349 research outputs found
Correspondence principle in quantum gravity
The problem of consistent formulation of the correspondence principle in
quantum gravity is considered. The usual approach based on the use of the
two-particle scattering amplitudes is shown to be in disagreement with the
classical result of General Relativity given by the Schwarzschild solution. It
is shown also that this approach fails to describe whatever non-Newtonian
interactions of macroscopic bodies. An alternative interpretation of the
correspondence principle is given directly in terms of the effective action.
Gauge independence of the \hbar^0 part of the one-loop radiative corrections to
the gravitational form factors of the scalar particle is proved, justifying the
interpretation proposed. Application to the black holes is discussed.Comment: Talk presented at the international meeting "Quantum Gravity and
Spectral Geometry", Naples, July 2001. 4 pages, 1 figur
Scaling of Entanglement Entropy in the Random Singlet Phase
We present numerical evidences for the logarithmic scaling of the
entanglement entropy in critical random spin chains. Very large scale exact
diagonalizations performed at the critical XX point up to L=2000 spins 1/2 lead
to a perfect agreement with recent real-space renormalization-group predictions
of Refael and Moore [Phys. Rev. Lett. {\bf 93}, 260602 (2004)] for the
logarithmic scaling of the entanglement entropy in the Random Singlet Phase
with an effective central charge . Moreover we
provide the first visual proof of the existence the Random Singlet Phase thanks
to the quantum entanglement concept.Comment: 4 pages, 3 figure
Effective Gravitational Field of Black Holes
The problem of interpretation of the \hbar^0-order part of radiative
corrections to the effective gravitational field is considered. It is shown
that variations of the Feynman parameter in gauge conditions fixing the general
covariance are equivalent to spacetime diffeomorphisms. This result is proved
for arbitrary gauge conditions at the one-loop order. It implies that the
gravitational radiative corrections of the order \hbar^0 to the spacetime
metric can be physically interpreted in a purely classical manner. As an
example, the effective gravitational field of a black hole is calculated in the
first post-Newtonian approximation, and the secular precession of a test
particle orbit in this field is determined.Comment: 8 pages, LaTeX, 1 eps figure. Proof of the theorem and typos
correcte
Universality of Entropy Scaling in 1D Gap-less Models
We consider critical models in one dimension. We study the ground state in
thermodynamic limit [infinite lattice]. Following Bennett, Bernstein, Popescu,
and Schumacher, we use the entropy of a sub-system as a measure of
entanglement. We calculate the entropy of a part of the ground state. At zero
temperature it describes entanglement of this part with the rest of the ground
state. We obtain an explicit formula for the entropy of the subsystem at low
temperature. At zero temperature we reproduce a logarithmic formula of Holzhey,
Larsen and Wilczek. Our derivation is based on the second law of
thermodynamics. The entropy of a subsystem is calculated explicitly for Bose
gas with delta interaction, the Hubbard model and spin chains with arbitrary
value of spin.Comment: A section on spin chains with arbitrary value of spin is included.
The entropy of a subsystem is calculated explicitly as a function of spin.
References update
Rotating Dilaton Black Holes
We consider the axially symmetric coupled system of gravitation,
electromagnetism and a dilaton field. Reducing from four to three dimensions,
the system is described by gravity coupled to a non-linear -model. We
find the target space isometries and use them to generate new solutions. It
seems that it is only possible to generate rotating solutions from non-rotating
ones for the special cases when the dilaton coupling parameter . For those particular values, the target space symmetry is enlarged.Comment: 11 pages, RevTex, one figure include
Quantum Probes of Spacetime Singularities
It is shown that there are static spacetimes with timelike curvature
singularities which appear completely nonsingular when probed with quantum test
particles. Examples include extreme dilatonic black holes and the fundamental
string solution. In these spacetimes, the dynamics of quantum particles is well
defined and uniquely determined.Comment: 12 pages, RevTeX, no figures, A few breif comments added and typos
correcte
Entropy for dilatonic black hole
The area formula for entropy is extended to the case of a dilatonic black
hole. The entropy of a scalar field in the background of such a black hole is
calculated semiclassically. The area and cutoff dependences are normal {\it
except in the extremal case}, where the area is zero but the entropy nonzero.Comment: 13 pages (Applicability of area formula justified and a reference
added
Relative entropy in 2d Quantum Field Theory, finite-size corrections and irreversibility of the Renormalization Group
The relative entropy in two-dimensional Field Theory is studied for its
application as an irreversible quantity under the Renormalization Group,
relying on a general monotonicity theorem for that quantity previously
established. In the cylinder geometry, interpreted as finite-temperature field
theory, one can define from the relative entropy a monotonic quantity similar
to Zamolodchikov's c function. On the other hand, the one-dimensional quantum
thermodynamic entropy also leads to a monotonic quantity, with different
properties. The relation of thermodynamic quantities with the complex
components of the stress tensor is also established and hence the entropic c
theorems are proposed as analogues of Zamolodchikov's c theorem for the
cylinder geometry.Comment: 5 pages, Latex file, revtex, reorganized to best show the generality
of the results, version to appear in Phys. Rev. Let
Semiclassical Stability of the Extreme Reissner-Nordstrom Black Hole
The stress-energy tensor of a free quantized scalar field is calculated in
the extreme Reissner-Nordstr\"{o}m black hole spacetime in the zero temperature
vacuum state. The stress-energy appears to be regular on the event horizon,
contrary to the suggestion provided by two-dimensional calculations. An
analytic calculation on the event horizon for a thermal state shows that if the
temperature is nonzero then the stress-energy diverges strongly there.Comment: 10 pages, REVTeX, 4 figures in separate uuencoded compressed fil
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