1,286 research outputs found
Entanglement and the Born-Oppenheimer approximation in an exactly solvable quantum many-body system
We investigate the correlations between different bipartitions of an exactly
solvable one-dimensional many-body Moshinsky model consisting of Nn "nuclei"
and Ne "electrons". We study the dependence of entanglement on the
inter-particle interaction strength, on the number of particles, and on the
particle masses. Consistent with kinematic intuition, the entanglement between
two subsystems vanishes when the subsystems have very different masses, while
it attains its maximal value for subsystems of comparable mass. We show how
this entanglement feature can be inferred by means of the Born-Oppenheimer
Ansatz, whose validity and breakdown can be understood from a quantum
information point of view.Comment: Accepted in Eur. Phys. J. D (2014
Binary black holes on a budget: Simulations using workstations
Binary black hole simulations have traditionally been computationally very
expensive: current simulations are performed in supercomputers involving dozens
if not hundreds of processors, thus systematic studies of the parameter space
of binary black hole encounters still seem prohibitive with current technology.
Here we show how the multi-layered refinement level code BAM can be used on
dual processor workstations to simulate certain binary black hole systems. BAM,
based on the moving punctures method, provides grid structures composed of
boxes of increasing resolution near the center of the grid. In the case of
binaries, the highest resolution boxes are placed around each black hole and
they track them in their orbits until the final merger when a single set of
levels surrounds the black hole remnant. This is particularly useful when
simulating spinning black holes since the gravitational fields gradients are
larger. We present simulations of binaries with equal mass black holes with
spins parallel to the binary axis and intrinsic magnitude of S/m^2= 0.75. Our
results compare favorably to those of previous simulations of this particular
system. We show that the moving punctures method produces stable simulations at
maximum spatial resolutions up to M/160 and for durations of up to the
equivalent of 20 orbital periods.Comment: 20 pages, 8 figures. Final version, to appear in a special issue of
Class. Quantum Grav. based on the New Frontiers in Numerical Relativity
Conference, Golm, July 200
Asymptotic Conditional Distribution of Exceedance Counts: Fragility Index with Different Margins
Let be a random vector, whose components are not
necessarily independent nor are they required to have identical distribution
functions . Denote by the number of exceedances among
above a high threshold . The fragility index, defined by
if this limit exists, measures the
asymptotic stability of the stochastic system as the threshold
increases. The system is called stable if and fragile otherwise. In this
paper we show that the asymptotic conditional distribution of exceedance counts
(ACDEC) , , exists, if the
copula of is in the domain of attraction of a multivariate extreme
value distribution, and if
exists for
and some . This enables the computation of
the FI corresponding to and of the extended FI as well as of the
asymptotic distribution of the exceedance cluster length also in that case,
where the components of are not identically distributed
Bosonic behavior of entangled fermions
Two bound, entangled fermions form a composite boson, which can be treated as
an elementary boson as long as the Pauli principle does not affect the behavior
of many such composite bosons. The departure of ideal bosonic behavior is
quantified by the normalization ratio of multi-composite-boson states. We
derive the two-fermion-states that extremize the normalization ratio for a
fixed single-fermion purity P, and establish general tight bounds for this
indicator. For very small purities, P<1/N^2, the upper and lower bounds
converge, which allows to quantify accurately the departure from perfectly
bosonic behavior, for any state of many composite bosons.Comment: 9 pages, 5 figures, accepted by PR
A single-domain spectral method for black hole puncture data
We calculate puncture initial data corresponding to both single and binary
black hole solutions of the constraint equations by means of a pseudo-spectral
method applied in a single spatial domain. Introducing appropriate coordinates,
these methods exhibit rapid convergence of the conformal factor and lead to
highly accurate solutions. As an application we investigate small mass ratios
of binary black holes and compare these with the corresponding test mass limit
that we obtain through a semi-analytical limiting procedure. In particular, we
compare the binding energy of puncture data in this limit with that of a test
particle in the Schwarzschild spacetime and find that it deviates by 50% from
the Schwarzschild result at the innermost stable circular orbit of
Schwarzschild, if the ADM mass at each puncture is used to define the local
black hole masses.Comment: 13 pages, 6 figures; published version with one important change, see
Fig. 4 and the corresponding changes to the tex
Numerical stability of the AA evolution system compared to the ADM and BSSN systems
We explore the numerical stability properties of an evolution system
suggested by Alekseenko and Arnold. We examine its behavior on a set of
standardized testbeds, and we evolve a single black hole with different gauges.
Based on a comparison with two other evolution systems with well-known
properties, we discuss some of the strengths and limitations of such simple
tests in predicting numerical stability in general.Comment: 16 pages, 12 figure
Feasibility of approximating spatial and local entanglement in long-range interacting systems using the extended Hubbard model
We investigate the extended Hubbard model as an approximation to the local
and spatial entanglement of a one-dimensional chain of nanostructures where the
particles interact via a long range interaction represented by a `soft' Coulomb
potential. In the process we design a protocol to calculate the
particle-particle spatial entanglement for the Hubbard model and show that, in
striking contrast with the loss of spatial degrees of freedom, the predictions
are reasonably accurate. We also compare results for the local entanglement
with previous results found using a contact interaction (PRA, 81 (2010) 052321)
and show that while the extended Hubbard model recovers a better agreement with
the entanglement of a long-range interacting system, there remain realistic
parameter regions where it fails to predict the quantitative and qualitative
behaviour of the entanglement in the nanostructure system.Comment: 6 pages, 5 figures and 1 table; added results with correlated hopping
term; accepted by EP
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