26,724 research outputs found
Non-Extensive Bose-Einstein Condensation Model
The imperfect Boson gas supplemented with a gentle repulsive interaction is
completely solved. In particular it is proved that it has non-extensive
Bose-Einstein condensation, i.e., there is condensation without macroscopic
occupation of the ground state (k=0) level
Exchange Monte Carlo Method and Application to Spin Glass Simulations
We propose an efficient Monte Carlo algorithm for simulating a
``hardly-relaxing" system, in which many replicas with different temperatures
are simultaneously simulated and a virtual process exchanging configurations of
these replica is introduced. This exchange process is expected to let the
system at low temperatures escape from a local minimum. By using this algorithm
the three-dimensional Ising spin glass model is studied. The ergodicity
time in this method is found much smaller than that of the multi-canonical
method. In particular the time correlation function almost follows an
exponential decay whose relaxation time is comparable to the ergodicity time at
low temperatures. It suggests that the system relaxes very rapidly through the
exchange process even in the low temperature phase.Comment: 10 pages + uuencoded 5 Postscript figures, REVTe
Forming peculiarities and manifestation of tectonic faults in soft rocks
Features of distribution of tectonic structures in soft rocks confirm the presence of horizontal tectonic forces in the formation of faults and are based on the manifestation of their morphological features. Linear dependences of the amplitude on the length of tectonic dislocation in the area of wedging were obtained as a result of mathematical processing of the experimental data. Actual position of the crossing lines of fault plane with the seam were considered while studying the distribution of co-fault fracturing. Analysis of the data confirms that the distribution of faulting has an undulating character. Analysis of observations showed that the deviation of the crossing line of fault plane with the seam from the middle line is subject to the normal law of random variable distribution. Thus, the studies and the obtained results allow planning mining operations assessing the utility while developing fault areas
The Canonical Perfect Bose Gas in Casimir Boxes
We study the problem of Bose-Einstein condensation in the perfect Bose gas in
the canonical ensemble, in anisotropically dilated rectangular parallelpipeds
(Casimir boxes). We prove that in the canonical ensemble for these anisotropic
boxes there is the same type of generalized Bose-Einstein condensation as in
the grand-canonical ensemble for the equivalent geometry. However the amount of
condensate in the individual states is different in some cases and so are the
fluctuations.Comment: 23 page
Optimization problems involving the first Dirichlet eigenvalue and the torsional rigidity
We present some open problems and obtain some partial results for spectral
optimization problems involving measure, torsional rigidity and first Dirichlet
eigenvalue.Comment: 18 pages, 4 figure
Large deviations for ideal quantum systems
We consider a general d-dimensional quantum system of non-interacting
particles, with suitable statistics, in a very large (formally infinite)
container. We prove that, in equilibrium, the fluctuations in the density of
particles in a subdomain of the container are described by a large deviation
function related to the pressure of the system. That is, untypical densities
occur with a probability exponentially small in the volume of the subdomain,
with the coefficient in the exponent given by the appropriate thermodynamic
potential. Furthermore, small fluctuations satisfy the central limit theorem.Comment: 28 pages, LaTeX 2
Parallelization of Markov chain generation and its application to the multicanonical method
We develop a simple algorithm to parallelize generation processes of Markov
chains. In this algorithm, multiple Markov chains are generated in parallel and
jointed together to make a longer Markov chain. The joints between the
constituent Markov chains are processed using the detailed balance. We apply
the parallelization algorithm to multicanonical calculations of the
two-dimensional Ising model and demonstrate accurate estimation of
multicanonical weights.Comment: 15 pages, 5 figures, uses elsart.cl
On the minimization of Dirichlet eigenvalues of the Laplace operator
We study the variational problem \inf \{\lambda_k(\Omega): \Omega\
\textup{open in}\ \R^m,\ |\Omega| < \infty, \ \h(\partial \Omega) \le 1 \},
where is the 'th eigenvalue of the Dirichlet Laplacian
acting in , \h(\partial \Omega) is the - dimensional
Hausdorff measure of the boundary of , and is the Lebesgue
measure of . If , and , then there exists a convex
minimiser . If , and if is a minimiser,
then is also a
minimiser, and is connected. Upper bounds are
obtained for the number of components of . It is shown that if
, and then has at most components.
Furthermore is connected in the following cases : (i) (ii) and (iii) and (iv) and
. Finally, upper bounds on the number of components are obtained for
minimisers for other constraints such as the Lebesgue measure and the torsional
rigidity.Comment: 16 page
Numerical study of Yang-Mills classical solutions on the twisted torus
We use the lattice cooling method to investigate the structure of some gauge
fixed SU(2) Yang-Mills classical solutions of the euclidean equations of motion
which are defined in the 3-torus with symmetric twisted boundary conditions.Comment: 20pp (fig.included
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