Abstract
In the first part of this review paper, the time-dependent Ginzburg-Landau theory is derived starting from the microscopic BCS model with the help of a derivative expansion. Special attention is paid to two space dimensions, where the entire crossover from the weak-coupling BCS limit to the strong-coupling BEC limit of tightly bound fermion pairs is accessible analytically. The second part deals with the dual approach to the time-independent Ginzburg-Landau theory in three space dimensions. In this approach, the magnetic vortices of a superconductor play the central role, and the superconductor-to-normal phase transition is understood as a proliferation of these vortices.
Keywords
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Berezinskii, V.L. (1972) Destruction of Long-Range Order Sov. Phys. JETP 34, pp. 610–616
Kosterlitz, J.M. and Thouless, D. J. (1973) Metastability and Phase Transitions in Two-Dimensional Systems J. Phys. C 6, pp. 1181–1203
Davis, A.-C. and Brandenberger, R. (Eds.) (1995) Formation and Interactions of Topological Defects Plenum Press, New York
Gorkov, L.P. (1959) Microscopic Derivation of the Ginzburg-Landau Equations in the Theory of Superconductivity Sov. Phys. JETP 9 pp. 1364–1367
Bardeen, J., Cooper, L. N. and Schrieffer, J. R. (1957) Theory of Superconductivity Phys. Rev. 108 pp. 1175–1204
Ginzburg, V.L. and Landau, L.D. (1950) Zh. Eksp. Teor. Fiz. 20 pp. 1064
Schakel, A.M.J. (1989) On Broken Symmetries in Fermi Systems, Ph. D. Thesis, University of Amsterdam
Eagles, D.M. (1969) Possible Pairing without Superconductivity at Low Carrier Concentrations in Bulk and Thin-Film Superconducting Semiconductors Phys. Rev. 186 pp. 456–463
Leggett, A.J. (1980) in: Pekalski, A. and Przystawa, J. (Eds.) Modern Trends in the Theory of Condensed Matter Springer-Verlag, Berlin pp. 13–27
Drechsler, M. and Zwerger, W. (1992) Crossover from BCS-Superconductivity to Bose-Condensation Ann. Phys. (Germany) 1 pp. 15–23
Haussmann, R. (1993) Crossover from BCS Superconductivity to Bose-Einstein Condensation—A Self-Consistent Theory Z. Phys. B 91 pp. 291–308
Sá de Melo, C.A.R., Randeria, M. and Engelbrecht, J.R. (1993) Crossover from BCS to Bose Superconductivity—Transition-Temperature and Time-Dependent Ginzburg-Landau Theory Phys. Rev. Lett. 71 pp. 3202–3205
Marini, M., Pistolesi, F. and Strinati, G.C. (1998) Evolution from BCS Superconductivity to Bose Condensation: Analytic Results for the Crossover in Three Dimensions Eur. Phys. J. B 1 pp. 151–159
Popov, V.N. (1987) Functional Integrals and Collective Excitations Cambridge University Press, Cambridge
Randeria, M. Duan, J.-M. and Shieh L.-Y. (1990) Superconductivity in a Two-Dimensional Fermi Gas: Evolution from Cooper Pairing to Bose Condensation Phys. Rev. B 41 pp. 327–343
Mattuck, R.D. (1976) A Guide to Feynman Diagrams in the Many-Body Problem McGraw-Hill, New York
Fraser, C.M. (1985) Calculation of Higher Derivative Terms in the One Loop Effective Lagrangian Z. Phys. C 28 pp. 101-106; Aitchison, U.R. and Fraser, C.M. (1985) Derivative Expansions of Fermion Determinants: Anomaly-Induced Vertices, Goldstone-Wilczek Currents, and Skyrme Terms Phys. Rev. D 31 pp. 2605–2615
