2,006 research outputs found
A homogenization theorem for Langevin systems with an application to Hamiltonian dynamics
This paper studies homogenization of stochastic differential systems. The
standard example of this phenomenon is the small mass limit of Hamiltonian
systems. We consider this case first from the heuristic point of view,
stressing the role of detailed balance and presenting the heuristics based on a
multiscale expansion. This is used to propose a physical interpretation of
recent results by the authors, as well as to motivate a new theorem proven
here. Its main content is a sufficient condition, expressed in terms of
solvability of an associated partial differential equation ("the cell
problem"), under which the homogenization limit of an SDE is calculated
explicitly. The general theorem is applied to a class of systems, satisfying a
generalized detailed balance condition with a position-dependent temperature.Comment: 32 page
Spacetime Structure of an Evaporating Black Hole in Quantum Gravity
The impact of the leading quantum gravity effects on the dynamics of the
Hawking evaporation process of a black hole is investigated. Its spacetime
structure is described by a renormalization group improved Vaidya metric. Its
event horizon, apparent horizon, and timelike limit surface are obtained taking
the scale dependence of Newton's constant into account. The emergence of a
quantum ergosphere is discussed. The final state of the evaporation process is
a cold, Planck size remnant.Comment: 23 pages, BibTeX, revtex4, 7 figure
The exponential law: Monopole detectors, Bogoliubov transformations, and the thermal nature of the Euclidean vacuum in RP^3 de Sitter spacetime
We consider scalar field theory on the RP^3 de Sitter spacetime (RP3dS),
which is locally isometric to de Sitter space (dS) but has spatial topology
RP^3. We compare the Euclidean vacua on RP3dS and dS in terms of three
quantities that are relevant for an inertial observer: (i) the stress-energy
tensor; (ii) the response of an inertial monopole particle detector; (iii) the
expansion of the Euclidean vacuum in terms of many-particle states associated
with static coordinates centered at an inertial world line. In all these
quantities, the differences between RP3dS and dS turn out to fall off
exponentially at early and late proper times along the inertial trajectory. In
particular, (ii) and (iii) yield at early and late proper times in RP3dS the
usual thermal result in the de Sitter Hawking temperature. This conforms to
what one might call an exponential law: in expanding locally de Sitter
spacetimes, differences due to global topology should fall off exponentially in
the proper time.Comment: 22 pages, REVTex v3.1 with amsfonts and epsf, includes 2 eps figures.
(v2: Minor typos corrected, references updated.
Einstein-Podolsky-Rosen correlations between two uniformly accelerated oscillators
We consider the quantum correlations, i.e. the entanglement, between two
systems uniformly accelerated with identical acceleration a in opposite Rindler
quadrants which have reached thermal equilibrium with the Unruh heat bath. To
this end we study an exactly soluble model consisting of two oscillators
coupled to a massless scalar field in 1+1 dimensions. We find that for some
values of the parameters the oscillators get entangled shortly after the moment
of closest approach. Because of boost invariance there are an infinite set of
pairs of positions where the oscillators are entangled. The maximal
entanglement between the oscillators is found to be approximately 1.4
entanglement bits.Comment: 11 page
Classical and quantum radiation from a moving charge in an expanding universe
We investigate photon emission from a moving particle in an expanding
universe. This process is analogous to the radiation from an accelerated charge
in the classical electromagnetic theory. Using the framework of quantum field
theory in curved spacetime, we demonstrate that the Wentzel-Kramers-Brillouin
(WKB) approximation leads to the Larmor formula for the rate of the radiation
energy from a moving charge in an expanding universe. Using exactly solvable
models in a radiation-dominated universe and in a Milne universe, we examine
the validity of the WKB formula. It is shown that the quantum effect suppresses
the radiation energy in comparison with the WKB formula.Comment: 16 pages, JCAP in pres
Conformally related massless fields in dS, AdS and Minkowski spaces
In this paper we write down the equation for a scalar conformally coupled
field simultaneously for de Sitter (dS), anti-de Sitter (AdS) and Minkowski
spacetime in d-dimensions. The curvature dependence appears in a very simple
way through a conformal factor. As a consequence the process of curvature free
limit, including wave functions limit and two-points functions, turns to be a
straightforward issue. We determine a set of modes, that we call de Sitter
plane waves, which become ordinary plane waves when the curvature vanishes.Comment: 7 pages, 1 figur
Feynman Propagator for a Free Scalar Field on a Causal Set
The Feynman propagator for a free bosonic scalar field on the discrete
spacetime of a causal set is presented. The formalism includes scalar field
operators and a vacuum state which define a scalar quantum field theory on a
causal set. This work can be viewed as a novel regularisation of quantum field
theory based on a Lorentz invariant discretisation of spacetime.Comment: 4 pages, 2 plots. Minor updates to match published versio
Weak-field limit of f(R)-gravity in three and more spatial dimensions
We investigate a point-like massive source in non-linear f(R) theories in the
case of arbitrary number of spatial dimensions D\geq 3. If D>3 then extra
dimensions undergo toroidal compactification. We consider a weak-field
approximation with Minkowski and de Sitter background solutions. In both these
cases point-like massive sources demonstrate good agreement with experimental
data only in the case of ordinary three-dimensional (D=3) space. We generalize
this result to the case of perfect fluid with dust-like equations of state in
the external and internal spaces. This perfect fluid is uniformly smeared over
all extra dimensions and enclosed in a three-dimensional sphere. In ordinary
three dimensional (D=3) space, our formulas are useful for experimental
constraints on parameters of f(R) models.Comment: 8 pages, Revtex4, no figure
Stress Tensor from the Trace Anomaly in Reissner-Nordstrom Spacetimes
The effective action associated with the trace anomaly provides a general
algorithm for approximating the expectation value of the stress tensor of
conformal matter fields in arbitrary curved spacetimes. In static, spherically
symmetric spacetimes, the algorithm involves solving a fourth order linear
differential equation in the radial coordinate r for the two scalar auxiliary
fields appearing in the anomaly action, and its corresponding stress tensor. By
appropriate choice of the homogeneous solutions of the auxiliary field
equations, we show that it is possible to obtain finite stress tensors on all
Reissner-Nordstrom event horizons, including the extreme Q=M case. We compare
these finite results to previous analytic approximation methods, which yield
invariably an infinite stress-energy on charged black hole horizons, as well as
with detailed numerical calculations that indicate the contrary. The
approximation scheme based on the auxiliary field effective action reproduces
all physically allowed behaviors of the quantum stress tensor, in a variety of
quantum states, for fields of any spin, in the vicinity of the entire family (0
le Q le M) of RN horizons.Comment: 43 pages, 12 figure
- …