18,356 research outputs found
Statistical Properties of Interacting Bose Gases in Quasi-2D Harmonic Traps
The analytical probability distribution of the quasi-2D (and purely 2D) ideal
and interacting Bose gas are investigated by using a canonical ensemble
approach. Using the analytical probability distribution of the condensate, the
statistical properties such as the mean occupation number and particle number
fluctuations of the condensate are calculated. Researches show that there is a
continuous crossover of the statistical properties from a quasi-2D to a purely
2D ideal or interacting gases. Different from the case of a 3D Bose gas, the
interaction between atoms changes in a deep way the nature of the particle
number fluctuations.Comment: RevTex, 10pages, 4 figures, E-mail: [email protected]
Navigation in a small world with local information
It is commonly known that there exist short paths between vertices in a
network showing the small-world effect. Yet vertices, for example, the
individuals living in society, usually are not able to find the shortest paths,
due to the very serious limit of information. To theoretically study this
issue, here the navigation process of launching messages toward designated
targets is investigated on a variant of the one-dimensional small-world network
(SWN). In the network structure considered, the probability of a shortcut
falling between a pair of nodes is proportional to , where is
the lattice distance between the nodes. When , it reduces to the SWN
model with random shortcuts. The system shows the dynamic small-world (SW)
effect, which is different from the well-studied static SW effect. We study the
effective network diameter, the path length as a function of the lattice
distance, and the dynamics. They are controlled by multiple parameters, and we
use data collapse to show that the parameters are correlated. The central
finding is that, in the one-dimensional network studied, the dynamic SW effect
exists for . For each given value of in this
region, the point that the dynamic SW effect arises is ,
where is the number of useful shortcuts and is the average
reduced (effective) length of them.Comment: 10 pages, 5 figures, accepted for publication in Physical Review
Anomalous particle-number fluctuations in a three-dimensional interacting Bose-Einstein condensate
The particle-number fluctuations originated from collective excitations are
investigated for a three-dimensional, repulsively interacting Bose-Einstein
condensate (BEC) confined in a harmonic trap. The contribution due to the
quantum depletion of the condensate is calculated and the explicit expression
of the coefficient in the formulas denoting the particle-number fluctuations is
given. The results show that the particle-number fluctuations of the condensate
follow the law and the fluctuations vanish when
temperature approaches to the BEC critical temperature.Comment: RevTex, 4 page
Warped embeddings between Einstein manifolds
Warped embeddings from a lower dimensional Einstein manifold into a higher
dimensional one are analyzed. Explicit solutions for the embedding metrics are
obtained for all cases of codimension 1 embeddings and some of the codimension
n>1 cases. Some of the interesting features of the embedding metrics are
pointed out and potential applications of the embeddings are discussed.Comment: 12 pages, to appear in Mod. Phys. Lett.
The Microsoft 2017 Conversational Speech Recognition System
We describe the 2017 version of Microsoft's conversational speech recognition
system, in which we update our 2016 system with recent developments in
neural-network-based acoustic and language modeling to further advance the
state of the art on the Switchboard speech recognition task. The system adds a
CNN-BLSTM acoustic model to the set of model architectures we combined
previously, and includes character-based and dialog session aware LSTM language
models in rescoring. For system combination we adopt a two-stage approach,
whereby subsets of acoustic models are first combined at the senone/frame
level, followed by a word-level voting via confusion networks. We also added a
confusion network rescoring step after system combination. The resulting system
yields a 5.1\% word error rate on the 2000 Switchboard evaluation set
Collective spin waves in arrays of Permalloy nanowires with single-side periodically modulated width
We have experimentally and numerically investigated the dispersion of
collective spin waves prop-agating through arrays of longitudinally magnetized
nanowires with periodically modulated width. Two nanowire arrays with
single-side modulation and different periodicity of modulation were studied and
compared to the nanowires with homogeneous width. The spin-wave dispersion,
meas-ured up to the third Brillouin zone of the reciprocal space, revealed the
presence of two dispersive modes for the width-modulated NWs, whose amplitude
of magnonic band depends on the modula-tion periodicity, and a set of
nondispersive modes at higher frequency. These findings are different from
those observed in homogeneous width NWs where only the lowest mode exhibits
sizeable dis-persion. The measured spin-wave dispersion has been satisfactorily
reproduced by means of dynam-ical matrix method. Results presented in this work
are important in view of the possible realization of frequency tunable magnonic
device
Entropy, Dynamics and Instantaneous Normal Modes in a Random Energy Model
It is shown that the fraction f of imaginary frequency instantaneous normal
modes (INM) may be defined and calculated in a random energy model(REM) of
liquids. The configurational entropy S and the averaged hopping rate among the
states R are also obtained and related to f, with the results R~f and
S=a+b*ln(f). The proportionality between R and f is the basis of existing INM
theories of diffusion, so the REM further confirms their validity. A link to S
opens new avenues for introducing INM into dynamical theories. Liquid 'states'
are usually defined by assigning a configuration to the minimum to which it
will drain, but the REM naturally treats saddle-barriers on the same footing as
minima, which may be a better mapping of the continuum of configurations to
discrete states. Requirements of a detailed REM description of liquids are
discussed
- …