Rivers, R.J (1987) Path Integrals in Quantum Field Theory Cambridge University Press, Cambridge
Kapusta, J.I. (1989) Finite-Temperature Field Theory Cambridge University Press, Cambridge
Stintzing, S. and Zwerger, W. (1997) Ginzburg-Landau Theory of Superconductors with Short Coherence Length Phys. Rev. B 56 pp. 9004–9014
Schmid, A. (1966) A Time-Dependent Ginzburg-Landau Equation and its Applications to the Problem of Resistivity in the Mixed State Phys. Kond. Materie 5 pp. 302–317
Abrahams, E. and Tsuneto, T. (1966) Time Variation of the Ginzburg-Landau Order Parameter Phys. Rev. 152 pp. 416–432
Schakel, A.M.J. (1994) Effective Theory of Bosonic Superfluids Int. J. Mod. Phys. B 8 pp. 2021–2039
de Germes, P.G. (1966) Superconductivity in Metals and Alloys Benjamin, New York
Tinkham, M. (1975) Introduction to Superconductivity McGraw-Hill, New York
Crisan, M. (1989) Theory of Superconductivity World Scientific, Singapore
Gross, E.P. (1961) Structure of a Quantized Vortex in Boson Systems Nuovo Cimento 20pp. 454-477; Pitaevskii, L.P. (1961) Vortex Lines in an Imperfect Bose Gas Sov. Phys. JETP 13 pp. 451–454
Schakel, A.M.J. (1999) in: Shopova, D.V. and Uzunov, D.I. (Eds.) Correlations, Coherence, and Order Plenum Press, New York pp. 295–382
Banks, T. Meyerson, B. and Kogut, J. (1977) Phase Transitions in Abelian Lattice Gauge Theories Nucl. Phys. B 129 pp. 493–510
Peskin, M. (1978) Mandelstam-’t Hooft Duality in Abelian Lattice Models Ann. Phys. 113 pp. 122–152
Thomas, P.R. and Stone, M. Nature of the Phase Transition in a Nonlinear O(2)3 Model (1978) Nucl. Phys. B 144 pp. 513–524
Helfrich, W. and Müller, W. (1980) Concentrated Thermally Equilibrated Polymer Solutions in: Continuum Models of Discrete Systems Waterloo University Press, Waterloo pp. 753–760
Dasgupta, C. and Halperin, B. I. (1981) Phase Transition in a Lattice Model of Superconductivity Phys. Rev. Lett. 47 pp. 1556–1560
Kleinert, H. (1982) Disorder Version of the Abelian Higgs Model and the Order of the Superconductive Phase Transition Lett. Nuovo Cimento 35 pp. 405–412
Bartholomew, J. (1983) Phase Structure of a Lattice Superconductor Phys. Rev. B 28 pp. 5378–5381
Savit, R. (1989) Duality in Field Theory and Statistical Systems Rev. Mod. Phys. 52 pp. 453–487
Kleinert, H. (1989) Gauge Fields in Condensed Matter, 1, World Scientific, Singapore
Schakel, A.M.J. (1998) Boulevard of Broken Symmetries, e-print cond-mat/9805152
Symanzik, K. (1969) in: Jost, R. (Ed.) Euclidean Quantum Field Theory Academic Press, New York
Feynman, R.P. (1950) Mathematical Formulation of the Quantum Theory of Eletromagnetic Interactions Phys. Rev. 80 pp. 440–457
Schwinger, J. (1951) On Gauge Invariance and Vacuum Polarization Phys. Rev. 82 pp. 664–679
Kleinert, H. (1995) Path Integrals in Quantum Mechanics, Statistics and Polymer Physics, 2nd Edition, World Scientific, Singapore
Feynman, R.P. (1948) Space-Time Approach to Non-Relativistic Quantum Mechanics Rev. Mod. Phys. 20 pp. 367–387
