4,519 research outputs found
Determining efficient temperature sets for the simulated tempering method
In statistical physics, the efficiency of tempering approaches strongly
depends on ingredients such as the number of replicas , reliable
determination of weight factors and the set of used temperatures, . For the simulated tempering (SP) in
particular -- useful due to its generality and conceptual simplicity -- the
latter aspect (closely related to the actual ) may be a key issue in
problems displaying metastability and trapping in certain regions of the phase
space. To determine 's leading to accurate thermodynamics
estimates and still trying to minimize the simulation computational time, here
it is considered a fixed exchange frequency scheme for the ST. From the
temperature of interest , successive 's are chosen so that the exchange
frequency between any adjacent pair and has a same value .
By varying the 's and analyzing the 's through relatively
inexpensive tests (e.g., time decay toward the steady regime), an optimal
situation in which the simulations visit much faster and more uniformly the
relevant portions of the phase space is determined. As illustrations, the
proposal is applied to three lattice models, BEG, Bell-Lavis, and Potts, in the
hard case of extreme first-order phase transitions, always giving very good
results, even for . Also, comparisons with other protocols (constant
entropy and arithmetic progression) to choose the set are
undertaken. The fixed exchange frequency method is found to be consistently
superior, specially for small 's. Finally, distinct instances where the
prescription could be helpful (in second-order transitions and for the parallel
tempering approach) are briefly discussed.Comment: 10 pages, 14 figure
Quantum effective force in an expanding infinite square-well potential and Bohmian perspective
The Schr\"{o}dinger equation is solved for the case of a particle confined to
a small region of a box with infinite walls. If walls of the well are moved,
then, due to an effective quantum nonlocal interaction with the boundary, even
though the particle is nowhere near the walls, it will be affected. It is shown
that this force apart from a minus sign is equal to the expectation value of
the gradient of the quantum potential for vanishing at the walls boundary
condition. Variation of this force with time is studied. A selection of Bohmian
trajectories of the confined particle is also computed.Comment: 7 figures, Accepted by Physica Script
Matter-wave 2D solitons in crossed linear and nonlinear optical lattices
It is demonstrated the existence of multidimensional matter-wave solitons in
a crossed optical lattice (OL) with linear OL in the direction and
nonlinear OL (NOL) in the direction, where the NOL can be generated by a
periodic spatial modulation of the scattering length using an optically induced
Feshbach resonance. In particular, we show that such crossed linear and
nonlinear OL allows to stabilize two-dimensional (2D) solitons against decay or
collapse for both attractive and repulsive interactions. The solutions for the
soliton stability are investigated analytically, by using a multi-Gaussian
variational approach (VA), with the Vakhitov-Kolokolov (VK) necessary criterion
for stability; and numerically, by using the relaxation method and direct
numerical time integrations of the Gross-Pitaevskii equation (GPE). Very good
agreement of the results corresponding to both treatments is observed.Comment: 8 pages (two-column format), with 16 eps-files of 4 figure
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