We propose a model and derive analytical expressions for conductivity in heterogeneous fully anisotropic conductors with ellipsoid superconducting inclusions. This model and calculations are useful to analyze the observed temperature dependence of conductivity anisotropy in various anisotropic superconductors, where superconductivity onset happens inhomogeneously in the form of isolated superconducting islands. The results are applied to explain the experimental data on resistivity above the transition temperature Tc in the high-temperature superconductor YBa2Cu4O8 and in the organic superconductor β-(BEDT-TTF)2I3. The comparison of resistivity data and diamagnetic response in β-(BEDT-TTF)2I3 allows us to estimate the size of superconducting inclusions as d ∼ 1µm.

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In the present paper a method of finding the dynamics of the Wigner function of a particle in an infinite quantum well is developed. Starting with the problem of a reflection from an impenetrable wall, the obtained solution is then generalized to the case of a particle confined in an infinite well in arbitrary dimensions. It is known, that boundary value problems in the phase space formulation of the quantum mechanics are surprisingly tricky. The complications arise from nonlocality of the expression involved in calculation of the Wigner function. Several ways of treating such problems were proposed. They are rather complicated and even exotic, involving, for example, corrections to the kinetic energy proportional to the derivatives of the Dirac delta--function. The presented in the manuscript approach is simpler both from analytical point of view and regarding numerical calculation. The solution is brought to a form of convolution of the free particle solution with some function, defined by the shape of the well. This procedure requires calculation of an integral, which can be done by developed analytical and numerical methods.

We study the emergence of a parity breaking coherent photonic state of a photon mode coupled to finite array of two-level systems, represented by pseudospins 1/2. The pseudospin-photon interaction is realised via a shift of the photonic oscillator equilibrium position by an amount linear in Cartesian component of the total pseudospin. We demonstrate analytically, that the instability is manifested in an upturn from concave to convex of the ground state energy dependence on the total pseudospin component coupled to the photons. The perturbation, sufficient for parity breaking, tends to zero in the ultrastrong limit of light–matter coupling. We present phase diagram of finite pseudospin-photon system, that demonstrates this feature. Evolution of Husimi Q-functions of the pseudospin and photon subsystems, and of the pseudospin entropy, along different trajectories across the phase diagram is presented.