9,485 research outputs found
Geometrical optics analysis of the short-time stability properties of the Einstein evolution equations
Many alternative formulations of Einstein's evolution have lately been
examined, in an effort to discover one which yields slow growth of
constraint-violating errors. In this paper, rather than directly search for
well-behaved formulations, we instead develop analytic tools to discover which
formulations are particularly ill-behaved. Specifically, we examine the growth
of approximate (geometric-optics) solutions, studied only in the future domain
of dependence of the initial data slice (e.g. we study transients). By
evaluating the amplification of transients a given formulation will produce, we
may therefore eliminate from consideration the most pathological formulations
(e.g. those with numerically-unacceptable amplification). This technique has
the potential to provide surprisingly tight constraints on the set of
formulations one can safely apply. To illustrate the application of these
techniques to practical examples, we apply our technique to the 2-parameter
family of evolution equations proposed by Kidder, Scheel, and Teukolsky,
focusing in particular on flat space (in Rindler coordinates) and Schwarzchild
(in Painleve-Gullstrand coordinates).Comment: Submitted to Phys. Rev.
Experimental study of vapor-cell magneto-optical traps for efficient trapping of radioactive atoms
We have studied magneto-optical traps (MOTs) for efficient on-line trapping
of radioactive atoms. After discussing a model of the trapping process in a
vapor cell and its efficiency, we present the results of detailed experimental
studies on Rb MOTs. Three spherical cells of different sizes were used. These
cells can be easily replaced, while keeping the rest of the apparatus
unchanged: atomic sources, vacuum conditions, magnetic field gradients, sizes
and power of the laser beams, detection system. By direct comparison, we find
that the trapping efficiency only weakly depends on the MOT cell size. It is
also found that the trapping efficiency of the MOT with the smallest cell,
whose diameter is equal to the diameter of the trapping beams, is about 40%
smaller than the efficiency of larger cells. Furthermore, we also demonstrate
the importance of two factors: a long coated tube at the entrance of the MOT
cell, used instead of a diaphragm; and the passivation with an alkali vapor of
the coating on the cell walls, in order to minimize the losses of trappable
atoms. These results guided us in the construction of an efficient
large-diameter cell, which has been successfully employed for on-line trapping
of Fr isotopes at INFN's national laboratories in Legnaro, Italy.Comment: 9 pages, 7 figures, submitted to Eur. Phys. J.
Dynamic crossover in the global persistence at criticality
We investigate the global persistence properties of critical systems relaxing
from an initial state with non-vanishing value of the order parameter (e.g.,
the magnetization in the Ising model). The persistence probability of the
global order parameter displays two consecutive regimes in which it decays
algebraically in time with two distinct universal exponents. The associated
crossover is controlled by the initial value m_0 of the order parameter and the
typical time at which it occurs diverges as m_0 vanishes. Monte-Carlo
simulations of the two-dimensional Ising model with Glauber dynamics display
clearly this crossover. The measured exponent of the ultimate algebraic decay
is in rather good agreement with our theoretical predictions for the Ising
universality class.Comment: 5 pages, 2 figure
Nonequilibrium critical dynamics of the two-dimensional Ising model quenched from a correlated initial state
The universality class, even the order of the transition, of the
two-dimensional Ising model depends on the range and the symmetry of the
interactions (Onsager model, Baxter-Wu model, Turban model, etc.), but the
critical temperature is generally the same due to self-duality. Here we
consider a sudden change in the form of the interaction and study the
nonequilibrium critical dynamical properties of the nearest-neighbor model. The
relaxation of the magnetization and the decay of the autocorrelation function
are found to display a power law behavior with characteristic exponents that
depend on the universality class of the initial state.Comment: 6 pages, 5 figures, submitted to Phys. Rev.
Exact boundary conditions in numerical relativity using multiple grids: scalar field tests
Cauchy-Characteristic Matching (CCM), the combination of a central 3+1 Cauchy
code with an exterior characteristic code connected across a time-like
interface, is a promising technique for the generation and extraction of
gravitational waves. While it provides a tool for the exact specification of
boundary conditions for the Cauchy evolution, it also allows to follow
gravitational radiation all the way to infinity, where it is unambiguously
defined.
