreakingPatterns 2.5 Bibliographic Notes Simplest Topological Defects 3.1 Domain Wall in the IsingUniversality 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 Characterizationof Solitons 4.1 Type I Solitons: Core as aTopological Defect 39 47 52 59 66 67 67 75 78 83 84 84 v
Contents vi 4.2 4.3 4.4 Part II Coreless (Type II) Topological Solitons Generalizations Bibliographical Notes 90 95 100 Structure of the Topological Matter Created by Gauge Field 101 Repulsion between Solitons and Viable Vortex Matter Created by a Gauge Field 5.1 Interactions between the ф4 Vortices, Difficulty to 5 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 7 *8 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 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 103 104 109 116 120 122 122 128 132 141 142 142 147 151 159 Structure and Magnetization of the Vortex Lattice within Abrikosov Approximation 160 8.1 Dense Topological Matter and the Lowest Landau-Level Approximation 160 8.2 Digression: Symmetry in a Gauge Field 164 8.3 Energy and Magnetization of a Lattice Structure and Current Distribution in an LLL Configuration 171 8.4 The Bifurcation Point Perturbation Theory at HC2 176 8.5 Bibliographic Notes 180 Part III Excitation Modes of Condensate: Elasticity and Stability of the Topological Matter 183 9 Linear Stability Analysis of the Homogeneous States
185
Contents 9.1 9.2 9.3 General Idea of Linear Stability Analysis and Linear Waves Waves in Homogeneous Condensates Bibliographic Notes vii 185 188 194 10 Stability and the Excitation Spectrum of the Single Soliton and the Vortex Lattice 195 10.1 Spectrum of Excitations of a Single Topological Soliton 195 *10. 2 The Vortex Lattice Magnetophonons at Intermediate Densities *10. 3 Dense Lattice and Supersoft Goldstone Modes 206 10.4 Bibliographic Notes 211 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 212 212 220 224 228 229 12 Dynamics of the Order Parameter Field 12.1 General Type A Dynamics 12.2 The Relaxation Time and Dissipation 12.3 Bibliographic Notes 231 231 234 239 13 240 240 247 249 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 15 Thermal Fluctuations 250 250 257 262 266 267 Statistical Physics of Mesoscopic Degrees of Freedom 269 15.1 Statistical Theory of Thermal Fluctuations of a Point-Like Object 269 15.2 Thermal Fluctuations of an Extended Object Described by the Path Integral 279 15.3 Mesoscopic
Thermal Fluctuations of the Order Parameter Field 289 199
Contents viii 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 293 298 300 300 310 315 318 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 319 319 Appendix A.l Abrikosov Quasimomentum Functions Averages A.2 Calculation of Gaussian Integrals A.3 Sparse Matrices and Their Determinants 335 335 338 340 Index 324 330 334 342 |
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| id | DE-604.BV048199825 |
| illustrated | Illustrated |
| index_date | 2024-07-03T19:46:16Z |
| indexdate | 2024-07-10T09:31:48Z |
| institution | BVB |
| isbn | 9781108836852 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-033580867 |
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| physical | x, 344 Seiten Illustrationen, Diagramme |
| publishDate | 2022 |
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| spelling | Rosenstein, Baruch 1958- Verfasser (DE-588)1248541278 aut Ginzburg-Landau theory of condensates thermodynamics, dynamics, and formation of topological matter Baruch Rosenstein, National Ying Ming Chiao Tung University, Dingping Li, Peking University Cambridge Cambridge University Press 2022 x, 344 Seiten Illustrationen, Diagramme txt rdacontent n rdamedia nc rdacarrier The phenomenological (Landau) description of the ordered condensed matter from magnets to Bose condensates -- Simplest topological defects -- Topological defects and their classification -- Repulsion between solitons and viable vortex matter created by a Gauge field -- Abrikosov vortices created by the magnetic field -- Structure and magnetization of the vortex lattice within London approximation -- Structure and magnetization of the vortex lattice within Abrikosov approximation -- Linear stability analysis of the homogeneous states -- Stability and the excitation spectrum of the