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We consider a problem of description of quantum correlations and dispersions of subsystems of complex open systems. Based on our previous results we proposed a method to evaluate pure quantum contributions from total statistical characteristics of two coupled oscillators interacting with thermal reservoirs. The natural way to extract pure quantum characteristic of the system under study is a calculation of difference between the total value and its pure classical part. A numerical study of temporal behavior of quantum variances and covariances from given initial states up to states in the infinite time limit is given using the proposed method. It is shown that at comparatively high temperatures the steady state total variances are almost classical, because their pure quantum parts tend to zero in this regime. Otherwise, at comparatively low temperatures, the pure quantum parts of variances are not zeroing in steady states manifesting a finite contribution to total values. The same is true for the covariance. The larger the temperature, the lower is the quantum contribution to the total covariance. As well as entanglement measures, quantum discord, the pure quantum contributions in the covariance matrix elements are important characteristics of the temporal dynamics of complex quantum systems., Comment: 4 figures

The paper deals with the problem of dynamics of externally driven open quantum systems. Using the path integral methods we found an analytical expression for time-dependent density matrix of two externally driven coupled quantum oscillators interacting with different baths of oscillators. It is shown that at the zeroing of external forces the density matrix becomes identical to the previously obtained one for freely developing coupled oscillators. Mean values of observables are computed by using the Hermitian part of the matrix. All elements of the covariance matrix composed by coordinates and momenta of two driven coupled oscillators are calculated. The time-dependent mean values, dispersions and covariances of coordinates of coupled oscillators at given external forces are numerically studied. It is shown that the larger the coupling constant the larger is the disturbances of the second oscillator due to external action on the first oscillator. Coupled dynamics of forced oscillators at relatively large coupling constant is demonstrated at different thermodynamic conditions., Comment: 4 figures

This work addresses the problem of relaxation of open systems to quasi-equilibrium states. Time-dependent density matrix of two arbitrary coupled quantum oscillators of arbitrary properties interacting with separate reservoirs is derived based on path integration. Temporal dynamics of spatial variances and covariances of the oscillators from any given time up to quasi-equilibrium steady states is studied. It is demonstrated for general case that asymptotic spatial variances of two arbitrary oscillators and their covariances achieve stationary values in the long-time limit. A comparison of steady state characteristics of coupled oscillators with those predicted by the fluctuation dissipation theorem (FDT) is performed. It is shown that the larger the difference in masses and eigenfrequencies of coupled oscillators, the smaller are the deviations of stationary variances from those given by the FDT at fixed coupling strength and fixed difference in temperatures between thermal baths. In framework of the model of the bilinear interaction and Ohmic dissipation and at any oscillators parameters the variances and covariances have divergent character at strong couplings., Comment: 27 pages, 3 figures

Spatial coherence of thermal fields in far- and near-field zones generated by heated half-space into vacuum is studied at essentially different thermodynamical conditions. It is shown that correlation lengths of fields in any field zone are different in equilibrium and out of equilibrium systems. In wide range of distances from sample surface correlation functions are should be calculated using a total sum of evanescent and propagating contributions due to their mutual compensation at some conditions because of anticorrelations. It is demonstrated that correlation lengths as calculated with a proposed formula are in agreement with a behavior of correlation functions of thermal fields in spectral range of surface excitations, Comment: 6 pages, 6 figures

The paper deals with the problem of open systems out of equilibrium. An analytical expression for time-dependent density matrix of two arbitrary coupled identical quantum oscillators interacting with separate reservoirs is derived using path integral methods. The temporal behavior of spatial variances and of covariance from given initial values up to stationary values is investigated. It was shown that at comparatively low coupling strengths the asymptotic variances in the long-time limit achieve steady states despite on initial conditions. Stationary values of variances differ from the case of total equilibrium due to their coupling simultaneously with thermal reservoirs of different temperatures. The larger the difference in temperatures of thermal baths, the larger is the difference of the stationary values of variances of coupled oscillators comparing with values given by the fluctuation dissipation theorem. At strong couplings the variances have divergent character. Otherwise, in the weak coupling limit the asymptotic stationary variances are always in accordance with the fluctuation dissipation theorem despite of the difference in temperatures within the whole system., Comment: 24 pages, 5 figures

