Ginzburg-Landau equations: A revisit
We study the Ginzburg-Landau equations in the context of both superconductivity theory and instability waves in nonlinear media. In the former context and for the model on a two-dimensional asymptotically Euclidean Riemannian manifold finite energy field configurations have the exponential decay property due to the broken U(1) symmetry and hence the magnetic flux is quantized at the classical level and the solutions are identified as homotopy classes in {pi}{sub 1}(T{sup k}). For a well-known choice of the coupling constant the minimization problem under an integral magnetic flux constraint of the Ginzburg-Landau free energy functional can be solved by the extended Bogomol'nyi equations and the obstruction to the uniqueness of a solution to the prescribed vortex problem of the Bogomol'nyi equations lies in the first de Rham cohomology group of the manifold. For a domain {Omega} in the Euclidean space R{sup d} (d = 2,3) existence of weak solutions for both interior and equations are established without any restriction on the range of the coupling constant {lambda}, the size of {Omega}, or the boundary data. For {lambda} = 1 we prove the existence of confined multivortices in a bounded domain by a monotone iteration method. It is well-known that a sufficiently strong or weak external magnetic field can switch off or on the superconducting state of a superconductor. This fast is examined mathematically via the Ginzburg-Landau equation of evolution type which can be viewed as a perturbation generalization of the extensively studied cubic Schroedinger equations.
- Research Organization:
- Massachusetts Univ., Amherst, MA (USA)
- OSTI ID:
- 7272733
- Country of Publication:
- United States
- Language:
- English
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Related Subjects
657000 -- Theoretical & Mathematical Physics
71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
75 CONDENSED MATTER PHYSICS
SUPERCONDUCTIVITY AND SUPERFLUIDITY
CALCULATION METHODS
ELECTRIC CONDUCTIVITY
ELECTRICAL PROPERTIES
FIELD THEORIES
FUNCTIONS
GINZBURG-LANDAU THEORY
MATHEMATICAL MANIFOLDS
MATHEMATICAL MODELS
PHYSICAL PROPERTIES
RIEMANN FUNCTION
SUPERCONDUCTIVITY