48,466 research outputs found
Inelastic scattering of atoms in a double well
We study a mixture of two light spin-1/2 fermionic atoms and two heavy atoms
%in a Mott state in a double well potential. Inelastic scattering processes
between both atomic species excite the heavy atoms and renormalize the
tunneling rate and the interaction of the light atoms (polaron effect). The
effective interaction of the light atoms changes its sign and becomes
attractive for strong inelastic scattering. This is accompanied by a crossing
of the energy levels from singly occupied sites at weak inelastic scattering to
a doubly occupied and an empty site for stronger inelastic scattering. We are
able to identify the polaron effect and the level crossing in the quantum
dynamics.Comment: 12 pages, 9 figure
The random geometry of equilibrium phases
This is a (long) survey about applications of percolation theory in
equilibrium statistical mechanics. The chapters are as follows:
1. Introduction
2. Equilibrium phases
3. Some models
4. Coupling and stochastic domination
5. Percolation
6. Random-cluster representations
7. Uniqueness and exponential mixing from non-percolation
8. Phase transition and percolation
9. Random interactions
10. Continuum modelsComment: 118 pages. Addresses: [email protected]
http://www.mathematik.uni-muenchen.de/~georgii.html [email protected]
http://www.math.chalmers.se/~olleh [email protected]
Critical behavior of the massless free field at the depinning transition
We consider the d-dimensional massless free field localized by a
delta-pinning of strength e. We study the asymptotics of the variance of the
field, and of the decay-rate of its 2-point function, as e goes to zero, for
general Gaussian interactions. Physically speaking, we thus rigorously obtain
the critical behavior of the transverse and longitudinal correlation lengths of
the corresponding d+1-dimensional effective interface model in a non-mean-field
regime. We also describe the set of pinned sites at small e, for a broad class
of d-dimensional massless models
Stochastic domination: the contact process, Ising models and FKG measures
We prove for the contact process on , and many other graphs, that the
upper invariant measure dominates a homogeneous product measure with large
density if the infection rate is sufficiently large. As a
consequence, this measure percolates if the corresponding product measure
percolates. We raise the question of whether domination holds in the symmetric
case for all infinite graphs of bounded degree. We study some asymmetric
examples which we feel shed some light on this question. We next obtain
necessary and sufficient conditions for domination of a product measure for
``downward'' FKG measures. As a consequence of this general result, we show
that the plus and minus states for the Ising model on dominate the same
set of product measures. We show that this latter fact fails completely on the
homogenous 3-ary tree. We also provide a different distinction between
and the homogenous 3-ary tree concerning stochastic domination and Ising
models; while it is known that the plus states for different temperatures on
are never stochastically ordered, on the homogenous 3-ary tree, almost
the complete opposite is the case. Next, we show that on , the set of
product measures which the plus state for the Ising model dominates is strictly
increasing in the temperature. Finally, we obtain a necessary and sufficient
condition for a finite number of variables, which are both FKG and
exchangeable, to dominate a given product measure.Comment: 27 page
Massive neutrinos and cosmology
The present experimental results on neutrino flavour oscillations provide
evidence for non-zero neutrino masses, but give no hint on their absolute mass
scale, which is the target of beta decay and neutrinoless double-beta decay
experiments. Crucial complementary information on neutrino masses can be
obtained from the analysis of data on cosmological observables, such as the
anisotropies of the cosmic microwave background or the distribution of
large-scale structure. In this review we describe in detail how free-streaming
massive neutrinos affect the evolution of cosmological perturbations. We
summarize the current bounds on the sum of neutrino masses that can be derived
from various combinations of cosmological data, including the most recent
analysis by the WMAP team. We also discuss how future cosmological experiments
are expected to be sensitive to neutrino masses well into the sub-eV range.Comment: 122 pages, 23 figures, misprints corrected and references added.
Review article to be published in Physics Report
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