1,107 research outputs found
The Paradox of Virtual Dipoles in the Einstein Action
The functional integral of pure Einstein 4D quantum gravity admits abnormally
large and long-lasting "dipolar fluctuations", generated by virtual sources
with the property Int d^4x Sqrt{g(x)} Tr T(x) = 0. These fluctuations would
exist also at macroscopic scales, with paradoxical consequences. We set out
their general features and give numerical estimates of possible suppression
processes.Comment: LaTeX, 5 pages; reference adde
Distributed Minimum Cut Approximation
We study the problem of computing approximate minimum edge cuts by
distributed algorithms. We use a standard synchronous message passing model
where in each round, bits can be transmitted over each edge (a.k.a.
the CONGEST model). We present a distributed algorithm that, for any weighted
graph and any , with high probability finds a cut of size
at most in
rounds, where is the size of the minimum cut. This algorithm is based
on a simple approach for analyzing random edge sampling, which we call the
random layering technique. In addition, we also present another distributed
algorithm, which is based on a centralized algorithm due to Matula [SODA '93],
that with high probability computes a cut of size at most
in rounds for any .
The time complexities of both of these algorithms almost match the
lower bound of Das Sarma et al. [STOC '11], thus
leading to an answer to an open question raised by Elkin [SIGACT-News '04] and
Das Sarma et al. [STOC '11].
Furthermore, we also strengthen the lower bound of Das Sarma et al. by
extending it to unweighted graphs. We show that the same lower bound also holds
for unweighted multigraphs (or equivalently for weighted graphs in which
bits can be transmitted in each round over an edge of weight ),
even if the diameter is . For unweighted simple graphs, we show
that even for networks of diameter , finding an -approximate minimum cut
in networks of edge connectivity or computing an
-approximation of the edge connectivity requires rounds
Quantum corrected geodesics
We compute the graviton-induced corrections to the trajectory of a classical
test particle. We show that the motion of the test particle is governed by an
effective action given by the expectation value (with respect to the graviton
state) of the classical action. We analyze the quantum corrected equations of
motion for the test particle in two particular backgrounds: a Robertson Walker
spacetime and a 2+1 dimensional spacetime with rotational symmetry. In both
cases we show that the quantum corrected trajectory is not a geodesic of the
background metric.Comment: LaTeX file, 15 pages, no figure
Vacuum fluctuations and topological Casimir effect in Friedmann-Robertson-Walker cosmologies with compact dimensions
We investigate the Wightman function, the vacuum expectation values of the
field squared and the energy-momentum tensor for a massless scalar field with
general curvature coupling parameter in spatially flat
Friedmann-Robertson-Walker universes with an arbitrary number of toroidally
compactified dimensions. The topological parts in the expectation values are
explicitly extracted and in this way the renormalization is reduced to that for
the model with trivial topology. In the limit when the comoving lengths of the
compact dimensions are very short compared to the Hubble length, the
topological parts coincide with those for a conformal coupling and they are
related to the corresponding quantities in the flat spacetime by standard
conformal transformation. In the opposite limit of large comoving lengths of
the compact dimensions, in dependence of the curvature coupling parameter, two
regimes are realized with monotonic or oscillatory behavior of the vacuum
expectation values. In the monotonic regime and for nonconformally and
nonminimally coupled fields the vacuum stresses are isotropic and the equation
of state for the topological parts in the energy density and pressures is of
barotropic type. In the oscillatory regime, the amplitude of the oscillations
for the topological part in the expectation value of the field squared can be
either decreasing or increasing with time, whereas for the energy-momentum
tensor the oscillations are damping.Comment: 20 pages, 2 figure
Bushes of vibrational modes for Fermi-Pasta-Ulam chains
Some exact solutions and multi-mode invariant submanifolds were found for the
Fermi-Pasta-Ulam (FPU) beta-model by Poggi and Ruffo in Phys. D 103 (1997) 251.
