15 research outputs found
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 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 ) 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