Statistical mechanics of a vortex system in a thin superconducting film in the cyclic approximation. II. Finite thickness and vortex bending

An expression for the interaction between two pointlike vortices in a superconducting film of finite thickness is obtained. The result differs from the well-known Pearl result by the new effective penetration depth'= coth d/2. The partition function is calculated in the cyclic approximation and the vortex bending fluctuations are taken into account as in the quasiclassical approximation. The influence of both these correction terms on the Kosterlitz-Thouless transition and the resistance curve is discussed.Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 104, No. 2, pp. 337–347, August, 1995.     

Phase separation and vortex states in the binary mixture of Bose-Einstein condensates

The phase separation and vortex states in a two-component Bose-Einstein condensate consisting of |F = 1, m _f = 1〉 and |2, 1〉 internal spin states of ⁸⁷Rb atoms are considered in the framework of the Thomas-Fermi approximation. It is shown that in the nonrotating system, the atoms in the state |1, ?1〉 form a shell around the atoms in the state |2, 1〉. The critical angular velocity for each state is calculated. These velocities depend drastically on the relative concentrations of the components, the critical angular velocity of the outer component being less than the angular velocity of the inner one. It is shown that the atoms in the |1, ?1〉 state can form a rotating ring around the resting core of the atoms in the |2, 1〉 state.     

A Simple Cluster Model for the Liquid–Glass Transition

Using the classical distribution-function approach to simple liquids, we estimate the orientational interaction between clusters consisting of a particle and its nearest neighbors. We show that there are density and temperature ranges where the interaction changes sign as a function of the cluster radius. On this basis, the corresponding model of interacting cubic and icosahedral clusters (of the type of a spin glass model) is proposed and solved in the replica-symmetric approximation. We show that the glass order parameter grows continuously on cooling and the replica-symmetry-breaking temperature can be identified with the glass transition temperature. We also show that on cooling a system of particles with a Lennard-Jones interaction, cubic clusters freeze first. The transition temperature for icosahedral clusters is somewhat lower; therefore, the cubic structure of the short-range order is more likely in a Lennard-Jones glass near transition.     

Stability of the Bose system in Bose-Fermi mixture with attraction between bosons and fermions

An effective Hamiltonian for the Bose system in the mixture of ultracold atomic clouds of bosons and fermions is obtained by integrating out the Fermi degrees of freedom. An instability of the Bose system is found in the case of attractive interaction between components that is in good agreement with an experiment on the bosonic ⁸⁷Rb and fermionic ⁴⁰K mixture.     

Spherical analogues of some non-Ising spin glass models: Exact solutions

We consider several models of non-Ising spin glass for which we can naturally formulate an analogue of spherical conditions well known for the Ising model. We calculate the partition functions of the obtained models exactly. The random matrix method and the replica method yield identical results.     

Spin-glass-type state in complex nonmagnetic systems

We briefly review our works concerned with generalized models of spin glass, which describe a wide class of glasses (multipole systems, real cluster glasses, and others). We consider several new models and discuss how the scenario of glass transition depends on different factors. We propose a classification of the behaviors of complex spin glasses depending on the system symmetry properties.     

The bifurcation approach to the theory of the first order isotropiv-nematic phase transition

The known results about the first order transition of the isotropic liquid of rod-like molecules into nematic phase are obtained in a simple way in terms of bifurcations of a nonlinear intergal equation solution.