Parisi, G. (1988) Statistical Field Theory Addison-Wesley, New-York
Copeland, E., Haws, D., Holbraad, S. and Rivers, R. (1990) The Statistical Properties of Strings. 1. Free Strings in: Gibbons, G.W., Hawking, S.W. and Vachaspati, T. (Eds.) The Formation and Evolution of Cosmic Strings Cambridge University Press, Cambridge pp. 35–47; The Statistical Properties of Strings. 2. Interacting Strings ibid pp. 49-69
Kiometzis, M., Kleinert, H. and Schakel, A.M.J. (1995) Dual Description of the Superconducting Phase Transition Fortschr. Phys. 43 pp. 697–732
Dirac, P.A.M. (1948) The Theory of Magnetic Poles Phys. Rev. 74 pp. 817–830
Nambu, Y. (1974) Strings, Monopoles and Gauge Fields Phys. Rev. D 10 pp. 4262–4268
Abrikosov, A.A. (1957) On the Magnetic Properties of Superconductors of the Second Group Sov. Phys. JETP 5 pp. 1174–1182
Marino, E.C. (1988) Quantum Theory of Nonlocal Vortex Fields Phys. Rev. D 38 pp. 3194–3198 (1988); Marino, E.C., Marques, G.C., Ramos, R.O. and Ruiz, J.S. (1992) Mass Spectrum and Correlation Function of Quantum Vortices in the Abelian Higgs Model Phys. Rev. D 45 pp. 3690-3700; Marino, E.C. (1993) Duality, Quantum Vortices and Anyons in Maxwell-Chern-Simons-Higgs Theories Ann. Phys. (NY) 224 pp. 225-274
Kovner, A., Rosenstein, B. and Eliezer, D. (1990) Photon as Goldstone Boson in (2+l)-Dimensional Higgs Model Mod. Phys. Lett. A 5 pp. 2733–2740; (1991) Photon as a Goldstone Boson in (2+l)-Dimensional Abelian Gauge Theories Nucl Phys. B 350 pp. 325-354; Kovner, A. and Rosenstein, B. (1991) Topological Interpretation of Electric Charge and the Aharonov-Bohm Effect in 2+1 Dimensions Phys. Rev. Lett. 67 pp. 1490-1493
Kiometzis, M. and Schakel, A.M.J. (1993) Landau Description of the Superconducting Phase-Transition Int. J. Mod. Phys. B 7 pp. 4271–4288
Bardakci, K. and Samuel, S. (1978) Local Field Theory for Solitons Phys. Rev. D 18 pp. 2849–2860
Kawai, H. (1981) A Dual Transformation of the Nielsen-Olesen Model Prog. Theor. Phys. 65 pp. 351–364
Kovner, A., Kurzepa, P. and Rosenstein, B. (1993) A Candidate for Exact Continuum Dual Theory for Scalar QED3 Mod. Phys. Lett. A. 8 pp. 1343–1355
Kiometzis, M., Kleinert, H. and Schakel, A.M.J. (1994) Critical Exponents of the Superconducting Phase-Transition Phys. Rev. Lett. 73 pp. 1975–1977
Herbut, I.F. (1996) Continuum Dual Theory of the Transition in 3D Lattice Superconductor J. Phys. A: Math. Gen. 29 pp. 423–429
de Calan, C. and Nogueira, F.S. (1999) e-print cond-mat/9903247
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2000 Springer Science+Business Media Dordrecht
About this chapter
Cite this chapter
Schakel, A.M.J. (2000). Time-Dependent Ginzburg-Landau Theory and Duality. In: Bunkov, Y.M., Godfrin, H. (eds) Topological Defects and the Non-Equilibrium Dynamics of Symmetry Breaking Phase Transitions. NATO Science Series, vol 549. Springer, Dordrecht. https://doi.org/10.1007/978-94-011-4106-2_11
Download citation
DOI: https://doi.org/10.1007/978-94-011-4106-2_11
Publisher Name: Springer, Dordrecht
Print ISBN: 978-0-7923-6205-0
Online ISBN: 978-94-011-4106-2
eBook Packages: Springer Book Archive