Analytic representation of the order parameter profiles and susceptibility of a Ginzburg-Landau type model with strongly adsorbing competing walls

2019 ◽  
Author(s):  
Vassil M. Vassilev ◽  
Peter A. Djondjorov ◽  
Daniel M. Danchev
Keyword(s):  
Order Parameter ◽  
Analytic Representation ◽  
Type Model ◽  
Ginzburg Landau

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 Order parameter profiles in a system with Neumann – Neumann boundary conditions

2018 ◽  
Vol 145 ◽  
pp. 01009 ◽  
Author(s):  
Vassil M. Vassilev ◽  
Daniel M. Dantchev ◽  
Peter A. Djondjorov
Keyword(s):  
Boundary Conditions ◽  
Order Parameter ◽  
Neumann Boundary ◽  
Elliptic Functions ◽  
Thermodynamic System ◽  
Neumann Boundary Conditions ◽  
Ginzburg Landau ◽  
One Dimensional ◽  
The One ◽  
Field Plane

In this article we consider a critical thermodynamic system with the shape of a thin film confined between two parallel planes. It is assumed that the state of the system at a given temperature and external ordering field is described by order-parameter profiles, which minimize the one-dimensional counterpart of the standard ϕ4 Ginzburg–Landau Hamiltonian and meet the so-called Neumann – Neumann boundary conditions. We give analytic representation of the extremals of this variational problem in terms ofWeierstrass elliptic functions. Then, depending on the temperature and ordering field we determine the minimizers and obtain the phase diagram in the temperature-field plane.

ELECTRODEPOSITION MODELING USING COUPLED PHASE-FIELD AND LATTICE BOLTZMANN APPROACH

2013 ◽  
Vol 25 (01) ◽  
pp. 1340018 ◽  
Author(s):  
D. V. PATIL ◽  
K. N. PREMNATH ◽  
D. DESAI ◽  
SANJOY BANERJEE
Keyword(s):  
Free Energy ◽  
Phase Field ◽  
Lattice Boltzmann ◽  
Order Parameter ◽  
Chemical Deposition ◽  
Energy Functional ◽  
Time Step ◽  
Ginzburg Landau ◽  
Two Phases ◽  
Boltzmann Method

In this paper, a coupled phase-field (PF) and lattice Boltzmann method (LBM) is presented to model the multiphysics phenomenon involving electro-chemical deposition. The deposition (or dissolution) of the electrode is represented using variations of an order-parameter. The time-evolution of an order-parameter is proportional to the variation of a Ginzburg–Landau free-energy functional. Further, the free-energy densities of the two phases are defined based on a dilute or an ideal solution approximation. An efficient LBM is used to obtain the converged electro-static potential field for each physical time-step of the evolution of the PF variable. The coupled approach demonstrates the applicability of the LBM in a multiphysics scenario. The numerical validation for the coupled approach is performed by the simulation of the electrodeposition process of Cu from CuSO 4 solution.

scholarly journals CHARGED VORTEX DYNAMICS IN GINZBURG–LANDAU THEORY OF THE FRACTIONAL QUANTUM HALL EFFECT

1995 ◽  
Vol 10 (05) ◽  
pp. 645-666 ◽  
Author(s):  
THEODORE J. ALLEN ◽  
ANDREW J. BORDNER
Keyword(s):  
Hall Effect ◽  
Quantum Hall Effect ◽  
Order Parameter ◽  
Quantum Hall ◽  
Fractional Quantum Hall Effect ◽  
Effective Theory ◽  
Ginzburg Landau ◽  
Fractional Quantum ◽  
Fractional Quantum Hall ◽  
Quantum Motion

We write a Ginzburg–Landau Hamiltonian for a charged order parameter interacting with a background electromagnetic field in 2 + 1 dimensions, which we propose as an effective theory for the fractional quantum Hall effect. We further propose to identify vortex excitations of the theory with Laughlin's fractionally charged quasiparticles. Using the method of Lund we derive a collective coordinate action for vortex defects in the order parameter and demonstrate that the vortices are charged. We examine the classical dynamics of the vortices and then quantize their motion, demonstrating that their peculiar classical motion is a result of the fact that the quantum motion takes place in the lowest Landau level. The classical and quantum motion in two-dimensional regions with boundaries is also investigated. The quantum theory is not invariant under magnetic translations. Magnetic translations add total time derivative terms to the collective action, but no extra constants of the motion result.

Zeros of a complex Ginzburg–Landau order parameter with applications to superconductivity

1994 ◽  
Vol 5 (4) ◽  
pp. 431-448 ◽  
Author(s):  
C. M. Elliott ◽  
H. Matano ◽  
Tang Qi
Keyword(s):  
Free Energy ◽  
Numerical Simulations ◽  
Gibbs Free Energy ◽  
Order Parameter ◽  
Magnetic Potential ◽  
Ginzburg Landau ◽  
Absolute Value ◽  
Complex Order ◽  
Isolated Points ◽  
The Absolute

We consider the minimizers of the Gibbs free energy which couples a complex Ginzburg–Landau order parameter with a magnetic potential. It is established that the set on which the complex order parameter equals zero consists only of isolated points. Some estimates concerning the set on which the absolute value of the order parameter is small are also given. Numerical simulations are presented for the problem without a magnetic potential.

scholarly journals Specific heat jump of two-band superconductor KFe2As2 using Ginzburg-Landau theory

2014 ◽  
Vol 32 (3) ◽  
pp. 465-469 ◽  
Author(s):  
I. Askerzade
Keyword(s):  
Specific Heat ◽  
Order Parameter ◽  
Landau Theory ◽  
Energy Functional ◽  
Order Parameters ◽  
Ginzburg Landau ◽  
Specific Heat Jump ◽  
Nonlinear Temperature Dependence ◽  
Nonlinear Temperature ◽  
Good Agreement

AbstractIn this study specific heat jump using two-gap Ginzburg-Landau (GL) theory has been calculated. In contrast to the previous approaches, we have taken into account intergradient order parameters interaction in the GL free energy functional. The thermodynamic magnetic field revealed nonlinear temperature dependence due to interband interaction between order parameters and their gradients. The calculations showed that the specific heat jump in two-order parameter superconductors was smaller than that of single-order parameter superconductors. It has been shown that such a model is in good agreement with experimental data for KFe2As2 superconductors.

s-Wave holographic superconductor in different ensembles and its thermodynamic consistency

2017 ◽  
Vol 26 (04) ◽  
pp. 1750027
Author(s):  
Lei Yin ◽  
Defu Hou
Keyword(s):  
Order Parameter ◽  
Helmholtz Free Energy ◽  
Canonical Ensemble ◽  
Landau Theory ◽  
Equation Of Motion ◽  
Superconducting Phase ◽  
S Wave ◽  
Holographic Superconductor ◽  
Thermodynamic Relation ◽  
Ginzburg Landau

In this paper, we analytically study the consistency between the Ginzburg–Landau theory of the holographic superconductor in different ensembles and the fundamental thermodynamic relation, we derive the equation of motion of the scalar field which depicts the superconducting phase in canonical ensemble (CE) and a consistent formula to connect the holographic order-parameter to the Ginzburg–Landau coefficients in different thermodynamic ensembles, and we also study the spatially nonuniform Helmholtz free energy.

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