1,884 research outputs found
Galois Groups in Rational Conformal Field Theory
It was established before that fusion rings in a rational conformal field
theory (RCFT) can be described as rings of polynomials, with integer
coefficients, modulo some relations. We use the Galois group of these relations
to obtain a local set of equation for the points of the fusion variety. These
equations are sufficient to classify all the RCFT, Galois group by Galois
group. It is shown that the Galois group is equivalent to the pseudo RCFT
group. We prove that the Galois groups encountered in RCFT are all abelian,
implying solvability by radicals of the modular matrix.Comment: 24 pages. Typos correcte
Semiclassical Description of Tunneling in Mixed Systems: The Case of the Annular Billiard
We study quantum-mechanical tunneling between symmetry-related pairs of
regular phase space regions that are separated by a chaotic layer. We consider
the annular billiard, and use scattering theory to relate the splitting of
quasi-degenerate states quantized on the two regular regions to specific paths
connecting them. The tunneling amplitudes involved are given a semiclassical
interpretation by extending the billiard boundaries to complex space and
generalizing specular reflection to complex rays. We give analytical
expressions for the splittings, and show that the dominant contributions come
from {\em chaos-assisted}\/ paths that tunnel into and out of the chaotic
layer.Comment: 4 pages, uuencoded postscript file, replaces a corrupted versio
Semiclassical dynamics and long time asymptotics of the central-spin problem in a quantum dot
The spin of an electron trapped in a quantum dot is a promising candidate
implementation of a qubit for quantum information processing. We study the
central spin problem of the effect of the hyperfine interaction between such an
electron and a large number of nuclear moments. Using a spin coherent path
integral, we show that in this limit the electron spin evolution is well
described by classical dynamics of both the nuclear and electron spins. We then
introduce approximate yet systematic methods to analyze aspects of the
classical dynamics, and discuss the importance of the exact integrability of
the central spin Hamiltonian. This is compared with numerical simulation.
Finally, we obtain the asymptotic long time decay of the electron spin
polarization. We show that this is insensitive to integrability, and determined
instead by the transfer of angular momentum to very weakly coupled spins far
from the center of the quantum dot. The specific form of the decay is shown to
depend sensitively on the form of the electronic wavefunction.Comment: 13 pages, 4 figures, accepted by PR
Neutrino neutral reaction on 4He, effects of final state interaction and realistic NN force
The inelastic neutral reaction of neutrino on 4He is calculated
microscopically, including full final state interaction among the four
nucleons. The calculation is performed using the Lorentz integral transform
(LIT) method and the hyperspherical-harmonic effective interaction approach
(EIHH), with a realistic nucleon-nucleon interaction. A detailed energy
dependent calculation is given in the impulse approximation. With respect to
previous calculations, this work predicts an increased reaction cross-section
by 10%-30% for neutrino temperature up to 15 MeV.Comment: 4 pages, 2 fig
Monte--Carlo Thermodynamic Bethe Ansatz
We introduce a Monte--Carlo simulation approach to thermodynamic Bethe ansatz
(TBA). We exemplify the method on one particle integrable models, which include
a free boson and a free fermions systems along with the scaling Lee--Yang model
(SLYM). It is confirmed that the central charges and energies are correct to a
very good precision, typically 0.1% or so. The advantage of the method is that
it enables the calculation of all the dimensions and even the particular
partition function.Comment: 22 pages. Added a footnote and realizations for the minimal models.
Fortran program, mont-s.f90, available from the source lin
A Meta-Algorithm for Creating Fast Algorithms for Counting ON Cells in Odd-Rule Cellular Automata
We develop a meta-algorithm that, given a polynomial (in one or more
variables), and a prime p, produces a fast (logarithmic time) algorithm that
takes a positive integer n and outputs the number of times each residue class
modulo p appears as a coefficient when the polynomial is raised to the power n
and the coefficients are read modulo p.Comment: 8 pages, accompanied by a Maple package, and numerous input and
output files that can be gotten from
http://www.math.rutgers.edu/~zeilberg/mamarim/mamarimhtml/CAcount.htm
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