On the distribution of the Wigner time delay in one-dimensional disordered systems

We consider the scattering by a one-dimensional random potential and derive the probability distribution of the corresponding Wigner time delay. It is shown that the limiting distribution is the same for two different models and coincides with the one predicted by random matrix theory. It is also shown that the corresponding stochastic process is given by an exponential functional of the potential.Comment: 11 pages, four references adde

Extended de Sitter Theory of Two Dimensional Gravitational Forces

We present a simple unifying gauge theoretical formulation of gravitational theories in two dimensional spacetime. This formulation includes the effects of a novel matter-gravity coupling which leads to an extended de Sitter symmetry algebra on which the gauge theory is based. Contractions of this theory encompass previously studied cases.Comment: 19pp, no figs., CTP 2228, UCONN-93-

Yang-Mills Solutions on Euclidean Schwarzschild Space

We show that the apparently periodic Charap-Duff Yang-Mills `instantons' in time-compactified Euclidean Schwarzschild space are actually time independent. For these solutions, the Yang-Mills potential is constant along the time direction (no barrier) and therefore, there is no tunneling. We also demonstrate that the solutions found to date are three dimensional monopoles and dyons. We conjecture that there are no time-dependent solutions in the Euclidean Schwarzschild background.Comment: 12 pages, references added, version to appear in PR

Quantum Mechanics and Thermodynamics of Particles with Distance Dependent Statistics

The general notion of distance dependent statistics in anyon-like systems is discussed. The two-body problem for such statistics is considered, the general formula for the second virial coefficient is derived and it is shown that in the limiting cases it reproduces the known results for ideal anyons.Comment: 9 pages, LATEX Kiev Institute for Theoretical Physics preprint ITP-93-5E, January 199

Borel Summation of the Derivative Expansion and Effective Actions

We give an explicit demonstration that the derivative expansion of the QED effective action is a divergent but Borel summable asymptotic series, for a particular inhomogeneous background magnetic field. A duality transformation B\to iE gives a non-Borel-summable perturbative series for a time dependent background electric field, and Borel dispersion relations yield the non-perturbative imaginary part of the effective action, which determines the pair production probability. Resummations of leading Borel approximations exponentiate to give perturbative corrections to the exponents in the non-perturbative pair production rates. Comparison with a WKB analysis suggests that these divergence properties are general features of derivative expansions and effective actions.Comment: 18 pp, Revtex, 2 fig

Perturbative Renormalizations of Anyon Quantum Mechanics

In bosonic end perturbative calculations for quantum mechanical anyon systems a regularization and renormalization procedure, analogous to those used in field theory, is necessary. I examine the reliability and the physical interpretation of the most commonly used bosonic end regularization procedures. I then use the regularization procedure with the most transparent physical interpretation to derive some bosonic end perturbation theory results on anyon spectra, including a 3-anyon ground state energy.Comment: 19 pages, Plain LaTex, MIT-CTP-232

Approximate formula for the ground state energy of anyons in 2D parabolic well

We determine approximate formula for the ground state energy of anyons in 2D parabolic well which is valid for the arbitrary anyonic factor \nu and number of particles N in the system. We assume that centre of mass motion energy is not excluded from the energy of the system. Formula for ground state energy calculated by variational principle contains logarithmic divergence at small distances between two anyons which is regularized by cut-off parameter. By equating this variational formula to the analogous formula of Wu near bosonic limit (\nu ~ 0)we determine the value of the cut-off and thus derive the approximate formula for the ground state energy for the any \nu and N. We checked this formula at \nu=1, when anyons become fermions, for the systems containing two to thirty particles. We find that our approximate formula has an accuracy within 6%. It turns out, at the big number N limit the ground state energy has square root dependence on factor \nu.Comment: 7 page

Analytic calculations of trial wave functions of the fractional quantum Hall effect on the sphere

We present a framework for the analytic calculations of the hierarchical wave functions and the composite fermion wave functions in the fractional quantum Hall effect on the sphere by using projective coordinates. Then we calculate the overlaps between these two wave functions at various fillings and small numbers of electrons. We find that the overlaps are all most equal to one. This gives a further evidence that two theories of the fractional quantum Hall effect, the hierarchical theory and the composite fermion theory, are physically equivalent.Comment: 37 pages, revte

A Note on the Symmetry Reduction of SU(2) on Horizons of Various Topologies

It is known that the SU(2) degrees of freedom manifest in the description of the gravitational field in loop quantum gravity are generally reduced to U(1) degrees of freedom on an $S^2$ isolated horizon. General relativity also allows black holes with planar, toroidal, or higher genus topology for their horizons. These solutions also meet the criteria for an isolated horizon, save for the topological criterion, which is not crucial. We discuss the relevant corresponding symmetry reduction for black holes of various topologies (genus 0 and $\geq 2$) here and discuss its ramifications to black hole entropy within the loop quantum gravity paradigm. Quantities relevant to the horizon theory are calculated explicitly using a generalized ansatz for the connection and densitized triad, as well as utilizing a general metric admitting hyperbolic sub-spaces. In all scenarios, the internal symmetry may be reduced to combinations of U(1).Comment: 13 pages, two figures. Version 2 has several references updated and added, as well as some minor changes to the text. Accepted for publication in Class. Quant. Gra

Landau Analog Levels for Dipoles in the Noncommutative Space and Phase Space

In the present contribution we investigate the Landau analog energy quantization for neutral particles, that possesses a nonzero permanent magnetic and electric dipole moments, in the presence of an homogeneous electric and magnetic external fields in the context of the noncommutative quantum mechanics. Also, we analyze the Landau--Aharonov--Casher and Landau--He--McKellar--Wilkens quantization due to noncommutative quantum dynamics of magnetic and electric dipoles in the presence of an external electric and magnetic fields and the energy spectrum and the eigenfunctions are obtained. Furthermore, we have analyzed Landau quantization analogs in the noncommutative phase space, and we obtain also the energy spectrum and the eigenfunctions in this context.Comment: 20 pages, references adde