single soliton and the vortex lattice -- Forces on solitons, pinning and elasticity of the vortex matter -- Dynamics of the order parameter field -- Solitary waves -- Viscous flow of the Abrikosov flux lattice -- Statistical physics of mesoscopic degrees of freedom -- The Landau-Wilson approach to statistical physics of the interacting field fluctuations -- Thermal fluctuations in the vortex matter Ginzburg-Landau theory is an important tool in condensed matter physics research, describing the ordered phases of condensed matter, including the dynamics, elasticity, and thermodynamics of the condensed configurations. In this systematic introduction to Ginzberg-Landau theory, both common and topological excitations are considered on the same footing (including their thermodynamics and dynamical phenomena). The role of the topological versus energetic considerations is made clear. Required mathematics (symmetry, including lattice translation, topology, and perturbative techniques) are introduced as needed. The results are illustrated using arguably the most fascinating class of such systems, high Tc superconductors subject to magnetic field. This book is an important reference for both researchers and graduate students working in condensed matter physics or can act as a textbook for those taking advanced courses on these topics Condensed matter Vortex-motion Superconductivity Topological defects (Physics) Phase transformations (Statistical physics) Ginzburg-Landau-Theorie (DE-588)4157357-2 gnd rswk-swf Ginzburg-Landau-Theorie (DE-588)4157357-2 s DE-604 Li, Dingping 1965- Sonstige (DE-588)1248541294 oth Erscheint auch als Online-Ausgabe 978-1-108-87273-7 Digitalisierung UB Regensburg - ADAM Catalogue Enrichment application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=033580867&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Rosenstein, Baruch 1958- Ginzburg-Landau theory of condensates thermodynamics, dynamics, and formation of topological matter Condensed matter Vortex-motion Superconductivity Topological defects (Physics) Phase transformations (Statistical physics) Ginzburg-Landau-Theorie (DE-588)4157357-2 gnd |
| subject_GND | (DE-588)4157357-2 |
| title | Ginzburg-Landau theory of condensates thermodynamics, dynamics, and formation of topological matter |
| title_auth | Ginzburg-Landau theory of condensates thermodynamics, dynamics, and formation of topological matter |
| title_exact_search | Ginzburg-Landau theory of condensates thermodynamics, dynamics, and formation of topological matter |
| title_exact_search_txtP | Ginzburg-Landau theory of condensates thermodynamics, dynamics, and formation of topological matter |
| title_full | Ginzburg-Landau theory of condensates thermodynamics, dynamics, and formation of topological matter Baruch Rosenstein, National Ying Ming Chiao Tung University, Dingping Li, Peking University |
| title_fullStr | Ginzburg-Landau theory of condensates thermodynamics, dynamics, and formation of topological matter Baruch Rosenstein, National Ying Ming Chiao Tung University, Dingping Li, Peking University |
| title_full_unstemmed | Ginzburg-Landau theory of condensates thermodynamics, dynamics, and formation of topological matter Baruch Rosenstein, National Ying Ming Chiao Tung University, Dingping Li, Peking University |
| title_short | Ginzburg-Landau theory of condensates |
| title_sort | ginzburg landau theory of condensates thermodynamics dynamics and formation of topological matter |
| title_sub | thermodynamics, dynamics, and formation of topological matter |
| topic | Condensed matter Vortex-motion Superconductivity Topological defects (Physics) Phase transformations (Statistical physics) Ginzburg-Landau-Theorie (DE-588)4157357-2 gnd |
| topic_facet | Condensed matter Vortex-motion Superconductivity Topological defects (Physics) Phase transformations (Statistical physics) Ginzburg-Landau-Theorie |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=033580867&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| work_keys_str_mv | AT rosensteinbaruch ginzburglandautheoryofcondensatesthermodynamicsdynamicsandformationoftopologicalmatter AT lidingping ginzburglandautheoryofcondensatesthermodynamicsdynamicsandformationoftopologicalmatter |