The paper addresses the problem of relaxation of open quantum systems. Using the path integral methods we found an analytical expression for time-dependent density matrix of two coupled quantum oscillators interacting with different baths of oscillators. The expression for density matrix was found in the linear regime with respect to the coupling constant between selected oscillators. Time-dependent spatial variances and covariance were investigated analytically and numerically. It was shown that asymptotic variances in the long-time limit are always in accordance with the fluctuation dissipation theorem despite on their initial values. In the weak coupling approach there is good reason to believe that subsystems asymptotically in equilibrium at their own temperatures even despite of the arbitrary difference in temperatures within the whole system., Comment: 31 pages, 6 figures

Another way to evaluate the spectral-correlation properties of thermal fields of solids is suggested. Such a method takes into account detailed structure of the interface transition layer separating one bulk region from those of the vacuum region. The principal element here is the surface linear response function of an arbitrary inhomogeneous electron subsystem of solids. Along with straightforward using the known response functions, for example in a hydrodynamic approach, the suggested method allows calculating the response functions self-consistently based on the time dependent density functional theory. The self-consistent calculation of the linear response function followed by an application of the fluctuation-dissipation theorem yield in the spectral power densities of the fluctuating charge and current correlation functions. The final step of this sequence of actions aiming in obtaining the spectral-correlation properties of thermal fields of solids at any distances., Comment: 17 pages, 3 figures

The paper is devoted to the thermodynamics of normal surface electromagnetic fields within a nonuniform dispersive and absorptive system. This system is formed by vacuum and lossy medium separated by a plane interface. As a medium, we used dielectric and metal samples characterized by local and nonlocal optical properties. Thermodynamic properties of surface eigenmodes of plane interfaces are discussed. Various definitions of density of states and spectral characteristics of surface polaritons in equilibrium at the interface formed by vacuum and lossy medium are described and discussed. All formulas for thermodynamic functions are represented in terms of density of states. The generalized density of states is calculated based on the Barash-Ginzburg theory and dispersion relations for the surface states in different approaches. It is exemplified that different definitions of the density of states are identical in the case of dissipationless materials. The spectral functions and integrated over all frequencies thermodynamic characteristics and their temperature dependences are demonstrated., Comment: 35 pages, 15 figures

System of the quantum Langevin equations for two quantum coupling oscillators within independent heat baths of quantum oscillators are obtained using a model Hamiltonian and corresponding Heisenberg equations of motion. Expressions for mean energy of coupled oscillators and their mean energy of interaction are derived and analyzed. Nonmonotonic dependence of the interaction energy versus a coupling constant is demonstrated and explained. Nontrivial dependence of the quantities as a consequence of the difference in temperatures of heat baths is shown., Comment: 13 pages, 3 figures

For two nearby pulsars, formed close to the galactic plane, their host open stellar clusters have been found., Comment: 7 pages, 3 figures, LATEX

Isolated electrons resting near a helium surface have a spectrum close to that of a quantum-defect atom. A precisely solvable model with Rydberg spectrum is sugguested and discussed., Comment: 4 pages, LaTex

Solutions, exactly expressed in terms of elementary functions (unique Laughlin states), of the correlated motion problem for a pair of 2D-electrons in a constant and uniform magnetic field have been shown to exist for a certain relation between the magnetic field induction and the electron charge. Arguments that can help to understand the physical meaning of these remarkable magnetic field values have been provided. The special interest to this problem is justified by the importance of the new state of matter recently observed., Comment: 6 pages, 3 figures, LATEX. Accepted for publication in Vest. Mosk. Univ., Fiz. Astron