2,127 research outputs found
The averaged null energy condition and difference inequalities in quantum field theory
Recently, Larry Ford and Tom Roman have discovered that in a flat cylindrical
space, although the stress-energy tensor itself fails to satisfy the averaged
null energy condition (ANEC) along the (non-achronal) null geodesics, when the
``Casimir-vacuum" contribution is subtracted from the stress-energy the
resulting tensor does satisfy the ANEC inequality. Ford and Roman name this
class of constraints on the quantum stress-energy tensor ``difference
inequalities." Here I give a proof of the difference inequality for a minimally
coupled massless scalar field in an arbitrary two-dimensional spacetime, using
the same techniques as those we relied on to prove ANEC in an earlier paper
with Robert Wald. I begin with an overview of averaged energy conditions in
quantum field theory.Comment: 20 page
Averaged Energy Conditions and Evaporating Black Holes
In this paper the averaged weak (AWEC) and averaged null (ANEC) energy
conditions, together with uncertainty principle-type restrictions on negative
energy (``quantum inequalities''), are examined in the context of evaporating
black hole backgrounds in both two and four dimensions. In particular,
integrals over only half-geodesics are studied. We determine the regions of the
spacetime in which the averaged energy conditions are violated. In all cases
where these conditions fail, there appear to be quantum inequalities which
bound the magnitude and extent of the negative energy, and hence the degree of
the violation. The possible relevance of these results for the validity of
singularity theorems in evaporating black hole spacetimes is discussed.Comment: Sections 2.1 and 2.2 have been revised and some erroneous statements
corrected. The main conclusions and the figures are unchanged. 27 pp, plain
Latex, 3 figures available upon reques
Quantum decoherence of a charge qubit in a spin-fermion model
We consider quantum decoherence in solid-state systems by studying the
transverse dynamics of a single qubit interacting with a fermionic bath and
driven by external pulses. Our interest is in investigating the extent to which
the lost coherence can be restored by the application of external pulses to the
qubit. We show that the qubit evolution under various pulse sequences can be
mapped onto Keldysh path integrals. This approach allows a simple diagrammatic
treatment of different bath excitation processes contributing to qubit
decoherence. We apply this theory to the evolution of the qubit coupled to the
Andreev fluctuator bath in the context of widely studied superconducting
qubits. We show that charge fluctuations within the Andreev-fluctuator model
lead to a 1/f noise spectrum with a characteristic temperature depedence. We
discuss the strategy for suppression of decoherence by the application of
higher-order (beyond spin echo) pulse sequences.Comment: 7 pages, 4 figures; extended version (accepted to Phys. Rev. B
The averaged null energy condition for general quantum field theories in two dimensions
It is shown that the averaged null energy condition is fulfilled for a dense,
translationally invariant set of vector states in any local quantum field
theory in two-dimensional Minkowski spacetime whenever the theory has a mass
gap and possesses an energy-momentum tensor. The latter is assumed to be a
Wightman field which is local relative to the observables, generates locally
the translations, is divergence-free, and energetically bounded. Thus the
averaged null energy condition can be deduced from completely generic, standard
assumptions for general quantum field theory in two-dimensional flat spacetime.Comment: LateX2e, 16 pages, 1 eps figur
Group classification of (1+1)-Dimensional Schr\"odinger Equations with Potentials and Power Nonlinearities
We perform the complete group classification in the class of nonlinear
Schr\"odinger equations of the form
where is an arbitrary
complex-valued potential depending on and is a real non-zero
constant. We construct all the possible inequivalent potentials for which these
equations have non-trivial Lie symmetries using a combination of algebraic and
compatibility methods. The proposed approach can be applied to solving group
classification problems for a number of important classes of differential
equations arising in mathematical physics.Comment: 10 page
Quantum Field Theory Constrains Traversable Wormhole Geometries
Recently a bound on negative energy densities in four-dimensional Minkowski
spacetime was derived for a minimally coupled, quantized, massless, scalar
field in an arbitrary quantum state. The bound has the form of an uncertainty
principle-type constraint on the magnitude and duration of the negative energy
density seen by a timelike geodesic observer. When spacetime is curved and/or
has boundaries, we argue that the bound should hold in regions small compared
