Relativistic generalization of the Ginzburg-Landau theory

A minimal generalization of the Ginzburg-Landau phenomenological theory of superconductivity is proposed for the curved space-time case. For a weak external gravitational field created by an island source, in the nonwave zone, a solution is found to the problem of the behavior of the wave function of the Cooper pair condensate in a straight segment of a superconducting wire. It is shown that a variable nonuniform field can generate electric current in a superconducting sample.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 4, pp. 92–97, April, 1989.     

Ginzburg-Landau theory of a supersolid

We develop a simple Ginsburg-Landau theory to study all the possible phases and phase transitions in 4He, analyze the condition for the existence of the supersolid (SS) and map out its global phase diagram from a unified framework. If the condition favors the existence of the SS, we use the GL theory to address several experimental facts and also make some predictions that are amenable to experimental tests. A key prediction is that the x-ray scattering intensity from the SS ought to have an additional modulation over that of the normal solid. The modulation amplitude is proportional to the nonclassical rotational-inertial observed in the torsional oscillator experiments.     

Extension of the de Broglie-Bohm theory to the Ginzburg-Landau equation

The de Broglie-Bohm approach permits to assign well defined trajectories to particles that obey the Schroedinger equation. We extend this approach to electron pairs in a superconductor. In the stationary regime this extension is completely natural; in the general case additional postulates are required. This approach gives enlightening views for the absence of Hall effect in the stationary regime and for the formation of permanent currents.     

Ginzburg-Landau theory for higher order phase transition

Ginzburg-Landau theory for studying phase transitions of higher order has been derived using coarse graining and lattice formulation within Ehrenfest thermodynamics. Our developed Hamiltonian leads directly to the functional of the system. We studied the evolution of the order parameter using our developed model equations for third and fourth order phase transitions. The periodic nature of the system can be likened to spatially varying periodic soliton/antisoliton lattice of holes in condensate. This is different from what one observes for any conventional solitary wave in the second order phase regime.     

Ginzburg-Landau theory of phase transitions in pseudo-one-dimensional systems

The static and dynamic properties of weakly coupled chains undergoing a phase transition are reviewed. The discussion is based on the functional generalization of the Ginzburg-Landau theory, including systems with real and complex order parameter. Various predictions of the theory, such as static correlations, renormalized phonon frequencies and a central resonance in the dynamic form factor near structural instabilities are discussed and compared with recent experiments on linear conductors that undergo a Peierls transition. New results are obtained for the thermodynamic anomalies near the onset of 3-d ordering and for the dynamic form factor of systems with an incommensurate Peierls distortion.     

On the role of the boundary conditions in the Ginzburg-Landau theory

The effect of the boundary conditions for solutions on the Ginzburg-Landau (GL) equations for superconducting plates in the vortex-free limit is studied by numerical methods. Based on the self-consistent solution of the system of GL equations, the dependence of the critical current I _c on the external magnetic field and the distribution of the order parameter over the plate thickness are determined. When solving the equations with general boundary conditions, it was found that the critical temperature and critical current density decreased in comparison with those obtained by solving equations with ordinary boundary conditions. According to the results of this study, the use of general boundary conditions leads to a number of interesting results which were not observed when using ordinary boundary conditions. The range of the applicability of the vortex-free limit for the films of thickness of the order of the coherence length ξ are discussed. The effect of boundary conditions on the applicability of this limit is analyzed.     

The onset of superconductivity in the time dependent Ginzburg-Landau theory

The fluctuations of the local order parameter above the superconducting transition temperature give rise to singularities in the electrical conductivity and the diamagnetic susceptibility. Using the time dependent Ginzburg-Landau equation the fluctuation of the current density is calculated. By means of the fluctuation-dissipation theorem and a dispersion relation the electromagnetic response function is then determined for small frequencies and wave-numbers. The dynamical conductivity for bulk material, thin films, and thin wires shows an increasing peak at zero frequency the width of which decreases as the transition temperature is approached. This structure should be observable in microwave experiments.     

Ginzburg-Landau theory and solitary waves in shape-memory alloys

A one-dimensional dynamic Ginzburg-Landau theory of the martensitic phase transition in shape-memory alloys is established. The nonlinear equations of motion yield solitary wave solutions of kink and of soliton type. The kink solutions which cannot move without external force represent single domain walls either between austenite and martensite or between two martensite variants. The soliton solutions correspond to a matrix of austenite or of martensite containing a moving sheet of the other phase. The velocity of the solitons depends on their amplitude. In the static case they reduce to the critical nucleus. The energy of each type of solitary waves is calculated.     

Real-time Ginzburg-Landau theory for bosons in optical lattices

Within the Schwinger-Keldysh formalism we derive a Ginzburg-Landau theory for the Bose-Hubbard model which describes the real-time dynamics of the complex order parameter field. Analyzing the excitations in the vicinity of the quantum phase transitions it turns out that particle/hole dispersions in the Mott phase map continuously onto corresponding amplitude/phase excitations in the superfluid phase. Furthermore, in the superfluid phase we find a sound mode, which is in accordance with recent Bragg spectroscopy measurements in the Bogoliubov regime, as well as an additional gapped mode, which seems to have been detected via lattice modulation.     

Description of thermal conductivity in the Ginzburg-Landau theory of phase transitions

A generalization of the Ginzburg-Landau theory of phase transitions is presented which allows one to describe states with variable temperatures. The approach is based on an expression for the entropy in the form of a functional which depends on the temperature gradient and the order parameter. It is shown that the theory is compatible with the zero-th law of thermodynamics (constancy of the temperature in equilibrium). For equilibrium thermodynamically stable states the results of the theory agree with the results of the isothermal approach based on the free energy functional. General limitations on the possible form of the nonlinear dynamic equations are given, in particular for the heat flux vector, and possible particular versions are given. The dynamics of linear fluctuations has been included, including temperature fluctuations. O. Yu. Shmidt Institute of Earth Physics, Russian Academy of Sciences. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 6, pp. 54–59, June, 1998.