Density of states of a two-dimensional electron gas in a non-quantizing magnetic field

We study local density of electron states of a two-dimentional conductor with a smooth disorder potential in a non-quantizing magnetic field, which does not cause the standart de Haas-van Alphen oscillations. It is found, that despite the influence of such ``classical'' magnetic field on the average electron density of states (DOS) is negligibly small, it does produce a significant effect on the DOS correlations. The corresponding correlation function exhibits oscillations with the characteristic period of cyclotron quantum $\hbar\omega_c$.Comment: 7 pages, including 3 figure

Algebras generated by two bounded holomorphic functions

We study the closure in the Hardy space or the disk algebra of algebras generated by two bounded functions, of which one is a finite Blaschke product. We give necessary and sufficient conditions for density or finite codimension of such algebras. The conditions are expressed in terms of the inner part of a function which is explicitly derived from each pair of generators. Our results are based on identifying z-invariant subspaces included in the closure of the algebra. Versions of these results for the case of the disk algebra are given.Comment: 22 pages ; a number of minor mistakes have been corrected, and some points clarified. Conditionally accepted by Journal d'Analyse Mathematiqu

Theory of microwave-induced oscillations in the magnetoconductivity of a 2D electron gas

We develop a theory of magnetooscillations in the photoconductivity of a two-dimensional electron gas observed in recent experiments. The effect is governed by a change of the electron distribution function induced by the microwave radiation. We analyze a nonlinearity with respect to both the dc field and the microwave power, as well as the temperature dependence determined by the inelastic relaxation rate.Comment: Extended version of cond-mat/0310668. 12 pages, 4 figures. V2: published version (minor changes, Fig. 4 corrected, references added

Analytical model for laser-assisted recombination of hydrogenic atoms

We introduce a new method that allows one to obtain an analytical cross section for the laser-assisted electron-ion collision in a closed form. As an example we perform a calculation for the hydrogen laser-assisted recombination. The $S$-matrix element for the process is constructed from an exact electron Coulomb-Volkov wave function and an approximate laser modified hydrogen state. An explicit expression for the field-enhancement coefficient of the process is expressed in terms of the dimensionless parameter $\kappa= |{e\epsilon_{0}}/{q\omega_{0}}|^{2}$, where $e$ and $q$ are the electron charge and momentum respectively, and $\epsilon_{0}$ and $\omega_{0}$ are the amplitude and frequency of the laser field respectively. The simplified version of the cross section of the process is derived and analyzed within a soft photon approximation.Comment: 10 page

Interaction-induced oscillations of the tunneling density of states in a non-quantizing magnetic field

We study tunneling into interacting disordered two-dimensional electron gas in a non-quantizing magnetic field, which does not cause the standard de Haas-- van Alphen oscillations. Interaction induces a new type of oscillations in the tunneling density of states with the characteristic period of cyclotron quantum.Comment: 4 pages, 1 .eps figure, submitted to Phys. Rev. Let

Pointwise consistency of the kriging predictor with known mean and covariance functions

This paper deals with several issues related to the pointwise consistency of the kriging predictor when the mean and the covariance functions are known. These questions are of general importance in the context of computer experiments. The analysis is based on the properties of approximations in reproducing kernel Hilbert spaces. We fix an erroneous claim of Yakowitz and Szidarovszky (J. Multivariate Analysis, 1985) that the kriging predictor is pointwise consistent for all continuous sample paths under some assumptions.Comment: Submitted to mODa9 (the Model-Oriented Data Analysis and Optimum Design Conference), 14th-19th June 2010, Bertinoro, Ital

Tunneling ``zero-bias'' anomaly in the quasi-ballistic regime

For the first time, we study the tunneling density of states (DOS) of the interacting electron gas beyond the diffusive limit. A strong correction to the DOS persists even at electron energies exceeding the inverse transport relaxation time, which could not be expected from the well-known Altshuler-Aronov-Lee (AAL) theory. This correction originates from the interference between the electron waves scattered by an impurity and by the Friedel oscillation this impurity creates. Account for such processes also revises the AAL formula for the DOS in the diffusive limit.Comment: 4 pages, 2 .eps figures, submitted to Phys. Rev. Let

Intersubband Electron Interaction in 1D-2D Junctions

We have shown that the electron transport through junctions of one-dimensional and two-dimensional systems, as well as through quantum point contacts, is considerably affected by the interaction of electrons of different subbands. The interaction mechanism is caused by Friedel oscillations, which are produced by electrons of the closed subbands even in smooth junctions. Because of the interaction with these oscillations, electrons of the open subbands experience a backscattering. The electron reflection coefficient, which describes the backscattering, has a sharp peak at the energy equal to the Fermi energy and may be as high as about 0.1. This result allows one to explain a number of available experimental facts.Comment: 5 pages, 3 figure

Distinguished quantum states in a class of cosmological spacetimes and their Hadamard property

In a recent paper, we proved that a large class of spacetimes, not necessarily homogeneous or isotropous and relevant at a cosmological level, possesses a preferred codimension one submanifold, i.e., the past cosmological horizon, on which it is possible to encode the information of a scalar field theory living in the bulk. Such bulk-to-boundary reconstruction procedure entails the identification of a preferred quasifree algebraic state for the bulk theory, enjoying remarkable properties concerning invariance under isometries (if any) of the bulk and energy positivity, and reducing to well-known vacua in standard situations. In this paper, specialising to open FRW models, we extend previously obtained results and we prove that the preferred state is of Hadamard form, hence the backreaction on the metric is finite and the state can be used as a starting point for renormalisation procedures. That state could play a distinguished role in the discussion of the evolution of scalar fluctuations of the metric, an analysis often performed in the development of any model describing the dynamic of an early Universe which undergoes an inflationary phase of rapid expansion in the past.Comment: 41 page

Topology of the gauge-invariant gauge field in two-color QCD

We investigate solutions to a nonlinear integral equation which has a central role in implementing the non-Abelian Gauss's Law and in constructing gauge-invariant quark and gluon fields. Here we concern ourselves with solutions to this same equation that are not operator-valued, but are functions of spatial variables and carry spatial and SU(2) indices. We obtain an expression for the gauge-invariant gauge field in two-color QCD, define an index that we will refer to as the ``winding number'' that characterizes it, and show that this winding number is invariant to a small gauge transformation of the gauge field on which our construction of the gauge-invariant gauge field is based. We discuss the role of this gauge field in determining the winding number of the gauge-invariant gauge field. We also show that when the winding number of the gauge field is an integer $\ell{\neq}0$, the gauge-invariant gauge field manifests winding numbers that are not integers, and are half-integers only when $\ell=0$.Comment: 26 pages including 6 encapsulated postscript figures. Numerical errors have been correcte