114 research outputs found
Entanglement in Quantum Spin Chains, Symmetry Classes of Random Matrices, and Conformal Field Theory
We compute the entropy of entanglement between the first spins and the
rest of the system in the ground states of a general class of quantum
spin-chains. We show that under certain conditions the entropy can be expressed
in terms of averages over ensembles of random matrices. These averages can be
evaluated, allowing us to prove that at critical points the entropy grows like
as , where and are determined explicitly. In an important class of systems,
is equal to one-third of the central charge of an associated Virasoro algebra.
Our expression for therefore provides an explicit formula for the
central charge.Comment: 4 page
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
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
Late-time evolution of a self-interacting scalar field in the spacetime of dilaton black hole
We investigate the late-time tails of self-interacting (massive) scalar
fields in the spacetime of dilaton black hole. Following the no hair theorem we
examine the mechanism by which self-interacting scalar hair decay. We revealed
that the intermediate asymptotic behavior of the considered field perturbations
is dominated by an oscillatory inverse power-law decaying tail. The numerical
simulations showed that at the very late-time massive self-interacting scalar
hair decayed slower than any power law.Comment: 8 pages, 4 figures, to appear in Phys. Rev.
Dilaton Black Holes with Electric Charge
Static spherically symmetric solutions of the Einstein-Maxwell gravity with
the dilaton field are described. The solutions correspond to black holes and
are generalizations of the previously known dilaton black hole solution. In
addition to mass and electric charge these solutions are labeled by a new
parameter, the dilaton charge of the black hole. Different effects of the
dilaton charge on the geometry of space-time of such black holes are studied.
It is shown that in most cases the scalar curvature is divergent at the
horizons. Another feature of the dilaton black hole is that there is a finite
interval of values of electric charge for which no black hole can exist.Comment: 20 pages, LaTeX file + 1 figure, CALT-68-1885. (the postscript file
is improved
Cosmological Multi-Black Hole Solutions
We present simple, analytic solutions to the Einstein-Maxwell equation, which
describe an arbitrary number of charged black holes in a spacetime with
positive cosmological constant . In the limit , these
solutions reduce to the well known Majumdar-Papapetrou (MP) solutions. Like the
MP solutions, each black hole in a solution has charge equal
to its mass , up to a possible overall sign. Unlike the limit,
however, solutions with are highly dynamical. The black holes move
with respect to one another, following natural trajectories in the background
deSitter spacetime. Black holes moving apart eventually go out of causal
contact. Black holes on approaching trajectories ultimately merge. To our
knowledge, these solutions give the first analytic description of coalescing
black holes. Likewise, the thermodynamics of the solutions is
quite interesting. Taken individually, a black hole is in thermal
equilibrium with the background deSitter Hawking radiation. With more than one
black hole, because the solutions are not static, no global equilibrium
temperature can be defined. In appropriate limits, however, when the black
holes are either close together or far apart, approximate equilibrium states
are established.Comment: 15 pages (phyzzx), UMHEP-380 (minor referencing error corrected
On scattering off the extreme Reissner-Nordstr\"om black hole in N=2 supergravity
The scattering amplitudes for the perturbed fields of the N=2 supergravity
about the extreme Reissner-Nordstr\"om black hole is examined. Owing to the
fact that the extreme hole is a BPS state of the theory and preserves an
unbroken global supersymmetry(N=1), the scattering amplitudes of the component
fields should be related to each other. In this paper, we derive the formula of
the transformation of the scattering amplitudes.Comment: 9 pages, revtex, no figures, a few typing errors correcte
Charged black points in General Relativity coupled to the logarithmic gauge theory
The exact solution for a static spherically symmetric field outside a charged
point particle is found in a non-linear gauge theory with a logarithmic
Lagrangian. The electromagnetic self-mass is finite, and for a particular
relation between mass, charge, and the value of the non-linearity coupling
constant, , the electromagnetic contribution to the Schwarzschild mass
is equal to the total mass. If we also require that the singularity at the
origin be hidden behind a horizon, the mass is fixed to be slightly less than
the charge. This object is a {\em black point.}Comment: 7 pages, REVTeX, no figure
Are the singularities stable?
The spacetime singularities play a useful role in gravitational theories by
distinguishing physical solutions from non-physical ones. The problem, we
studying in this paper is: are these singularities stable? To answer this
question, we have analyzed the general problem of stability of the family of
the static spherically symmetric solutions of the standard Einstein-Maxwell
model coupled to an extra free massless scalar field. We have obtained the
equations for the axial and polar perturbations. The stability against axial
perturbations has been proven.Comment: 13 pages, LaTeX, no figure
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