scholarly journals Magnetic Flux Lines in Complex Geometry Type-II Superconductors Studied by the Time Dependent Ginzburg-Landau Equation

2010 ◽  
Vol 115 (1) ◽  
pp. 63-74 ◽  
Author(s):  
Tommy Sonne Alstrøm ◽  
Mads Peter Sørensen ◽  
Niels Falsig Pedersen ◽  
Søren Madsen
Keyword(s):  
Magnetic Flux ◽  
Complex Geometry ◽  
Landau Equation ◽  
Time Dependent ◽  
Type Ii ◽  
Ginzburg Landau ◽  
Type Ii Superconductors ◽  
Flux Lines ◽  
Ginzburg Landau Equation ◽  
Magnetic Flux Lines

scholarly journals Large enhancement of conductivity in a strongly layered type-II superconductor with an artificial pinning array

2020 ◽  
Vol 2020 (4) ◽  
Author(s):  
Bui Duc Tinh
Keyword(s):  
Landau Equation ◽  
Thermal Fluctuations ◽  
Energy Scale ◽  
Time Dependent ◽  
Type Ii ◽  
Ginzburg Landau ◽  
Fluctuation Conductivity ◽  
Ginzburg Landau Equation ◽  
Type Ii Superconductor ◽  
Large Enhancement

Abstract We use the time-dependent Ginzburg–Landau equation to describe a type-II superconductor in a magnetic field in the presence of both strong thermal fluctuations and an artificial pinning array. Thermal fluctuations are represented by the Langevin white noise. The layered structure of the superconductor is taken into accounted with the Lawrence–Doniach model. The self-consistent Gaussian approximation is used to treat the nonlinear interaction term in the time-dependent Ginzburg–Landau equation. In the case of the $\delta $-function model for the pinning centers and the matching field, analytic expressions for the fluctuation electrical and thermoelectric conductivity are obtained. It is found that the fluctuations in electrical and thermoelectric conductivities increase with increasing pinning strength, and when the pinning strength comes near a critical value, the fluctuation conductivity is greatly enhanced. Our result shows that if a pinning array is added to a mixed state superconductor, the original properties of the superconductor are recovered. Physically, in the presence of thermal fluctuations, when the energy scale of the vortex lattice shear fluctuations becomes comparable to the pinning energy scale there is a large enhancement of the fluctuation conductivity in the presence of pinning.

scholarly journals Nonstationary Superconductivity: Quantum Dissipation and Time-Dependent Ginzburg-Landau Equation

2011 ◽  
Vol 2011 ◽  
pp. 1-10
Author(s):  
Anatoly A. Barybin
Keyword(s):  
Order Parameter ◽  
Continuity Equation ◽  
Chemical Potential ◽  
Landau Equation ◽  
Time Dependent ◽  
Quantum Dissipation ◽  
Ginzburg Landau ◽  
Superfluid Component ◽  
Ginzburg Landau Equation ◽  
Conservation Property

Transport equations of the macroscopic superfluid dynamics are revised on the basis of a combination of the conventional (stationary) Ginzburg-Landau equation and Schrödinger's equation for the macroscopic wave function (often called the order parameter) by using the well-known Madelung-Feynman approach to representation of the quantum-mechanical equations in hydrodynamic form. Such an approach has given (a) three different contributions to the resulting chemical potential for the superfluid component, (b) a general hydrodynamic equation of superfluid motion, (c) the continuity equation for superfluid flow with a relaxation term involving the phenomenological parameters and , (d) a new version of the time-dependent Ginzburg-Landau equation for the modulus of the order parameter which takes into account dissipation effects and reflects the charge conservation property for the superfluid component. The conventional Ginzburg-Landau equation also follows from our continuity equation as a particular case of stationarity. All the results obtained are mutually consistent within the scope of the chosen phenomenological description and, being model-neutral, applicable to both the low- and high- superconductors.

scholarly journals CORTICAL PHASE TRANSITIONS, NONEQUILIBRIUM THERMODYNAMICS AND THE TIME-DEPENDENT GINZBURG–LANDAU EQUATION

2012 ◽  
Vol 26 (06) ◽  
pp. 1250035 ◽  
Author(s):  
WALTER J. FREEMAN ◽  
ROBERTO LIVI ◽  
MASASHI OBINATA ◽  
GIUSEPPE VITIELLO
Keyword(s):  
Phase Transitions ◽  
Landau Equation ◽  
Power Laws ◽  
Time Dependent ◽  
Many Body ◽  
Ginzburg Landau ◽  
Ginzburg Landau Equation ◽  
Characteristic Space ◽  
The Many ◽  
The Brain

The formation of amplitude modulated and phase modulated assemblies of neurons is observed in the brain functional activity. The study of the formation of such structures requires that the analysis has to be organized in hierarchical levels, microscopic, mesoscopic, macroscopic, each with its characteristic space-time scales and the various forms of energy, electric, chemical, thermal produced and used by the brain. In this paper, we discuss the microscopic dynamics underlying the mesoscopic and the macroscopic levels and focus our attention on the thermodynamics of the nonequilibrium phase transitions. We obtain the time-dependent Ginzburg–Landau equation for the nonstationary regime and consider the formation of topologically nontrivial structures such as the vortex solution. The power laws observed in functional activities of the brain is also discussed and related to coherent states characterizing the many-body dissipative model of brain.

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