H-theorem in quantum physics

Remarkable progress of quantum information theory (QIT) allowed to formulate mathematical theorems for conditions that data-transmitting or data-processing occurs with a non-negative entropy gain. However, relation of these results formulated in terms of entropy gain in quantum channels to temporal evolution of real physical systems is not thoroughly understood. Here we build on the mathematical formalism provided by QIT to formulate the quantum H-theorem in terms of physical observables. We discuss the manifestation of the second law of thermodynamics in quantum physics and uncover special situations where the second law can be violated. We further demonstrate that the typical evolution of energy-isolated quantum systems occurs with non-diminishing entropy.Comment: 8 pages, 4 figure

Spin Polarization Phenomena and Pseudospin Quantum Hall Ferromagnetism in the HgTe Quantum Well

The parallel field of a full spin polarization of the electron gas in a \Gamma8 conduction band of the HgTe quantum well was obtained from the magnetoresistance by three different ways in a zero and quasi-classical range of perpendicular field component Bper. In the quantum Hall range of Bper the spin polarization manifests in anticrossings of magnetic levels, which were found to strongly nonmonotonously depend on Bper.Comment: to be published in AIP Conf. Proc.: 15-th International Conference on Narrow Gap Systems (NGS-15

The Degenerate Parametric Oscillator and Ince's Equation

We construct Green's function for the quantum degenerate parametric oscillator in terms of standard solutions of Ince's equation in a framework of a general approach to harmonic oscillators. Exact time-dependent wave functions and their connections with dynamical invariants and SU(1,1) group are also discussed.Comment: 10 pages, no figure

Elastično raspršenje piona na polariziranom 3He u energijskom području ∆-rezonancije

The π3He interaction for the polarized target is studied in the fixed-centers approximation with all rescatterings included. Only the P33 wave is taken for the πN interaction. The nuclear wave function is taken either as a sum of Gaussians or as a Faddeev wave function in the s-wave approximation. The asymmetries for elastic π + 3He scattering at the lab energies Tπ =142, 180 and 256 MeV are calculated. The results are compared with experimental data.Razmatra se π3He interakcija s polariziranom metom u približenju nepomičnih središta, uključujući sva višestruka raspršenja. Za πN interakciju uzima se samo P33 val. Nuklearna se valna funkcija uzima bilo kao zbroj Gaussovih funkcija ili kao Faddeeva valna funkcija u aproksimaciji s-vala. Izračunali smo asimetrije za elastično π +3He raspršenje za laboratorijske energije Tπ =142, 180 i 256 MeV. Rezultati se uspoređuju s eksperimentalnim podacima

Elastično raspršenje piona na polariziranom 3He u energijskom području ∆-rezonancije

The π3He interaction for the polarized target is studied in the fixed-centers approximation with all rescatterings included. Only the P33 wave is taken for the πN interaction. The nuclear wave function is taken either as a sum of Gaussians or as a Faddeev wave function in the s-wave approximation. The asymmetries for elastic π + 3He scattering at the lab energies Tπ =142, 180 and 256 MeV are calculated. The results are compared with experimental data.Razmatra se π3He interakcija s polariziranom metom u približenju nepomičnih središta, uključujući sva višestruka raspršenja. Za πN interakciju uzima se samo P33 val. Nuklearna se valna funkcija uzima bilo kao zbroj Gaussovih funkcija ili kao Faddeeva valna funkcija u aproksimaciji s-vala. Izračunali smo asimetrije za elastično π +3He raspršenje za laboratorijske energije Tπ =142, 180 i 256 MeV. Rezultati se uspoređuju s eksperimentalnim podacima

Renormalization Group Functions for Two-Dimensional Phase Transitions: To the Problem of Singular Contributions

According to the available publications, the field theoretical renormalization group (RG) approach in the two-dimensional case gives the critical exponents that differ from the known exact values. This fact was attempted to explain by the existence of nonanalytic contributions in the RG functions. The situation is analysed in this work using a new algorithm for summing divergent series that makes it possible to analyse dependence of the results for the critical exponents on the expansion coefficients for RG functions. It has been shown that the exact values of all the exponents can be obtained with a reasonable form of the coefficient functions. These functions have small nonmonotonities or inflections, which are poorly reproduced in natural interpolations. It is not necessary to assume the existence of singular contributions in RG functions.Comment: PDF, 11 page

The Minimum-Uncertainty Squeezed States for for Atoms and Photons in a Cavity

We describe a six-parameter family of the minimum-uncertainty squeezed states for the harmonic oscillator in nonrelativistic quantum mechanics. They are derived by the action of corresponding maximal kinematical invariance group on the standard ground state solution. We show that the product of the variances attains the required minimum value 1/4 only at the instances that one variance is a minimum and the other is a maximum, when the squeezing of one of the variances occurs. The generalized coherent states are explicitly constructed and their Wigner function is studied. The overlap coefficients between the squeezed, or generalized harmonic, and the Fock states are explicitly evaluated in terms of hypergeometric functions. The corresponding photons statistics are discussed and some applications to quantum optics, cavity quantum electrodynamics, and superfocusing in channeling scattering are mentioned. Explicit solutions of the Heisenberg equations for radiation field operators with squeezing are found.Comment: 27 pages, no figures, 174 references J. Phys. B: At. Mol. Opt. Phys., Special Issue celebrating the 20th anniversary of quantum state engineering (R. Blatt, A. Lvovsky, and G. Milburn, Guest Editors), May 201