1,088 research outputs found
Turing machines can be efficiently simulated by the General Purpose Analog Computer
The Church-Turing thesis states that any sufficiently powerful computational
model which captures the notion of algorithm is computationally equivalent to
the Turing machine. This equivalence usually holds both at a computability
level and at a computational complexity level modulo polynomial reductions.
However, the situation is less clear in what concerns models of computation
using real numbers, and no analog of the Church-Turing thesis exists for this
case. Recently it was shown that some models of computation with real numbers
were equivalent from a computability perspective. In particular it was shown
that Shannon's General Purpose Analog Computer (GPAC) is equivalent to
Computable Analysis. However, little is known about what happens at a
computational complexity level. In this paper we shed some light on the
connections between this two models, from a computational complexity level, by
showing that, modulo polynomial reductions, computations of Turing machines can
be simulated by GPACs, without the need of using more (space) resources than
those used in the original Turing computation, as long as we are talking about
bounded computations. In other words, computations done by the GPAC are as
space-efficient as computations done in the context of Computable Analysis
The Landshoff-Nachtmann Pomeron on the Lattice
We investigate the Landshoff-Nachtmann two-gluon-exchange model of the
Pomeron using gluon propagators computed in the Landau gauge within quenched
lattice QCD calculations. We first determine an effective gluon-quark coupling
by constraining the Pomeron-quark coupling to its phenomenological value
\beta_0 = 2\, \gev^{-1}. We then provide predictions for a variety of
diffractive processes. As the propagators have been evaluated entirely from QCD
first principles (although in the quenched approximation), our results provide
a consistency check of the Landshoff-Nachtmann model. We address the issue of
the possible gauge-dependence of our results, which will be the object of a
future study.Comment: uuencoded, compressed tar file, 13 pages latex, 4 Postscript figures,
requires epsf.st
Quantum gates with neutral atoms: Controlling collisional interactions in time dependent traps
We theoretically study specific schemes for performing a fundamental
two-qubit quantum gate via controlled atomic collisions by switching
microscopic potentials. In particular we calculate the fidelity of a gate
operation for a configuration where a potential barrier between two atoms is
instantaneously removed and restored after a certain time. Possible
implementations could be based on microtraps created by magnetic and electric
fields, or potentials induced by laser light.Comment: 10 pages, 3 figure
"Dark energy" in the Local Void
The unexpected discovery of the accelerated cosmic expansion in 1998 has
filled the Universe with the embarrassing presence of an unidentified "dark
energy", or cosmological constant, devoid of any physical meaning. While this
standard cosmology seems to work well at the global level, improved knowledge
of the kinematics and other properties of our extragalactic neighborhood
indicates the need for a better theory. We investigate whether the recently
suggested repulsive-gravity scenario can account for some of the features that
are unexplained by the standard model. Through simple dynamical considerations,
we find that the Local Void could host an amount of antimatter
() roughly equivalent to the mass of a typical
supercluster, thus restoring the matter-antimatter symmetry. The antigravity
field produced by this "dark repulsor" can explain the anomalous motion of the
Local Sheet away from the Local Void, as well as several other properties of
nearby galaxies that seem to require void evacuation and structure formation
much faster than expected from the standard model. At the global cosmological
level, gravitational repulsion from antimatter hidden in voids can provide more
than enough potential energy to drive both the cosmic expansion and its
acceleration, with no need for an initial "explosion" and dark energy.
