424 research outputs found
Dynamical Universal Behavior in Quantum Chaotic Systems
We discover numerically that a moving wave packet in a quantum chaotic
billiard will always evolve into a quantum state, whose density probability
distribution is exponential. This exponential distribution is found to be
universal for quantum chaotic systems with rigorous proof. In contrast, for the
corresponding classical system, the distribution is Gaussian. We find that the
quantum exponential distribution can smoothly change to the classical Gaussian
distribution with coarse graining.Comment: 4 figure
Phase transitions, geometrothermodynamics and critical exponents of black holes with conformal anomaly
We investigate the phase transitions of black holes with conformal anomaly in
canonical ensemble from different perspectives. Some interesting and novel
phase transition phenomena have been discovered. Firstly, we discuss the
behavior of the specific heat and the inverse of the isothermal
compressibility. It is shown that there are striking differences in Hawking
temperature and phase structure between black holes with conformal anomaly and
those without it. In the case with conformal anomaly, there exists local
minimum temperature corresponding to the phase transition point. Phase
transitions take place not only from an unstable large black hole to a locally
stable medium black hole but also from an unstable medium black hole to a
locally stable small black hole. Secondly, we probe in details the dependence
of phase transitions on the choice of parameters. The results show that black
holes with conformal anomaly have much richer phase structure than those
without it. There would be two, only one or no phase transition points
depending on the parameters we have chosen. The corresponding parameter region
are derived both numerically and graphically. Thirdly, geometrothermodynamics
are built up to examine the phase structure we have discovered. It is shown
that Legendre invariant thermodynamic scalar curvature diverges exactly where
the specific heat diverges. Furthermore, critical behaviors are investigated by
calculating the relevant critical exponents. It is proved that these critical
exponents satisfy the thermodynamic scaling laws, leading to the conclusion
that critical exponents and the scaling laws can reserve even when we consider
conformal anomaly.Comment: some new references adde
Non-extended phase space thermodynamics of Lovelock AdS black holes in grand canonical ensemble
Recently, extended phase space thermodynamics of Lovelock AdS black holes has
been of great interest. To provide insight from a different perspective and
gain a unified phase transition picture, non-extended phase space
thermodynamics of -dimensional charged topological Lovelock AdS black
holes is investigated detailedly in the grand canonical ensemble. Specifically,
the specific heat at constant electric potential is calculated and phase
transition in the grand canonical ensemble is discussed. To probe the impact of
the various parameters, we utilize the control variate method and solve the
phase transition condition equation numerically for the case . There
are two critical points for the case while there is only one for
other cases. For , there exists no phase transition point. To figure out
the nature of phase transition in the grand canonical ensemble, we carry out an
analytic check of the analog form of Ehrenfest equations proposed by Banerjee
et al. It is shown that Lovelock AdS black holes in the grand canonical
ensemble undergo a second order phase transition. To examine the phase
structure in the grand canonical ensemble, we utilize the thermodynamic
geometry method and calculate both the Weinhold metric and Ruppeiner metric. It
is shown that for both analytic and graphical results that the divergence
structure of the Ruppeiner scalar curvature coincides with that of the specific
heat. Our research provides one more example that Ruppeiner metric serves as a
wonderful tool to probe the phase structures of black holes
P-V criticality of conformal anomaly corrected AdS black holes
The effects of conformal anomaly on the thermodynamics of black holes are
investigated in this Letter from the perspective of criticality of AdS
black holes. Treating the cosmological constant as thermodynamic pressure, we
extend the recent research to the extended phase space. Firstly, we study the
- criticality of the uncharged AdS black holes with conformal anomaly and
find that conformal anomaly does not influence whether there exists Van der
Waals like critical behavior. Secondly, we investigate the - criticality
of the charged cases and find that conformal anomaly influences not only the
critical physical quantities but also the ratio . The ratio
is no longer a constant as before but a function of conformal anomaly parameter
. We also show that the conformal parameter should satisfy a
certain range to guarantee the existence of critical point that has physical
meaning. Our results show the effects of conformal anomaly
P-V Criticality of Topological Black Holes in Lovelock-Born-Infeld Gravity
To understand the effect of third order Lovelock gravity, criticality
of topological AdS black holes in Lovelock-Born-Infeld gravity is investigated.
The thermodynamics is further explored with some more extensions and details
than the former literature. A detailed analysis of the limit case
is performed for the seven-dimensional black holes. It
is shown that for the spherical topology, criticality exists for both the
uncharged and charged cases. Our results demonstrate again that the charge is
not the indispensable condition of criticality. It may be attributed to
the effect of higher derivative terms of curvature because similar phenomenon
was also found for Gauss-Bonnet black holes. For , there would be no
criticality. Interesting findings occur in the case , in which positive
solutions of critical points are found for both the uncharged and charged
cases. However, the diagram is quite strange. To check whether these
findings are physical, we give the analysis on the non-negative definiteness
condition of entropy. It is shown that for any nontrivial value of ,
the entropy is always positive for any specific volume . Since no
criticality exists for in Einstein gravity and Gauss-Bonnet gravity, we
can relate our findings with the peculiar property of third order Lovelock
gravity. The entropy in third order Lovelock gravity consists of extra terms
which is absent in the Gauss-Bonnet black holes, which makes the critical
points satisfy the constraint of non-negative definiteness condition of
entropy. We also check the Gibbs free energy graph and the "swallow tail"
behavior can be observed. Moreover, the effect of nonlinear electrodynamics is
also included in our research.Comment: 13 pages, 7 figure
BattRAE: Bidimensional Attention-Based Recursive Autoencoders for Learning Bilingual Phrase Embeddings
In this paper, we propose a bidimensional attention based recursive
autoencoder (BattRAE) to integrate clues and sourcetarget interactions at
multiple levels of granularity into bilingual phrase representations. We employ
recursive autoencoders to generate tree structures of phrases with embeddings
at different levels of granularity (e.g., words, sub-phrases and phrases). Over
these embeddings on the source and target side, we introduce a bidimensional
attention network to learn their interactions encoded in a bidimensional
attention matrix, from which we extract two soft attention weight distributions
simultaneously. These weight distributions enable BattRAE to generate
compositive phrase representations via convolution. Based on the learned phrase
representations, we further use a bilinear neural model, trained via a
max-margin method, to measure bilingual semantic similarity. To evaluate the
effectiveness of BattRAE, we incorporate this semantic similarity as an
additional feature into a state-of-the-art SMT system. Extensive experiments on
NIST Chinese-English test sets show that our model achieves a substantial
improvement of up to 1.63 BLEU points on average over the baseline.Comment: 7 pages, accepted by AAAI 201
Critical correlations in an ultracold Bose gas revealed by means of a temporal Talbot-Lau interferometer
We study experimentally the critical correlation in an ultra-cold Bose gas
with a temporal Talbot-Lau (TL) interferometer. Near the critical temperature,
we observe a bi-modal density distribution in an ultra-cold Bose gas after the
application of the TL interferometer. The measured fraction of the narrower
peak in the density distribution displays a clear peak within the critical
regime. The peak position agrees with the critical temperature calculated with
the finite-size and interaction corrections. The critical exponents are
extracted from the peak and they agree with the critical exponents for the
correlation length.Comment: 5 pages, 3 figures and supplemental materia
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