In the present paper we demonstrate how results of such a type can be obtained
for an arbitrary N-particle chain with periodic boundary conditions with the
aid of our group-theoretical approach [Phys. D 117 (1998) 43] based on the
concept of bushes of normal modes for mechanical systems with discrete
symmetry. The integro-differential equation describing the FPU-alfa dynamics in
the modal space is derived. The loss of stability of the bushes of modes for
the FPU-alfa model, in particular, for the limiting case N >> 1 for the
dynamical regime with displacement pattern having period twice the lattice
spacing (Pi-mode) is studied. Our results for the FPU-alfa chain are compared
with those by Poggi and Ruffo for the FPU-beta chain.Comment: To be published in Physica
Droplet actuation induced by coalescence: experimental evidences and phenomenological modeling
This paper considers the interaction between two droplets placed on a
substrate in immediate vicinity. We show here that when the two droplets are of
different fluids and especially when one of the droplet is highly volatile, a
wealth of fascinating phenomena can be observed. In particular, the interaction
may result in the actuation of the droplet system, i.e. its displacement over a
finite length. In order to control this displacement, we consider droplets
confined on a hydrophilic stripe created by plasma-treating a PDMS substrate.
This controlled actuation opens up unexplored opportunities in the field of
microfluidics. In order to explain the observed actuation phenomenon, we
propose a simple phenomenological model based on Newton's second law and a
simple balance between the driving force arising from surface energy gradients
and the viscous resistive force. This simple model is able to reproduce
qualitatively and quantitatively the observed droplet dynamics
The Dirichlet Casimir effect for theory in (3+1) dimensions: A new renormalization approach
We calculate the next to the leading order Casimir effect for a real scalar
field, within theory, confined between two parallel plates in three
spatial dimensions with the Dirichlet boundary condition. In this paper we
introduce a systematic perturbation expansion in which the counterterms
automatically turn out to be consistent with the boundary conditions. This will
inevitably lead to nontrivial position dependence for physical quantities, as a
manifestation of the breaking of the translational invariance. This is in
contrast to the usual usage of the counterterms in problems with nontrivial
boundary conditions, which are either completely derived from the free cases or
at most supplemented with the addition of counterterms only at the boundaries.
Our results for the massive and massless cases are different from those
reported elsewhere. Secondly, and probably less importantly, we use a
supplementary renormalization procedure, which makes the usage of any analytic
continuation techniques unnecessary.Comment: JHEP3 format,20 pages, 2 figures, to appear in JHE
The Effective Action in Gauged Supergravity on Hyperbolic Background and Induced Cosmological Constant
The one-loop effective action for 4-dimensional gauged supergravity with
negative cosmological constant, is investigated in space-times with compact
hyperbolic spatial section. The explicit expansion of the effective action as a
power series of the curvature on hyperbolic background is derived, making use
of heat-kernel and zeta-regularization techniques. The induced cosmological and
Newton constants are computed.Comment: 9 pages, UTF 23
Ricci flows and expansion in axion-dilaton cosmology
We study renormalization-group flows by deforming a class of conformal
sigma-models. We consider overall scale factor perturbation of Einstein spaces
as well as more general anisotropic deformations of three-spheres. At leading
order in alpha, renormalization-group equations turn out to be Ricci flows. In
the three-sphere background, the latter is the Halphen system, which is exactly
solvable in terms of modular forms. We also analyze time-dependent deformations
of these systems supplemented with an extra time coordinate and time-dependent
dilaton. In some regimes time evolution is identified with
renormalization-group flow and time coordinate can appear as Liouville field.
The resulting space-time interpretation is that of a homogeneous isotropic
Friedmann-Robertson-Walker universe in axion-dilaton cosmology. We find as
general behaviour the superposition of a big-bang (polynomial) expansion with a
finite number of oscillations at early times. Any initial anisotropy disappears
during the evolution.Comment: 22 page
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