90,028 research outputs found
Local conjugacy classes for analytic torus flows
If a real-analytic flow on the multidimensional torus close enough to linear
has a unique rotation vector which satisfies an arithmetical condition Y, then
it is analytically conjugate to linear. We show this by proving that the orbit
under renormalization of a constant Y vector field attracts all nearby orbits
with the same rotation vector.Comment: inc bib
Ensemble averaged coherent state path integral for disordered bosons with a repulsive interaction (Derivation of mean field equations)
We consider bosonic atoms with a repulsive contact interaction in a trap
potential for a Bose-Einstein condensation and additionally include a random
potential. The ensemble averages for two models of static and dynamic disorder
are performed and investigated in parallel. The bosonic many body systems of
the two disorder models are represented by coherent state path integrals on the
Keldysh time contour which allow exact ensemble averages for zero and finite
temperatures. These ensemble averages of coherent state path integrals
therefore present alternatives to replica field theories or supersymmetric
averaging techniques
Brownian motion on disconnected sets, basic hypergeometric functions, and some continued fractions of Ramanujan
Motivated by L\'{e}vy's characterization of Brownian motion on the line, we
propose an analogue of Brownian motion that has as its state space an arbitrary
closed subset of the line that is unbounded above and below: such a process
will be a martingale, will have the identity function as its quadratic
variation process, and will be ``continuous'' in the sense that its sample
paths don't skip over points. We show that there is a unique such process,
which turns out to be automatically a reversible Feller-Dynkin Markov process.
We find its generator, which is a natural generalization of the operator
. We then consider the special case where the state space is
the self-similar set for some .
Using the scaling properties of the process, we represent the Laplace
transforms of various hitting times as certain continued fractions that appear
in Ramanujan's ``lost'' notebook and evaluate these continued fractions in
terms of basic hypergeometric functions (that is, -analogues of classical
hypergeometric functions). The process has 0 as a regular instantaneous point,
and hence its sample paths can be decomposed into a Poisson process of
excursions from 0 using the associated continuous local time. Using the
reversibility of the process with respect to the natural measure on the state
space, we find the entrance laws of the corresponding It\^{o} excursion measure
and the Laplace exponent of the inverse local time -- both again in terms of
basic hypergeometric functions. By combining these ingredients, we obtain
explicit formulae for the resolvent of the process. We also compute the moments
of the process in closed form. Some of our results involve -analogues of
classical distributions such as the Poisson distribution that have appeared
elsewhere in the literature.Comment: Published in at http://dx.doi.org/10.1214/193940307000000383 the IMS
Collections (http://www.imstat.org/publications/imscollections.htm) by the
Institute of Mathematical Statistics (http://www.imstat.org
Solving spin quantum-master equations with matrix continued-fraction methods: application to superparamagnets
We implement continued-fraction techniques to solve exactly quantum master
equations for a spin with arbitrary S coupled to a (bosonic) thermal bath. The
full spin density matrix is obtained, so that along with relaxation and
thermoactivation, coherent dynamics is included (precession, tunnel, etc.). The
method is applied to study isotropic spins and spins in a bistable anisotropy
potential (superparamagnets). We present examples of static response, the
dynamical susceptibility including the contribution of the different relaxation
modes, and of spin resonance in transverse fields.Comment: Resubmitted to J. Phys. A: Math. Gen. Some rewriting here and there.
Discussion on positivity in App.D3 at request of one refere
- …