56 research outputs found
Transient Dynamics in Magnetic Force Microscopy for a Single-Spin Measurement
We analyze a single-spin measurement using a transient process in magnetic
force microscopy (MFM) which could increase the maximum operating temperature
by a factor of Q (the quality factor of the cantilever) in comparison with the
static Stern-Gerlach effect. We obtain an exact solution of the master
equation, which confirms this result. We also discuss the conditions required
to create a macroscopic Schrodinger cat state in the cantilever.Comment: 22 pages 2 figure
Perfect quantum error correction coding in 24 laser pulses
An efficient coding circuit is given for the perfect quantum error correction
of a single qubit against arbitrary 1-qubit errors within a 5 qubit code. The
circuit presented employs a double `classical' code, i.e., one for bit flips
and one for phase shifts. An implementation of this coding circuit on an
ion-trap quantum computer is described that requires 26 laser pulses. A further
circuit is presented requiring only 24 laser pulses, making it an efficient
protection scheme against arbitrary 1-qubit errors. In addition, the
performance of two error correction schemes, one based on the quantum Zeno
effect and the other using standard methods, is compared. The quantum Zeno
error correction scheme is found to fail completely for a model of noise based
on phase-diffusion.Comment: Replacement paper: Lost two laser pulses gained one author; added
appendix with circuits easily implementable on an ion-trap compute
Linking the trans-Planckian and the information loss problems in black hole physics
The trans-Planckian and information loss problems are usually discussed in
the literature as separate issues concerning the nature of Hawking radiation.
Here we instead argue that they are intimately linked, and can be understood as
"two sides of the same coin" once it is accepted that general relativity is an
effective field theory.Comment: 10 pages, 2 figures. Replaced with the version to be published in
General Relativity and Gravitatio
First-principles study of the ferroelastic phase transition in CaCl_2
First-principles density-functional calculations within the local-density
approximation and the pseudopotential approach are used to study and
characterize the ferroelastic phase transition in calcium chloride (CaCl_2). In
accord with experiment, the energy map of CaCl_2 has the typical features of a
pseudoproper ferroelastic with an optical instability as ultimate origin of the
phase transition. This unstable optic mode is close to a pure rigid unit mode
of the framework of chlorine atoms and has a negative Gruneisen parameter. The
ab-initio ground state agrees fairly well with the experimental low temperature
structure extrapolated at 0K. The calculated energy map around the ground state
is interpreted as an extrapolated Landau free-energy and is successfully used
to explain some of the observed thermal properties. Higher-order anharmonic
couplings between the strain and the unstable optic mode, proposed in previous
literature as important terms to explain the soft-phonon temperature behavior,
are shown to be irrelevant for this purpose. The LAPW method is shown to
reproduce the plane-wave results in CaCl_2 within the precision of the
calculations, and is used to analyze the relative stability of different phases
in CaCl_2 and the chemically similar compound SrCl_2.Comment: 9 pages, 6 figures, uses RevTeX
G\"odel Incompleteness and the Black Hole Information Paradox
Semiclassical reasoning suggests that the process by which an object
collapses into a black hole and then evaporates by emitting Hawking radiation
may destroy information, a problem often referred to as the black hole
information paradox. Further, there seems to be no unique prediction of where
the information about the collapsing body is localized. We propose that the
latter aspect of the paradox may be a manifestation of an inconsistent
self-reference in the semiclassical theory of black hole evolution. This
suggests the inadequacy of the semiclassical approach or, at worst, that
standard quantum mechanics and general relavity are fundamentally incompatible.
