18 research outputs found
Drifting diffusion on a circle as continuous limit of a multiurn Ehrenfest model
We study the continuous limit of a multibox Erhenfest urn model proposed
before by the authors. The evolution of the resulting continuous system is
governed by a differential equation, which describes a diffusion process on a
circle with a nonzero drifting velocity. The short time behavior of this
diffusion process is obtained directly by solving the equation, while the long
time behavior is derived using the Poisson summation formula. They reproduce
the previous results in the large (number of boxes) limit. We also discuss
the connection between this diffusion equation and the Schrdinger
equation of some quantum mechanical problems.Comment: 4 pages prevtex4 file, 1 eps figur
Poincar\'{e} cycle of a multibox Ehrenfest urn model with directed transport
We propose a generalized Ehrenfest urn model of many urns arranged
periodically along a circle. The evolution of the urn model system is governed
by a directed stochastic operation. Method for solving an -ball, -urn
problem of this model is presented. The evolution of the system is studied in
detail. We find that the average number of balls in a certain urn oscillates
several times before it reaches a stationary value. This behavior seems to be a
peculiar feature of this directed urn model. We also calculate the Poincar\'{e}
cycle, i.e., the average time interval required for the system to return to its
initial configuration. The result can be easily understood by counting the
total number of all possible microstates of the system.Comment: 10 pages revtex file with 7 eps figure
Dynamics of vibrofluidized granular gases in periodic structures
The behavior of a driven granular gas in a container consisting of
connected compartments is studied employing a microscopic kinetic model. After
obtaining the governing equations for the occupation numbers and the granular
temperatures of each compartment we consider the various dynamical regimes. The
system displays interesting analogies with the ordering processes of phase
separating mixtures quenched below the their critical point. In particular, we
show that below a certain value of the driving intensity the populations of the
various compartments become unequal and the system clusterizes. Such a
phenomenon is not instantaneous, but is characterized by a time scale, ,
which follows a Vogel-Vulcher exponential behavior. On the other hand, the
reverse phenomenon which involves the ``evaporation'' of a cluster due to the
driving force is also characterized by a second time scale which diverges at
the limit of stability of the cluster.Comment: 11 pages, 17 figure
Transition Temperature of the Interacting Dipolar Bose Gas
[[abstract]]We investigate the effects of long-ranged dipole-dipole potential on the transition temperature of a weakly interacting Bose gas. We apply the two-fluid model to derive the energy spectra of the thermal and the condensate parts. From the interaction modified spectra of the system, the formula for the shift of transition temperature was derived. Compared to the conventional weakly interacting Bose system with contact potential only where thermal effect is larger, we find that the condensate effect is about two times that of the thermal part in the dipolar system. Due to the relative smallness of dipole-dipole interaction with respect to the contact interaction in current dipolar Bose-Einstein condensation, we suggest to measure the dipolar effect by tuning the scattering length to negligible small by the Feshbach resonance technique
Poincar� Cycle of an Ehrenfest Multiurn Model in a One-dimensional Ring
[[abstract]]We study an Ehrenfest multiurn model of a one-dimensional ring, generalizing the directed transport in the previous model to arbitrary transports. We analytically study the evolution of the system and calculate the Poincar� cycle for given transport probabilities. The result shows that the average number of balls in an urn evolves according to the transport probability, but the Poincar� cycle is only related to the initial configuration
Adomian's Decomposition Method for Eigenvalue Problems
[[abstract]]We extend the Adomian’s decomposition method to work for the general eigenvalue problems, in addition to the existing applications of the method to boundary and initial value problems with nonlinearity. We develop the Hamiltonian inverse iteration method which will provide the ground state eigenvalue and the explicit form eigenfunction within a few iterations. The method for finding the excited states is also proposed. We present a space partition method for the case that the usual way of series expansion failed to converge
Transition Temperature of a Weakly Interacting Bose Gas
[[abstract]]We report a theoretical study of the transition temperature of a trapped interacting dilute Bose gas. The system is treated like a two-fluid model consisting of a thermal component and a condensate component. Through the calculation of the energy spectra, the origins of various effects on the transition temperature are derived. We found that the interactive shift is affected by both the thermal component and the condensate component. The latter effect, which is about 34% of the former, has never been reported so far. With these two effects, our calculated interactive shift agrees very well with the recent measurement
LOW-TEMPERATURE SERIES EXPANSIONS FOR SQUARE-LATTICE ISING MODEL WITH FIRST AND SECOND NEIGHBOUR INTERACTIONS
[[abstract]]We have calculated the low-temperature series expansions of the spontaneous magnetization and the zero-field susceptibility of the square-lattice ferromagnetic Ising model with first-neighbour interaction J1 and second-neighbour interaction J2 to the 30th and 26th order respectively by computer. Our results extend the previous calculations by Lee and Lin to six more orders. We use the Pad� approximants to estimate the critical exponents and the critical temperature for different ratios of R = J2/J1. The estimated critical temperature as a function of R agrees with the estimation by Oitmaa from high-temperature series expansions
Boundary and Particle Number Effects on the Thermodynamic Properties of Trapped Ideal Bose Gases
[[abstract]]The ideal noninteracting Bose gases trapped in a generic power-law potential in an anydimensional
space are studied. We present theoretical results of the corrections of thermodynamic properties
due to finite particle number effects. The calculation uses the Euler-Maclaurin approximation to
simplify the condensate fraction, and it also uses the Maslov index to discuss the boundary effect. Recently
BEC (Bose-Einstein Condensation) has also been observed in a microelectronic chip; therefore,
with a similar microstructure, we can obtain the effects of a rigid wall in a trap that have never been
found before