We present a new fourth order accurate finite difference CCM scheme for a
first order reduction of the wave equation around a Schwarzschild black hole in
axisymmetry. The matching at the interface between the Cauchy and the
characteristic regions is done by transfering appropriate characteristic/null
variables. Numerical experiments indicate that the algorithm is fourth order
convergent. As an application we reproduce the expected late-time tail decay
for the scalar field.Comment: 14 pages, 5 figures. Included changes suggested by referee
Universal parity effects in the entanglement entropy of XX chains with open boundary conditions
We consider the Renyi entanglement entropies in the one-dimensional XX
spin-chains with open boundary conditions in the presence of a magnetic field.
In the case of a semi-infinite system and a block starting from the boundary,
we derive rigorously the asymptotic behavior for large block sizes on the basis
of a recent mathematical theorem for the determinant of Toeplitz plus Hankel
matrices. We conjecture a generalized Fisher-Hartwig form for the corrections
to the asymptotic behavior of this determinant that allows the exact
characterization of the corrections to the scaling at order o(1/l) for any n.
By combining these results with conformal field theory arguments, we derive
exact expressions also in finite chains with open boundary conditions and in
the case when the block is detached from the boundary.Comment: 24 pages, 9 figure
Exact relationship between the entanglement entropies of XY and quantum Ising chains
We consider two prototypical quantum models, the spin-1/2 XY chain and the
quantum Ising chain and study their entanglement entropy, S(l,L), of blocks of
l spins in homogeneous or inhomogeneous systems of length L. By using two
different approaches, free-fermion techniques and perturbational expansion, an
exact relationship between the entropies is revealed. Using this relation we
translate known results between the two models and obtain, among others, the
additive constant of the entropy of the critical homogeneous quantum Ising
chain and the effective central charge of the random XY chain.Comment: 6 page
Infinite Randomness Phases and Entanglement Entropy of the Disordered Golden Chain
Topological insulators supporting non-abelian anyonic excitations are at the
center of attention as candidates for topological quantum computation. In this
paper, we analyze the ground-state properties of disordered non-abelian anyonic
chains. The resemblance of fusion rules of non-abelian anyons and real space
decimation strongly suggests that disordered chains of such anyons generically
exhibit infinite-randomness phases. Concentrating on the disordered golden
chain model with nearest-neighbor coupling, we show that Fibonacci anyons with
the fusion rule exhibit two
infinite-randomness phases: a random-singlet phase when all bonds prefer the
trivial fusion channel, and a mixed phase which occurs whenever a finite
density of bonds prefers the fusion channel. Real space RG analysis
shows that the random-singlet fixed point is unstable to the mixed fixed point.
By analyzing the entanglement entropy of the mixed phase, we find its effective
central charge, and find that it increases along the RG flow from the random
singlet point, thus ruling out a c-theorem for the effective central charge.Comment: 16 page
Aging at Criticality in Model C Dynamics
We study the off-equilibrium two-point critical response and correlation
functions for the relaxational dynamics with a coupling to a conserved density
(Model C) of the O(N) vector model. They are determined in an \epsilon=4-d
expansion for vanishing momentum. We briefly discuss their scaling behaviors
and the associated scaling forms are determined up to first order in epsilon.
The corresponding fluctuation-dissipation ratio has a non trivial large time
limit in the aging regime and, up to one-loop order, it is the same as that of
the Model A for the physically relevant case N=1. The comparison with
predictions of local scale invariance is also discussed.Comment: 13 pages, 1 figur
Entanglement entropy of two disjoint intervals in c=1 theories
We study the scaling of the Renyi entanglement entropy of two disjoint blocks
of critical lattice models described by conformal field theories with central
charge c=1. We provide the analytic conformal field theory result for the
second order Renyi entropy for a free boson compactified on an orbifold
describing the scaling limit of the Ashkin-Teller (AT) model on the self-dual
line. We have checked this prediction in cluster Monte Carlo simulations of the
classical two dimensional AT model. We have also performed extensive numerical
simulations of the anisotropic Heisenberg quantum spin-chain with tree-tensor
network techniques that allowed to obtain the reduced density matrices of
disjoint blocks of the spin-chain and to check the correctness of the
predictions for Renyi and entanglement entropies from conformal field theory.
In order to match these predictions, we have extrapolated the numerical results
by properly taking into account the corrections induced by the finite length of
the blocks to the leading scaling behavior.Comment: 37 pages, 23 figure
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