26,305 research outputs found
Thermodynamics of two-dimensional conformal field theory dual to black holes
In this note we investigate the first law of thermodynamics of the
two-dimensional conformal field theory (CFT) that is dual to black holes. We
start from the Cardy formula and get the CFT thermodynamics with minimal
reasonable assumptions. We use both the microcanonical ensemble and canonical
ensemble versions of the Cardy formula. In the black hole/CFT correspondence
the black hole is dual to a CFT with excitations, and the black hole mass
and charge correspond to the energy and charge of the excited CFT. The CFT
left- and right-moving central charges should be quantized, and so we
assume that they are mass-independent. Also we assume the difference of the
left- and right-moving sector levels is mass-independent dual to
level matching condition. The thermodynamics of two-dimensional CFT we get is
universal and supports the thermodynamics method of black hole/CFT
correspondence.Comment: 10 page
User Cooperation in Wireless Powered Communication Networks
This paper studies user cooperation in the emerging wireless powered
communication network (WPCN) for throughput optimization. For the purpose of
exposition, we consider a two-user WPCN, in which one hybrid access point
(H-AP) broadcasts wireless energy to two distributed users in the downlink (DL)
and the users transmit their independent information using their individually
harvested energy to the H-AP in the uplink (UL) through
time-division-multiple-access (TDMA). We propose user cooperation in the WPCN
where the user which is nearer to the H-AP and has a better channel for DL
energy harvesting and UL information transmission uses part of its allocated UL
time and DL harvested energy to help to relay the far user's information to the
H-AP, in order to achieve more balanced throughput optimization. We maximize
the weighted sum-rate (WSR) of the two users by jointly optimizing the time and
power allocations in the network for both wireless energy transfer in the DL
and wireless information transmission and relaying in the UL. Simulation
results show that the proposed user cooperation scheme can effectively improve
the achievable throughput in the WPCN with desired user fairness.Comment: 7 figure
Thermodynamics in Black-hole/CFT Correspondence
The area law of Bekenstein-Hawking entropy of the black hole suggests that
the black hole should have a lower-dimensional holographic description. It has
been found recently that a large class of rotating and charged black holes
could be holographically described a two-dimensional (2D) conformal field
theory (CFT). We show that the universal information of the dual CFT, including
the central charges and the temperatures, is fully encoded in the
thermodynamics laws of both outer and inner horizons. These laws,
characterizing how the black hole responds under the perturbation, allows us to
read different dual pictures with respect to different kinds of perturbations.
The remarkable effectiveness of this thermodynamics method suggest that the
inner horizon could play a key role in the study of holographic description of
the black hole.Comment: 8 pages. Essay awarded honourable mention in the Gravity Research
Foundation 2013 Awards for Essays on Gravitatio
On short interval expansion of R\'enyi entropy
R\'enyi entanglement entropy provides a new window to study the AdS/CFT
correspondence. In this paper we consider the short interval expansion of
R\'enyi entanglement entropy in two-dimensional conformal field theory. This
amounts to do the operator product expansion of the twist operators. We focus
on the vacuum Verma module and consider the quasiprimary operators constructed
from the stress tensors. After obtaining the expansion coefficients of the
twist operators to level 6 in vacuum Verma module, we compute the leading
contributions to the R\'enyi entropy, to order 6 in the short interval
expansion. In the case of one short interval on cylinder, we reproduce the
first several leading contributions to the R\'enyi entropy. In the case of two
short disjoint intervals with a small cross ratio , we obtain not only the
classical and 1-loop quantum contributions to the R\'enyi entropy to order
, both of which are in perfect match with the ones found in gravity, but
also the leading contributions, which corresponds to 2-loop corrections
in the bulk.Comment: V1, 23 pages, 5 figures; V2, published version, typos corrected,
references adde
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