824 research outputs found
Field Theory on Quantum Plane
We build the defomation of plane on a product of two copies of
algebras of functions on the plane. This algebra constains a subalgebra of
functions on the plane. We present general scheme (which could be used as well
to construct quaternion from pairs of complex numbers) and we use it to derive
differential structures, metric and discuss sample field theoretical models.Comment: LaTeX, 10 page
Spontaneous emission of non-dispersive Rydberg wave packets
Non dispersive electronic Rydberg wave packets may be created in atoms
illuminated by a microwave field of circular polarization. We discuss the
spontaneous emission from such states and show that the elastic incoherent
component (occuring at the frequency of the driving field) dominates the
spectrum in the semiclassical limit, contrary to earlier predictions. We
calculate the frequencies of single photon emissions and the associated rates
in the "harmonic approximation", i.e. when the wave packet has approximately a
Gaussian shape. The results agree well with exact quantum mechanical
calculations, which validates the analytical approach.Comment: 14 pages, 4 figure
Nonuniversality in level dynamics
Statistical properties of parametric motion in ensembles of Hermitian banded
random matrices are studied. We analyze the distribution of level velocities
and level curvatures as well as their correlation functions in the crossover
regime between three universality classes. It is shown that the statistical
properties of level dynamics are in general non-universal and strongly depend
on the way in which the parametric dynamics is introduced.Comment: 24 pages + 10 figures (not included, avaliable from the author),
submitted to Phys. Rev.
Statistical properties of energy levels of chaotic systems: Wigner or non-Wigner
For systems whose classical dynamics is chaotic, it is generally believed
that the local statistical properties of the quantum energy levels are well
described by Random Matrix Theory. We present here two counterexamples - the
hydrogen atom in a magnetic field and the quartic oscillator - which display
nearest neighbor statistics strongly different from the usual Wigner
distribution. We interpret the results with a simple model using a set of
regular states coupled to a set of chaotic states modeled by a random matrix.Comment: 10 pages, Revtex 3.0 + 4 .ps figures tar-compressed using uufiles
package, use csh to unpack (on Unix machine), to be published in Phys. Rev.
Let
Moduli-Space Dynamics of Noncommutative Abelian Sigma-Model Solitons
In the noncommutative (Moyal) plane, we relate exact U(1) sigma-model
solitons to generic scalar-field solitons for an infinitely stiff potential.
The static k-lump moduli space C^k/S_k features a natural K"ahler metric
induced from an embedding Grassmannian. The moduli-space dynamics is blind
against adding a WZW-like term to the sigma-model action and thus also applies
to the integrable U(1) Ward model. For the latter's two-soliton motion we
compare the exact field configurations with their supposed moduli-space
approximations. Surprisingly, the two do not match, which questions the
adiabatic method for noncommutative solitons.Comment: 1+15 pages, 2 figures; v2: reference added, to appear in JHE
Many-body Anderson localization in one dimensional systems
We show, using quasi-exact numerical simulations, that Anderson localization
of one-dimensional particles in a disordered potential survives in the presence
of attractive interaction between particles. The localization length of the
composite particle can be computed analytically for weak disorder and is in
good agreement with the quasi-exact numerical observations using Time Evolving
Block Decimation. Our approach allows for simulation of the entire experiment
including the final measurement of all atom positions.Comment: 12pp, 5 fig, version accepted in NJ
- …