627 research outputs found
Off-diagonal long-range order, cycle probabilities, and condensate fraction in the ideal Bose gas
We discuss the relationship between the cycle probabilities in the
path-integral representation of the ideal Bose gas, off-diagonal long-range
order, and Bose--Einstein condensation. Starting from the Landsberg recursion
relation for the canonic partition function, we use elementary considerations
to show that in a box of size L^3 the sum of the cycle probabilities of length
k >> L^2 equals the off-diagonal long-range order parameter in the
thermodynamic limit. For arbitrary systems of ideal bosons, the integer
derivative of the cycle probabilities is related to the probability of
condensing k bosons. We use this relation to derive the precise form of the
\pi_k in the thermodynamic limit. We also determine the function \pi_k for
arbitrary systems. Furthermore we use the cycle probabilities to compute the
probability distribution of the maximum-length cycles both at T=0, where the
ideal Bose gas reduces to the study of random permutations, and at finite
temperature. We close with comments on the cycle probabilities in interacting
Bose gases.Comment: 6 pages, extensive rewriting, new section on maximum-length cycle
Critical Current Peaks at in Superconductors with Columnar Defects: Recrystalizing the Interstitial Glass
The role of commensurability and the interplay of correlated disorder and
interactions on vortex dynamics in the presence of columnar pins is studied via
molecular dynamics simulations. Simulations of dynamics reveal substantial
caging effects and a non-monotonic dependence of the critical current with
enhancements near integer values of the matching field and
in agreement with experiments on the cuprates. We find qualitative
differences in the phase diagram for small and large values of the matching
field.Comment: 5 pages, 4 figures (3 color
Statistical mechanics of lossy compression using multilayer perceptrons
Statistical mechanics is applied to lossy compression using multilayer
perceptrons for unbiased Boolean messages. We utilize a tree-like committee
machine (committee tree) and tree-like parity machine (parity tree) whose
transfer functions are monotonic. For compression using committee tree, a lower
bound of achievable distortion becomes small as the number of hidden units K
increases. However, it cannot reach the Shannon bound even where K -> infty.
For a compression using a parity tree with K >= 2 hidden units, the rate
distortion function, which is known as the theoretical limit for compression,
is derived where the code length becomes infinity.Comment: 12 pages, 5 figure
Mean properties and Free Energy of a few hard spheres confined in a spherical cavity
We use analytical calculations and event-driven molecular dynamics
simulations to study a small number of hard sphere particles in a spherical
cavity. The cavity is taken also as the thermal bath so that the system
thermalizes by collisions with the wall. In that way, these systems of two,
three and four particles, are considered in the canonical ensemble. We
characterize various mean and thermal properties for a wide range of number
densities. We study the density profiles, the components of the local pressure
tensor, the interface tension, and the adsorption at the wall. This spans from
the ideal gas limit at low densities to the high-packing limit in which there
are significant regions of the cavity for which the particles have no access,
due the conjunction of excluded volume and confinement. The contact density and
the pressure on the wall are obtained by simulations and compared to exact
analytical results. We also obtain the excess free energy for N=4, by using a
simulated-assisted approach in which we combine simulation results with the
knowledge of the exact partition function for two and three particles in a
spherical cavity.Comment: 11 pages, 9 figures and two table
Adding a Myers Term to the IIB Matrix Model
We show that Yang-Mills matrix integrals remain convergent when a Myers term
is added, and stay in the same topological class as the original model. It is
possible to add a supersymmetric Myers term and this leaves the partition
function invariant.Comment: 8 pages, v2 2 refs adde
Two-dimensional Superfluidity and Localization in the Hard-Core Boson Model: a Quantum Monte Carlo Study
Quantum Monte Carlo simulations are used to investigate the two-dimensional
superfluid properties of the hard-core boson model, which show a strong
dependence on particle density and disorder. We obtain further evidence that a
half-filled clean system becomes superfluid via a finite temperature
Kosterlitz-Thouless transition. The relationship between low temperature
superfluid density and particle density is symmetric and appears parabolic
about the half filling point. Disorder appears to break the superfluid phase up
into two distinct localized states, depending on the particle density. We find
that these results strongly correlate with the results of several experiments
on high- superconductors.Comment: 10 pages, 3 figures upon request, RevTeX version 3, (accepted for
Phys. Rev. B
Ultracold Bosonic Atoms in Disordered Optical Superlattices
The influence of disorder on ultracold atomic Bose gases in quasiperiodic
optical lattices is discussed in the framework of the one-dimensional
Bose-Hubbard model. It is shown that simple periodic modulations of the well
depths generate a rich phase diagram consisting of superfluid, Mott insulator,
Bose-glass and Anderson localized phases. The detailed evolution of mean
occupation numbers and number fluctuations as function of modulation amplitude
and interaction strength is discussed. Finally, the signatures of the different
phases, especially of the Bose-glass phase, in matter-wave interference
experiments are investigated.Comment: 4 pages, 4 figures, using REVTEX
Polyakov Lines in Yang-Mills Matrix Models
We study the Polyakov line in Yang-Mills matrix models, which include the
IKKT model of IIB string theory. For the gauge group SU(2) we give the exact
formulae in the form of integral representations which are convenient for
finding the asymptotic behaviour. For the SU(N) bosonic models we prove upper
bounds which decay as a power law at large momentum p. We argue that these
capture the full asymptotic behaviour. We also indicate how to extend the
results to some correlation functions of Polyakov lines.Comment: 19 pages, v2 typos corrected, v3 ref adde
Multifractality and percolation in the coupling space of perceptrons
The coupling space of perceptrons with continuous as well as with binary
weights gets partitioned into a disordered multifractal by a set of random input patterns. The multifractal spectrum can be
calculated analytically using the replica formalism. The storage capacity and
the generalization behaviour of the perceptron are shown to be related to
properties of which are correctly described within the replica
symmetric ansatz. Replica symmetry breaking is interpreted geometrically as a
transition from percolating to non-percolating cells. The existence of empty
cells gives rise to singularities in the multifractal spectrum. The analytical
results for binary couplings are corroborated by numerical studies.Comment: 13 pages, revtex, 4 eps figures, version accepted for publication in
Phys. Rev.
On the conditions for the existence of Perfect Learning and power law in learning from stochastic examples by Ising perceptrons
In a previous letter, we studied learning from stochastic examples by
perceptrons with Ising weights in the framework of statistical mechanics. Under
the one-step replica symmetry breaking ansatz, the behaviours of learning
curves were classified according to some local property of the rules by which
examples were drawn. Further, the conditions for the existence of the Perfect
Learning together with other behaviors of the learning curves were given. In
this paper, we give the detailed derivation about these results and further
argument about the Perfect Learning together with extensive numerical
calculations.Comment: 28 pages, 43 figures. Submitted to J. Phys.
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