Quantum batteries, which are quantum systems to be used for the storage and transformation of energy, have been recently attracting research interest. A promising candidate for their investigation is the Dicke model, which describes an ensemble of two-level systems interacting with a single-mode electromagnetic wave in a resonator cavity. In order to charge the battery, a coupling between the ensemble of two-level systems and resonator cavity should be turned off at a certain moment of time. This moment of time is chosen in such a way that the energy gets fully stored in an ensemble of two-level systems. In our previous works we have investigated a bound-luminosity superradiant state of the extended Dicke model and found analytical expressions for the dynamics of coherent energy transfer between the superradiant condensate and the ensemble of two-level systems. Here, using our previous results, we have derived analytically the superlinear law for the quantum battery charging power $P\sim N^{3/2}$ as a function of the number $N$ of two-level systems in the battery, and also the $N$ dependence for the charging time $t_c\sim N^{-1/2}$. The $N$ exponent $3/2$ of the charging power is in quantitative correspondence with the recent result $1.541$ obtained numerically by other authors. The physics of Dicke quantum battery charging is considered in detail.

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 $T_c$ in the high-temperature superconductor ${\mathrm{YBa}}_2{\mathrm{Cu}}_4{\mathrm{O}}_8$ and in the organic superconductor $\beta \text{−}{\left(\mathrm{BEDT}\text{−}\mathrm{TTF}\right)}_2{\mathrm{I}}_3$. The comparison of resistivity data and diamagnetic response in $\beta \text{−}{\left(\mathrm{BEDT}\text{−}\mathrm{TTF}\right)}_2{\mathrm{I}}_3$ allows us to estimate the size of superconducting inclusions as $d\sim 1\mu \text{m}$.

Most high-$T_c$ superconductors are spatially inhomogeneous. Usually, this heterogeneity originates from the interplay of various types of electronic ordering. It affects various superconducting properties, such as the transition temperature, the magnetic upper critical field, the critical current, etc. In this paper, we analyze the parameters of spatial phase segregation during the first-order transition between superconductivity (SC) and a charge- or spin-density wave state in quasi-one-dimensional metals with imperfect nesting, typical of organic superconductors. An external pressure or another driving parameter increases the transfer integrals in electron dispersion, which only slightly affects SC but violates the Fermi surface nesting and suppresses the density wave (DW). At a critical pressure $P_c$, the transition from a DW to SC occurs. We estimate the characteristic size of superconducting islands during this phase transition in organic metals in two ways. Using the Ginzburg–Landau expansion, we analytically obtain a lower bound for the size of SC domains. To estimate a more specific interval of the possible size of the superconducting islands in (TMTSF)${}_2$PF${}_6$ samples, we perform numerical calculations of the percolation probability via SC domains and compare the results with experimental resistivity data. This helps to develop a consistent microscopic description of SC spatial heterogeneity in various organic superconductors.

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.

Analytic expression is found for the frequency dependence of the transmission coefficient of a transmission line inductively coupled to the microwave cavity with the superradiant condensate. Sharp transmission drops reflect the condensate's frequencies spectrum. These results pave the way to direct detection of emergence of the superradiant condensates in quantum metamaterials. Results are based on the analytic solutions of the nonlinear semiclassical dynamics of the superradiant photonic condensate in the Dicke model of an ensemble of two-level atoms dipolar coupled to the electromagnetic field in the microwave cavity. In the adiabatic limit with respect to the photon degree of freedom, the system is approximately integrable with evolution being expressed via Jacobi elliptic functions of real time. Depending on the coupling strength, the semiclassical coordinate of the superradiant condensate in the ground state either oscillates in one of the two degenerate minima of the condensate's potential energy or traverses between them over the saddle point. An experimental setup for measuring of the breakdown of the normal phase of the Dicke model via coupling to the transmission line is proposed. A one-to-one mapping of the semiclassical motion of the superradiant condensate on the nodding of unstable Lagrange “sleeping top” also turns the Dicke model into an analog device for modeling the dynamics of mechanical systems.

In the present paper we derive the Wigner current of the particle in a multidimensional billiard—the compact region of space in which the particle moves freely. The calculation is based on proposed by us previously method of imposing boundary conditions by convolution of the free particle Wigner function with some time independent function, defined by the shape of the billiard. This method allowed to greatly simplify the general expression for the Wigner current, representing its p –component as a surface integral of the product of the shifted particles wave functions. The results are also connected to an alternative approach, which takes into account the boundary conditions by adding the ∝ δ ′ ( x ) term to the Hamiltonian. The latter is also generalized to the multidimensional case.