scholarly journals Attempt to Describe Phase Slips by Means of an Adiabatic Approximation

2021 ◽  
Author(s):  
Jorge Berger
Keyword(s):  
Superconducting State ◽  
Adiabatic Approximation ◽  
Landau Equation ◽  
Time Derivative ◽  
Time Dependent ◽  
Critical Voltage ◽  
Ginzburg Landau ◽  
Phase Drift ◽  
Derivative Term ◽  
Phase Slips

Abstract As a plausibility test for the feasibility of extension of the quasiclassical Keldysh–Usadel technique to slowly varying situations, we assess the influence of the time-derivative term in the time-dependent Ginzburg–Landau equation. We consider cases in which the superconducting state in a nanowire varies slowly, either because the voltage applied on it is small, or because most of phase drift takes place next to the boundaries. An approximation without this time derivative can describe the superconducting state away from phase slips, but is unable to predict the value or the existence of a critical voltage at which evolution becomes non-stationary.

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.

COMPLEX DYNAMICS IN COUPLED NONLINEAR ELEMENT SYSTEMS

1991 ◽  
Vol 05 (08) ◽  
pp. 1179-1214 ◽  
Author(s):  
KENJU OTSUKA
Keyword(s):  
Nonlinear Oscillator ◽  
Complex Dynamics ◽  
Landau Equation ◽  
Computer Experiments ◽  
Time Dependent ◽  
Chain Model ◽  
Ginzburg Landau ◽  
Physical Systems ◽  
Local Attractors ◽  
Discrete Complex

This paper reviews complex dynamics which arise through the interaction of simple nonlinear elements without chaotic response, including self-induced switching among local attractors (chaotic itinerancy) and related phenomena. Several realistic physical systems consisting of coupled nonlinear elements are considered on the basis of computer experiments: coupled nonlinear oscillator (e.g., discrete complex time-dependent Ginzburg-Landau equation) systems, coupled laser arrays, and a coupled multistable optical chain model.

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