One option for the resolution for the paradox in the localization is to
identify the G\"odel-like incompleteness that corresponds to an imposition of
consistency, and introduce possibly new physics that supplies this
incompleteness. Another option is to modify the theory in such a way as to
prohibit self-reference. We discuss various possible scenarios to implement
these options, including eternally collapsing objects, black hole remnants,
black hole final states, and simple variants of semiclassical quantum gravity.Comment: 14 pages, 2 figures; revised according to journal requirement
Relativistic Hydrodynamic Evolutions with Black Hole Excision
We present a numerical code designed to study astrophysical phenomena
involving dynamical spacetimes containing black holes in the presence of
relativistic hydrodynamic matter. We present evolutions of the collapse of a
fluid star from the onset of collapse to the settling of the resulting black
hole to a final stationary state. In order to evolve stably after the black
hole forms, we excise a region inside the hole before a singularity is
encountered. This excision region is introduced after the appearance of an
apparent horizon, but while a significant amount of matter remains outside the
hole. We test our code by evolving accurately a vacuum Schwarzschild black
hole, a relativistic Bondi accretion flow onto a black hole, Oppenheimer-Snyder
dust collapse, and the collapse of nonrotating and rotating stars. These
systems are tracked reliably for hundreds of M following excision, where M is
the mass of the black hole. We perform these tests both in axisymmetry and in
full 3+1 dimensions. We then apply our code to study the effect of the stellar
spin parameter J/M^2 on the final outcome of gravitational collapse of rapidly
rotating n = 1 polytropes. We find that a black hole forms only if J/M^2<1, in
agreement with previous simulations. When J/M^2>1, the collapsing star forms a
torus which fragments into nonaxisymmetric clumps, capable of generating
appreciable ``splash'' gravitational radiation.Comment: 17 pages, 14 figures, submitted to PR
Horizons, Constraints, and Black Hole Entropy
Black hole entropy appears to be ``universal''--many independent
calculations, involving models with very different microscopic degrees of
freedom, all yield the same density of states. I discuss the proposal that this
universality comes from the behavior of the underlying symmetries of the
classical theory. To impose the condition that a black hole be present, we must
partially break the classical symmetries of general relativity, and the
resulting Goldstone boson-like degrees of freedom may account for the
Bekenstein-Hawking entropy. In particular, I demonstrate that the imposition of
a ``stretched horizon'' constraint modifies the algebra of symmetries at the
horizon, allowing the use of standard conformal field theory techniques to
determine the asymptotic density of states. The results reproduce the
Bekenstein-Hawking entropy without any need for detailed assumptions about the
microscopic theory.Comment: 16 pages, talk given at the "Peyresq Physics 10 Meeting on Micro and
Macro structures of spacetime
A Self Assembled Nanoelectronic Quantum Computer Based on the Rashba Effect in Quantum Dots
Quantum computers promise vastly enhanced computational power and an uncanny
ability to solve classically intractable problems. However, few proposals exist
for robust, solid state implementation of such computers where the quantum
gates are sufficiently miniaturized to have nanometer-scale dimensions. Here I
present a new approach whereby a complete computer with nanoscale gates might
be self-assembled using chemical synthesis. Specifically, I demonstrate how to
self-assemble the fundamental unit of this quantum computer - a 2-qubit
universal quantum controlled-NOT gate - based on two exchange coupled
multilayered quantum dots. Then I show how these gates can be wired using
thiolated conjugated molecules as electrical connectors. A qubit is encoded in
the ground state of a quantum dot spin-split by the Rashba interaction.
Arbitrary qubit rotations are effected by bringing the spin splitting energy in
a target quantum dot in resonance with a global ac magnetic field by applying a
potential pulse of appropriate amplitude and duration to the dot. The
controlled dynamics of the 2-qubit controlled-NOT operation (XOR) can be
realized by exploiting the exchange coupling with the nearest neighboring dot.
A complete prescription for initialization of the computer and data
input/output operations is presented.Comment: 22 pages, 4 figure
Categorizing Different Approaches to the Cosmological Constant Problem
We have found that proposals addressing the old cosmological constant problem
come in various categories. The aim of this paper is to identify as many
different, credible mechanisms as possible and to provide them with a code for
future reference. We find that they all can be classified into five different
schemes of which we indicate the advantages and drawbacks.
Besides, we add a new approach based on a symmetry principle mapping real to
imaginary spacetime.Comment: updated version, accepted for publicatio
Relativistic superfluid models for rotating neutron stars
This article starts by providing an introductory overview of the theoretical
mechanics of rotating neutron stars as developped to account for the frequency
variations, and particularly the discontinuous glitches, observed in pulsars.
The theory suggests, and the observations seem to confirm, that an essential
role is played by the interaction between the solid crust and inner layers
whose superfluid nature allows them to rotate independently. However many
significant details remain to be clarified, even in much studied cases such as
the Crab and Vela. The second part of this article is more technical,
concentrating on just one of the many physical aspects that needs further
development, namely the provision of a satisfactorily relativistic (local but
not microscopic) treatment of the effects of the neutron superfluidity that is
involved.Comment: 42 pages LateX. Contribution to Physics of Neutron Star Interiors,
ed. D. Blasche, N.K. Glendenning, A. Sedrakian (ECT workshop, Trento, June
2000
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