86,401 research outputs found
Van der Waals phase transition in the framework of holography
Phase structure of the quintessence Reissner-Nordstr\"{o}m-AdS black hole is
probed with the nonlocal observables such as holographic entanglement entropy
and two point correlation function. Our result shows that, as the case of the
thermal entropy, both the observables exhibit the similar Van der Waals-like
phase transition. To reinforce the conclusion, we further check the equal area
law for the first order phase transition and critical exponent of the heat
capacity for the second order phase transition. We also discuss the effect of
the state parameter on the phase structure of the nonlocal observables.Comment: 16 pages, 6 figures. arXiv admin note: text overlap with
arXiv:1511.0038
Testing the Sphericity of a covariance matrix when the dimension is much larger than the sample size
This paper focuses on the prominent sphericity test when the dimension is
much lager than sample size . The classical likelihood ratio test(LRT) is no
longer applicable when . Therefore a Quasi-LRT is proposed and
asymptotic distribution of the test statistic under the null when
is well established in this paper.
Meanwhile, John's test has been found to possess the powerful {\it
dimension-proof} property, which keeps exactly the same limiting distribution
under the null with any -asymptotic, i.e. ,
. All asymptotic results are derived for general population
with finite fourth order moment. Numerical experiments are implemented for
comparison
Holographic Van der Waals-like phase transition in the Gauss-Bonnet gravity
The Van der Waals-like phase transition is observed in temperature-thermal
entropy plane in spherically symmetric charged Gauss-Bonnet-AdS black hole
background. In terms of AdS/CFT, the non-local observables such as holographic
entanglement entropy, Wilson loop, and two point correlation function of very
heavy operators in the field theory dual to spherically symmetric charged
Gauss-Bonnet-AdS black hole have been investigated. All of them exhibit the Van
der Waals-like phase transition for a fixed charge parameter or Gauss-Bonnet
parameter in such gravity background. Further, with choosing various values of
charge or Gauss-Bonnet parameter, the equal area law and the critical exponent
of the heat capacity are found to be consistent with phase structures in
temperature-thermal entropy plane.Comment: Some statements about the analogy between the black hole phase
transition in plane and Van der Waals-like phase transition in
plane are added. This is the published versio
Phase transition of holographic entanglement entropy in massive gravity
The phase structure of holographic entanglement entropy is studied in massive
gravity for the quantum systems with finite and infinite volumes, which in the
bulk is dual to calculate the minimal surface area for a black hole and black
brane respectively. In the entanglement entropytemperature plane, we find
for both the black hole and black brane there is a Van der Waals-like phase
transition as the case in thermal entropytemperature plane. That is, there
is a first order phase transition for the small charge and a second order phase
transition at the critical charge. For the first order phase transition, the
equal area law is checked and for the second order phase transition, the
critical exponent of the heat capacity is obtained. All the results show that
the phase structure of holographic entanglement entropy is the same as that of
thermal entropy regardless of the volume of the spacetime on the boundary.Comment: 15 pages, many figures, some statments are adde
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