9,036 research outputs found
Collective modes of a harmonically trapped one-dimensional Bose gas: the effects of finite particle number and nonzero temperature
Following the idea of the density functional approach, we develop a
generalized Bogoliubov theory of an interacting Bose gas confined in a
one-dimensional harmonic trap, by using a local chemical potential - calculated
with the Lieb-Liniger exact solution - as the exchange energy. At zero
temperature, we use the theory to describe collective modes of a
finite-particle system in all interaction regimes from the ideal gas limit, to
the mean-field Thomas-Fermi regime, and to the strongly interacting
Tonks-Girardeau regime. At finite temperature, we investigate the temperature
dependence of collective modes in the weak-coupling regime by means of a
Hartree-Fock-Bogoliubov theory with Popov approximation. By emphasizing the
effects of finite particle number and nonzero temperature on collective mode
frequencies, we make comparisons of our results with the recent experimental
measurement [E. Haller et al., Science 325, 1224 (2009)] and some previous
theoretical predictions. We show that the experimental data are still not fully
explained within current theoretical framework.Comment: 10 pages, 8 figure
Particle collisions in the lower dimensional rotating black hole space-time with the cosmological constant
In this paper, we study the effect of ultra-high energy collisions of two
particles with different energies near the horizon of a 2+1 dimensional BTZ
black hole (BSW effect). We find that the particle with the critical angular
momentum could exist inside the outer horizon of BTZ black hole regardless of
the particle energy. Therefore, for the non-extremal BTZ black hole, the BSW
process is possible on the inner horizon with the fine tuning of parameters
which are characterized by the motion of particle. While for the extremal BTZ
black hole, the particle with the critical angular momentum could only exist on
the degenerate horizon, and the BSW process could also happen there.Comment: 12 pages,3 figure
Possible singlet and triplet superconductivity on honeycomb lattice
We study the possible superconducting pairing symmetry mediated by spin and
charge fluctuations on the honeycomb lattice using the extended Hubbard model
and the random-phase-approximation method. From to doping levels,
a spin-singlet -wave is shown to be the leading
superconducting pairing symmetry when only the on-site Coulomb interaction
is considered, with the gap function being a mixture of the nearest-neighbor
and next-nearest-neighbor pairings. When the offset of the energy level between
the two sublattices exceeds a critical value, the most favorable pairing is a
spin-triplet -wave which is mainly composed of the next-nearest-neighbor
pairing. We show that the next-nearest-neighbor Coulomb interaction is also
in favor of the spin-triplet -wave pairing.Comment: 6 pages, 4 figure
Statistics of Chaotic Resonances in an Optical Microcavity
Distributions of eigenmodes are widely concerned in both bounded and open
systems. In the realm of chaos, counting resonances can characterize the
underlying dynamics (regular vs. chaotic), and is often instrumental to
identify classical-to-quantum correspondence. Here, we study, both
theoretically and experimentally, the statistics of chaotic resonances in an
optical microcavity with a mixed phase space of both regular and chaotic
dynamics. Information on the number of chaotic modes is extracted by counting
regular modes, which couple to the former via dynamical tunneling. The
experimental data are in agreement with a known semiclassical prediction for
the dependence of the number of chaotic resonances on the number of open
channels, while they deviate significantly from a purely
random-matrix-theory-based treatment, in general. We ascribe this result to the
ballistic decay of the rays, which occurs within Ehrenfest time, and
importantly, within the timescale of transient chaos. The present approach may
provide a general tool for the statistical analysis of chaotic resonances in
open systems.Comment: 5 pages, 5 figures, and a supplemental informatio
Inverse Projection Representation and Category Contribution Rate for Robust Tumor Recognition
Sparse representation based classification (SRC) methods have achieved
remarkable results. SRC, however, still suffer from requiring enough training
samples, insufficient use of test samples and instability of representation. In
this paper, a stable inverse projection representation based classification
(IPRC) is presented to tackle these problems by effectively using test samples.
An IPR is firstly proposed and its feasibility and stability are analyzed. A
classification criterion named category contribution rate is constructed to
match the IPR and complete classification. Moreover, a statistical measure is
introduced to quantify the stability of representation-based classification
methods. Based on the IPRC technique, a robust tumor recognition framework is
presented by interpreting microarray gene expression data, where a two-stage
hybrid gene selection method is introduced to select informative genes.
Finally, the functional analysis of candidate's pathogenicity-related genes is
given. Extensive experiments on six public tumor microarray gene expression
datasets demonstrate the proposed technique is competitive with
state-of-the-art methods.Comment: 14 pages, 19 figures, 10 table
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