11,806 research outputs found
Bijective enumeration of some colored permutations given by the product of two long cycles
Let be the permutation on symbols defined by $\gamma_n = (1\
2\...\ n)\betannp\gamma_n \beta^{-1}\frac{1}{n- p+1}\alpha\gamma_n\alphamn+1$, an
unexpected connection previously found by several authors by means of algebraic
methods. Moreover, our bijection allows us to refine the latter result with the
cycle type of the permutations.Comment: 22 pages. Version 1 is a short version of 12 pages, entitled "Linear
coefficients of Kerov's polynomials: bijective proof and refinement of
Zagier's result", published in DMTCS proceedings of FPSAC 2010, AN, 713-72
The second critical point for the Perfect Bose gas in quasi-one-dimensional traps
We present a new model of quasi-one-dimensional trap with some unknown
physical predictions about a second transition, including about a change in
fractions of condensed coherence lengths due to the existence of a second
critical temperature Tm < Tc. If this physical model is acceptable, we want to
challenge experimental physicists in this regard
Dynamics of an Open System for Repeated Harmonic Perturbation
We use the Kossakowski-Lindblad-Davies formalism to consider an open system
defined as the Markovian extension of one-mode quantum oscillator S, perturbed
by a piecewise stationary harmonic interaction with a chain of oscillators C.
The long-time asymptotic behaviour of various subsystems of S+C are obtained in
the framework of the dual W-dynamical system approach
Random point field approach to analysis of anisotropic Bose-Einstein condensations
Position distributions of constituent particles of the perfect Bose-gas
trapped in exponentially and polynomially anisotropic boxes are investigated by
means of the boson random point fields (processes) and by the spatial random
distribution of particle density. Our results include the case of
\textit{generalised} Bose-Einstein Condensation. For exponentially anisotropic
quasi two-dimensional system (SLAB), we obtain \textit{three} qualitatively
different particle density distributions. They correspond to the
\textit{normal} phase, the quasi-condensate phase (type III generalised
condensation) and to the phase when the type III and the type I Bose
condensations co-exist. An interesting feature is manifested by the type II
generalised condensation in one-directional polynomially anisotropic system
(BEAM). In this case the particle density distribution rests truly random even
in the \textit{macroscopic} scaling limit
Escape of mass in zero-range processes with random rates
We consider zero-range processes in with site dependent jump
rates. The rate for a particle jump from site to in is
given by , where is a probability in
, is a bounded nondecreasing function of the number
of particles in and is a collection of i.i.d.
random variables with values in , for some . For almost every
realization of the environment the zero-range process has product
invariant measures parametrized by ,
the average total jump rate from any given site. The density of a measure,
defined by the asymptotic average number of particles per site, is an
increasing function of . There exists a product invariant measure , with maximal density. Let be a probability measure
concentrating mass on configurations whose number of particles at site
grows less than exponentially with . Denoting by the
semigroup of the process, we prove that all weak limits of as are dominated, in the natural partial
order, by . In particular, if dominates , then converges to .
The result is particularly striking when the maximal density is finite and the
initial measure has a density above the maximal.Comment: Published at http://dx.doi.org/10.1214/074921707000000300 in the IMS
Lecture Notes Monograph Series
(http://www.imstat.org/publications/lecnotes.htm) by the Institute of
Mathematical Statistics (http://www.imstat.org
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