Gell-Mann - Low Function in QED for the arbitrary coupling constant

The Gell-Mann -- Low function \beta(g) in QED (g is the fine structure constant) is reconstructed. At large g, it behaves as \beta_\infty g^\alpha with \alpha\approx 1, \beta_\infty\approx 1.Comment: 5 pages, PD

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

Magnetotransport in Double Quantum Well with Inverted Energy Spectrum: HgTe/CdHgTe

We present the first experimental study of the double-quantum-well (DQW) system made of 2D layers with inverted energy band spectrum: HgTe. The magnetotransport reveals a considerably larger overlap of the conduction and valence subbands than in known HgTe single quantum wells (QW), which may be regulated by an applied gate voltage $V_g$. This large overlap manifests itself in a much higher critical field $B_c$ separating the range above it where the quantum peculiarities shift linearly with $V_g$ and the range below with a complicated behavior. In the latter case the $N$-shaped and double-$N$-shaped structures in the Hall magnetoresistance $\rho_{xy}(B)$ are observed with their scale in field pronouncedly enlarged as compared to the pictures observed in an analogous single QW. The coexisting electrons and holes were found in the whole investigated range of positive and negative $V_g$ as revealed from fits to the low-field $N$-shaped $\rho_{xy}(B)$ and from the Fourier analysis of oscillations in $\rho_{xx}(B)$. A peculiar feature here is that the found electron density $n$ remains almost constant in the whole range of investigated $V_g$ while the hole density $p$ drops down from the value a factor of 6 larger than $n$ at extreme negative $V_g$ to almost zero at extreme positive $V_g$ passing through the charge neutrality point. We show that this difference between $n$ and $p$ stems from an order of magnitude larger density of states for holes in the lateral valence band maxima than for electrons in the conduction band minimum. We interpret the observed reentrant sign-alternating $\rho_{xy}(B)$ between electronic and hole conductivities and its zero resistivity state in the quantum Hall range of fields on the basis of a calculated picture of magnetic levels in a DQW.Comment: 15 pages, 13 figure

Quantum Electrodynamics at Extremely Small Distances

The asymptotics of the Gell-Mann - Low function in QED can be determined exactly, \beta(g)= g at g\to\infty, where g=e^2 is the running fine structure constant. It solves the problem of pure QED at small distances L and gives the behavior g\sim L^{-2}.Comment: Latex, 6 pages, 1 figure include

Asymptotic behavior in the scalar field theory

An asymptotic solution of the system of Schwinger-Dyson equations for four-dimensional Euclidean scalar field theory with interaction $\frac{\lambda}{2}(\phi^*\phi)^2$ is obtained. For $\lambda>\lambda_{cr}=16\pi^2$ the two-particle amplitude has the pathology-free asymptotic behavior at large momenta. For $\lambda<\lambda_{cr}$ the amplitude possesses Landau-type singularity.Comment: 16 pages; journal version; references adde

Analytical realization of finite-size scaling for Anderson localization. Does the band of critical states exist for d>2?

An analytical realization is suggested for the finite-size scaling algorithm based on the consideration of auxiliary quasi-1D systems. Comparison of the obtained analytical results with the results of numerical calculations indicates that the Anderson transition point is splitted into the band of critical states. This conclusion is supported by direct numerical evidence (Edwards and Thouless, 1972; Last and Thouless, 1974; Schreiber, 1985; 1990). The possibility of restoring the conventional picture still exists but requires a radical reinterpretetion of the raw numerical data.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

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