Moreover, the discrete distribution of these dark repulsors, in contrast to the
uniformly permeating dark energy, can also explain dark flows and other
recently observed excessive inhomogeneities and anisotropies of the Universe.Comment: 6 pages, accepted as a Letter to the Editor by Astrophysics and Space
Scienc
Mott insulators in strong electric fields
Recent experiments on ultracold atomic gases in an optical lattice potential
have produced a Mott insulating state of Rb atoms. This state is stable to a
small applied potential gradient (an `electric' field), but a resonant response
was observed when the potential energy drop per lattice spacing (E), was close
to the repulsive interaction energy (U) between two atoms in the same lattice
potential well. We identify all states which are resonantly coupled to the Mott
insulator for E close to U via an infinitesimal tunneling amplitude between
neighboring potential wells. The strong correlation between these states is
described by an effective Hamiltonian for the resonant subspace. This
Hamiltonian exhibits quantum phase transitions associated with an Ising density
wave order, and with the appearance of superfluidity in the directions
transverse to the electric field. We suggest that the observed resonant
response is related to these transitions, and propose experiments to directly
detect the order parameters. The generalizations to electric fields applied in
different directions, and to a variety of lattices, should allow study of
numerous other correlated quantum phases.Comment: 17 pages, 14 figures; (v2) minor additions and new reference
Localized Flux Lines and the Bose Glass
Columnar defects provide effective pinning centers for magnetic flux lines in
high-- superconductors. Utilizing a mapping of the statistical
mechanics of directed lines to the quantum mechanics of two--dimensional
bosons, one expects an entangled flux liquid phase at high temperatures,
separated by a second--order localization transition from a low--temperature
``Bose glass'' phase with infinite tilt modulus. Recent decoration experiments
have demonstrated that below the matching field the repulsive forces between
the vortices may be sufficiently large to produce strong spatial correlations
in the Bose glass. This is confirmed by numerical simulations, and a remarkably
wide soft ``Coulomb gap'' at the chemical potential is found in the
distribution of pinning energies. At low currents, the dominant transport
mechanism in the Bose glass phase proceeds via the formation of double kinks
between not necessarily adjacent columnar pins, similar to variable--range
hopping in disordered semiconductors. The strong correlation effects
originating in the long--range vortex interactions drastically reduce
variable--range hopping transport.Comment: 10 pages, latex ("lamuphys.sty" file included), 6 figures can be
obtained from the author ([email protected]); to appear in Proc. XIV
Sitges conference on "Complex Behaviour of Glassy Systems" (Springer--Verlag
Measuring Selection when Parents and Offspring Interact
Non-social and social selection gradients are key evolutionary parameters in systems where individuals interact. They are most easily obtained by regressing an individual's fitness on the trait values of the individual and its social partner. In the context of parental care it is more common to regress the trait value of the parents (i.e. the social partner) on a âmixedâ fitness measure that is a function of the parent's and offspring's fitness (for example, the number of recruits, which equals parental fecundity multiplied by offspring survival). For such an approach to yield correct estimates of net-selection, the trait must be sex-limited and not affect the parentsâ own survival. When a trait is not sex-limited, the non-social selection should be weighted by one (because all individuals express the trait) and social selection should be weighted by a half (because the relatedness between parents and the offspring they care for is a half, usually). The âmixedâ fitness approach does not give estimates of both components of selection and so they cannot be weighted appropriately. We show that mixed fitness components are frequently used in place of direct fitness measures in the literature (37% of fecundity selection estimates use a mixed fitness approach), but that the frequency is much higher in some taxa, such as birds and mammals. We suggest alternative methods that could be used to estimate both social and non-social selection gradients, while at the same time assessing the importance of unmeasured traits
Sensitive Observations of Radio Recombination Lines in Orion and W51: The Data and Detection of Systematic Recombination Line Blueshifts Proportional to Impact Broadening
Sensitive spectral observations made in two frequency bands near 6.0 and 17.6
GHz are described for Orion and W51. Using frequency switching we were able to
achieve a dynamic range in excess of 10,000 without fitting sinusoidal or
polynomial baselines. This enabled us to detect lines as weak as T\Delta n$ as
high as 25 have been detected in Orion. In the Orion data, where the lines are
stronger, we have also detected a systematic shift in the line center
frequencies proportional to linewidth that cannot be explained by normal
optical depth effects.Comment: 22 pages, 13 figures. Accepted for publication in Astrophysics and
Space Scienc
Unitarity of Quantum Theory and Closed Time-Like Curves
Interacting quantum fields on spacetimes containing regions of closed
timelike curves (CTCs) are subject to a non-unitary evolution . Recently, a
prescription has been proposed, which restores unitarity of the evolution by
modifying the inner product on the final Hilbert space. We give a rigorous
description of this proposal and note an operational problem which arises when
one considers the composition of two or more non-unitary evolutions. We propose
an alternative method by which unitarity of the evolution may be regained, by
extending to a unitary evolution on a larger (possibly indefinite) inner
product space. The proposal removes the ambiguity noted by Jacobson in
assigning expectation values to observables localised in regions spacelike
separated from the CTC region. We comment on the physical significance of the
possible indefiniteness of the inner product introduced in our proposal.Comment: 13 pages, LaTeX. Final revised paper to be published in Phys Rev D.
Some changes are made to expand our discussion of Anderson's Proposal for
restoring unitarit
The problem of equilibration and the computation of correlation functions on a quantum computer
We address the question of how a quantum computer can be used to simulate
experiments on quantum systems in thermal equilibrium. We present two
approaches for the preparation of the equilibrium state on a quantum computer.
For both approaches, we show that the output state of the algorithm, after long
enough time, is the desired equilibrium. We present a numerical analysis of one
of these approaches for small systems. We show how equilibrium
(time)-correlation functions can be efficiently estimated on a quantum
computer, given a preparation of the equilibrium state. The quantum algorithms
that we present are hard to simulate on a classical computer. This indicates
that they could provide an exponential speedup over what can be achieved with a
classical device.Comment: 25 pages LaTex + 8 figures; various additional comments, results and
correction
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