37 research outputs found
Mott transition in lattice boson models
We use mathematically rigorous perturbation theory to study the transition
between the Mott insulator and the conjectured Bose-Einstein condensate in a
hard-core Bose-Hubbard model. The critical line is established to lowest order
in the tunneling amplitude.Comment: 20 page
Shift in critical temperature for random spatial permutations with cycle weights
We examine a phase transition in a model of random spatial permutations which
originates in a study of the interacting Bose gas. Permutations are weighted
according to point positions; the low-temperature onset of the appearance of
arbitrarily long cycles is connected to the phase transition of Bose-Einstein
condensates. In our simplified model, point positions are held fixed on the
fully occupied cubic lattice and interactions are expressed as Ewens-type
weights on cycle lengths of permutations. The critical temperature of the
transition to long cycles depends on an interaction-strength parameter
. For weak interactions, the shift in critical temperature is expected
to be linear in with constant of linearity . Using Markov chain
Monte Carlo methods and finite-size scaling, we find .
This finding matches a similar analytical result of Ueltschi and Betz. We also
examine the mean longest cycle length as a fraction of the number of sites in
long cycles, recovering an earlier result of Shepp and Lloyd for non-spatial
permutations.Comment: v2 incorporated reviewer comments. v3 removed two extraneous figures
which appeared at the end of the PDF
'Return to equilibrium' for weakly coupled quantum systems: a simple polymer expansion
Recently, several authors studied small quantum systems weakly coupled to
free boson or fermion fields at positive temperature. All the approaches we are
aware of employ complex deformations of Liouvillians or Mourre theory (the
infinitesimal version of the former). We present an approach based on polymer
expansions of statistical mechanics. Despite the fact that our approach is
elementary, our results are slightly sharper than those contained in the
literature up to now. We show that, whenever the small quantum system is known
to admit a Markov approximation (Pauli master equation \emph{aka} Lindblad
equation) in the weak coupling limit, and the Markov approximation is
exponentially mixing, then the weakly coupled system approaches a unique
invariant state that is perturbatively close to its Markov approximation.Comment: 23 pages, v2-->v3: Revised version: The explanatory section 1.7 has
changed and Section 3.2 has been made more explici
Phase separation due to quantum mechanical correlations
Can phase separation be induced by strong electron correlations? We present a
theorem that affirmatively answers this question in the Falicov-Kimball model
away from half-filling, for any dimension. In the ground state the itinerant
electrons are spatially separated from the classical particles.Comment: 4 pages, 1 figure. Note: text and figure unchanged, title was
misspelle
Lattice permutations and Poisson-Dirichlet distribution of cycle lengths
We study random spatial permutations on Z^3 where each jump x -> \pi(x) is
penalized by a factor exp(-T ||x-\pi(x)||^2). The system is known to exhibit a
phase transition for low enough T where macroscopic cycles appear. We observe
that the lengths of such cycles are distributed according to Poisson-Dirichlet.
This can be explained heuristically using a stochastic
coagulation-fragmentation process for long cycles, which is supported by
numerical data.Comment: 18 pages, 14 figure