Abstract:
We present a description of finite dimensional quantum entanglement, based on a study of the space of all convex decompositions of a given density matrix. On this space we construct a system of real polynomial equations describing separable states. We further study this system using statistical mechanical methods. Finally, we apply our techniques to Werner states of two qubits and obtain a sufficient criterion for separability.

Abstract:
It is known that homogeneous distribution of particles in Coulomb-like systems can be unstable, and spatially inhomogeneous structures can be formed. A simple method for describing such inhomogeneous systems and obtaining spacial distributions of electron density is proposed and applied to the case of two-dimensional electron systems on surface of liquid helium. A free energy functional for the model in mean field approximation is obtained. Creation of various types of structures, such as long-range periodical modulation and multi-electron dimples, is predicted by minimizing this functional.

Abstract:
Thermodynamic properties of liquids and liquid mixtures play very important role in understanding the nature of molecular interactions occurring in the system. In the present work different thermodynamic properties of 15 pure liquids and 34 equimolar binary liquid mixtures of benzene, toluene, p-xylene, chlorobenzene and 1-chloronaphthalene with linear and branched alkanes have been computed with the help of Flory’s statistical theory (FST), Hard sphere equation of state (HSE) and Hole theory (HT) simultaneously. The calculated values are compared with the experimental findings collected from literature and quite satisfactory results are obtained.

Abstract:
We apply the statistical mechanical approach based on the ``flat'' measure proposed by Edwards and coworkers to the parking lot model, a model that reproduces the main features of the phenomenology of vibrated granular materials. We first build the flat measure for the case of vanishingly small tapping strength and then generalize the approach to finite tapping strengths by introducing a new ``thermodynamic'' parameter, the available volume for particle insertion, in addition to the particle density. This description is able to take into account the various memory effects observed in vibrated granular media. Although not exact, the approach gives a good description of the behavior of the parking-lot model in the regime of slow compaction.

Abstract:
We present results of theoretical description of ultrasonic phenomena in molecular liquids. In particular, we are interested in the development of microscopical, i.e., statistical-mechanical framework capable to explain the long living puzzle of the excess ultrasonic absorption in liquids. Typically, ultrasonic wave in a liquid can be generated by applying the periodically alternating external pressure with the angular frequency that corresponds to the ultrasound. If the perturbation introduced by such process is weak - its statistical-mechanical treatment can be done with the use of the linear response theory. We treat the liquid as a system of interacting sites, so that all the response/aftereffect functions as well as the energy dissipation and generalized (wave-vector and frequency dependent) ultrasonic absorption coefficient are obtained in terms of familiar site-site static and time correlation functions such as static structure factors or intermediate scattering functions. To express the site-site intermediate scattering functions we refer to the site-site memory equations in the mode-coupling approximation for the first-order memory kernels, while equilibrium properties such as site-site static structure factors, direct and total correlation functions are deduced from the integral equation theory of molecular liquids known as RISM or one of its generalizations. All the formalism is phrased in a general manner, hence the obtained results are expected to work for arbitrary type of molecular liquid including simple, ionic, polar, and non-polar liquids.

Abstract:
We propose to introduce a new stochastic process in molecular dynamics in order to improve the description of the nucleon emission process from a hot nucleus. We give momentum fluctuations originating from the momentum width of the nucleon wave packet to the nucleon stochastically when it is being emitted from the nucleus. We show by calculating the liquid gas phase equilibrium in the case of antisymmetrized molecular dynamics, that with this improvement, we can recover the quantum mechanical statistical property of the nucleus for the particle emission process.

Abstract:
In this paper, applying the spinor representation of the electromagnetic field, we present a quantum-mechanical description of waveguides. As an example of application, a potential qubit generated via photon tunneling is discussed.

Abstract:
We present a general theory of electric field effects in liquid crystals where the dielectric tensor depends on the orientation order. As applications, we examine (i) the director fluctuations in nematic states in electric field for arbitrary strength of the dielectric anisotropy and (ii) deformation of the nematic order around a charged particle. Some predictions are made for these effects.

Abstract:
It is shown that the statistical conception of quantum mechanics is dynamical but not probabilistic, i.e. the statistical description in quantum mechanics is founded on dynamics. A use of the probability theory, when it takes place, is auxiliary. Attention is drawn to the fact that in the quantum mechanics there are two different objects: an individual object to be statistically described and a statistical average object, which is a result of the statistical description. Identification of the two different objects (a use of the same term for both) is an origin of many known quantum mechanics paradoxes.

Abstract:
A general theoretical description of the magnetic resonance is given. General formulas describing a behavior of all components of the polarization vector at the magnetic resonance are derived in the case of an arbitrary initial polarization. The equations obtained are exact on condition that the nonresonance rotating field is neglected. The spin dynamics is also calculated at frequencies far from resonance without neglecting the above-mentioned field. A quantum-mechanical analysis of the spin evolution at the magnetic resonance is fulfilled and the full agreement between the classical and quantum-mechanical approaches is proven. Distinguishing features of magnetic and quasimagnetic resonances for nuclei and particles moving in accelerators and storage rings which include resonances caused by the electric dipole moment are considered.