to the minimum local characteristic radius of curvature or the distance to any
boundaries, since spacetime can be considered approximately Minkowski on these
scales. We apply the bound to the stress-energy of static traversable wormhole
spacetimes. Our analysis implies that either the wormhole must be only a little
larger than Planck size or that there is a large discrepancy in the length
scales which characterize the wormhole. In the latter case, the negative energy
must typically be concentrated in a thin band many orders of magnitude smaller
than the throat size. These results would seem to make the existence of
macroscopic traversable wormholes very improbable.Comment: 26 pages, plain LaTe
Survival probability and order statistics of diffusion on disordered media
We investigate the first passage time t_{j,N} to a given chemical or
Euclidean distance of the first j of a set of N>>1 independent random walkers
all initially placed on a site of a disordered medium. To solve this
order-statistics problem we assume that, for short times, the survival
probability (the probability that a single random walker is not absorbed by a
hyperspherical surface during some time interval) decays for disordered media
in the same way as for Euclidean and some class of deterministic fractal
lattices. This conjecture is checked by simulation on the incipient percolation
aggregate embedded in two dimensions. Arbitrary moments of t_{j,N} are
expressed in terms of an asymptotic series in powers of 1/ln N which is
formally identical to those found for Euclidean and (some class of)
deterministic fractal lattices. The agreement of the asymptotic expressions
with simulation results for the two-dimensional percolation aggregate is good
when the boundary is defined in terms of the chemical distance. The agreement
worsens slightly when the Euclidean distance is used.Comment: 8 pages including 9 figure
Probability Distribution of the Shortest Path on the Percolation Cluster, its Backbone and Skeleton
We consider the mean distribution functions Phi(r|l), Phi(B)(r|l), and
Phi(S)(r|l), giving the probability that two sites on the incipient percolation
cluster, on its backbone and on its skeleton, respectively, connected by a
shortest path of length l are separated by an Euclidean distance r. Following a
scaling argument due to de Gennes for self-avoiding walks, we derive analytical
expressions for the exponents g1=df+dmin-d and g1B=g1S-3dmin-d, which determine
the scaling behavior of the distribution functions in the limit x=r/l^(nu) much
less than 1, i.e., Phi(r|l) proportional to l^(-(nu)d)x^(g1), Phi(B)(r|l)
proportional to l^(-(nu)d)x^(g1B), and Phi(S)(r|l) proportional to
l^(-(nu)d)x^(g1S), with nu=1/dmin, where df and dmin are the fractal dimensions
of the percolation cluster and the shortest path, respectively. The theoretical
predictions for g1, g1B, and g1S are in very good agreement with our numerical
results.Comment: 10 pages, 3 figure
Quantum Inequalities on the Energy Density in Static Robertson-Walker Spacetimes
Quantum inequality restrictions on the stress-energy tensor for negative
energy are developed for three and four-dimensional static spacetimes. We
derive a general inequality in terms of a sum of mode functions which
constrains the magnitude and duration of negative energy seen by an observer at
rest in a static spacetime. This inequality is evaluated explicitly for a
minimally coupled scalar field in three and four-dimensional static
Robertson-Walker universes. In the limit of vanishing curvature, the flat
spacetime inequalities are recovered. More generally, these inequalities
contain the effects of spacetime curvature. In the limit of short sampling
times, they take the flat space form plus subdominant curvature-dependent
corrections.Comment: 18 pages, plain LATEX, with 3 figures, uses eps
Restrictions on negative energy density in a curved spacetime
Recently a restriction ("quantum inequality-type relation") on the
(renormalized) energy density measured by a static observer in a "globally
static" (ultrastatic) spacetime has been formulated by Pfenning and Ford for
the minimally coupled scalar field, in the extension of quantum inequality-type
relation on flat spacetime of Ford and Roman. They found negative lower bounds
for the line integrals of energy density multiplied by a sampling (weighting)
function, and explicitly evaluate them for some specific spacetimes. In this
paper, we study the lower bound on spacetimes whose spacelike hypersurfaces are
compact and without boundary. In the short "sampling time" limit, the bound has
asymptotic expansion. Although the expansion can not be represented by locally
invariant quantities in general due to the nonlocal nature of the integral, we
explicitly evaluate the dominant terms in the limit in terms of the invariant
quantities. We also make an estimate for the bound in the long sampling time
limit.Comment: LaTex, 23 Page
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