6,584 research outputs found
Innermost stable circular orbits around relativistic rotating stars
We investigate the innermost stable circular orbit (ISCO) of a test particle
moving on the equatorial plane around rotating relativistic stars such as
neutron stars. First, we derive approximate analytic formulas for the angular
velocity and circumferential radius at the ISCO making use of an approximate
relativistic solution which is characterized by arbitrary mass, spin, mass
quadrupole, current octapole and mass -pole moments. Then, we show that
the analytic formulas are accurate enough by comparing them with numerical
results, which are obtained by analyzing the vacuum exterior around numerically
computed geometries for rotating stars of polytropic equation of state. We
demonstrate that contribution of mass quadrupole moment for determining the
angular velocity and, in particular, the circumferential radius at the ISCO
around a rapidly rotating star is as important as that of spin.Comment: 12 pages, 2 figures, accepted for publication in Phys. Rev.
Implementation of NMR quantum computation with para-hydrogen derived high purity quantum states
We demonstrate the first implementation of a quantum algorithm on a liquid
state nuclear magnetic resonance (NMR) quantum computer using almost pure
states. This was achieved using a two qubit device where the initial state is
an almost pure singlet nuclear spin state of a pair of 1H nuclei arising from a
chemical reaction involving para-hydrogen. We have implemented Deutsch's
algorithm for distinguishing between constant and balanced functions with a
single query.Comment: 7 pages RevTex including 6 figures. Figures 4-6 are low quality to
save space. Submitted to Phys Rev
Dynamics of a Bose-Einstein Condensate in an Anharmonic Trap
We present a theoretical model to describe the dynamics of Bose-Einstein
condensates in anharmonic trapping potentials. To first approximation the
center-of-mass motion is separated from the internal condensate dynamics and
the problem is reduced to the well known scaling solutions for the Thomas-Fermi
radii. We discuss the validity of this approach and analyze the model for an
anharmonic waveguide geometry which was recently realized in an experiment
\cite{Ott2002c}
Analytic Controllability of Time-Dependent Quantum Control Systems
The question of controllability is investigated for a quantum control system
in which the Hamiltonian operator components carry explicit time dependence
which is not under the control of an external agent. We consider the general
situation in which the state moves in an infinite-dimensional Hilbert space, a
drift term is present, and the operators driving the state evolution may be
unbounded. However, considerations are restricted by the assumption that there
exists an analytic domain, dense in the state space, on which solutions of the
controlled Schrodinger equation may be expressed globally in exponential form.
The issue of controllability then naturally focuses on the ability to steer the
quantum state on a finite-dimensional submanifold of the unit sphere in Hilbert
space -- and thus on analytic controllability. A relatively straightforward
strategy allows the extension of Lie-algebraic conditions for strong analytic
controllability derived earlier for the simpler, time-independent system in
which the drift Hamiltonian and the interaction Hamiltonia have no intrinsic
time dependence. Enlarging the state space by one dimension corresponding to
the time variable, we construct an augmented control system that can be treated
as time-independent. Methods developed by Kunita can then be implemented to
establish controllability conditions for the one-dimension-reduced system
defined by the original time-dependent Schrodinger control problem. The
applicability of the resulting theorem is illustrated with selected examples.Comment: 13 page
Geodesics for Efficient Creation and Propagation of Order along Ising Spin Chains
Experiments in coherent nuclear and electron magnetic resonance, and optical
spectroscopy correspond to control of quantum mechanical ensembles, guiding
them from initial to final target states by unitary transformations. The
control inputs (pulse sequences) that accomplish these unitary transformations
should take as little time as possible so as to minimize the effects of
relaxation and decoherence and to optimize the sensitivity of the experiments.
Here we give efficient syntheses of various unitary transformations on Ising
spin chains of arbitrary length. The efficient realization of the unitary
transformations presented here is obtained by computing geodesics on a sphere
under a special metric. We show that contrary to the conventional belief, it is
possible to propagate a spin order along an Ising spin chain with coupling
strength J (in units of Hz), significantly faster than 1/(2J) per step. The
methods presented here are expected to be useful for immediate and future
applications involving control of spin dynamics in coherent spectroscopy and
quantum information processing
Inelastically scattering particles and wealth distribution in an open economy
Using the analogy with inelastic granular gasses we introduce a model for
wealth exchange in society. The dynamics is governed by a kinetic equation,
which allows for self-similar solutions. The scaling function has a power-law
tail, the exponent being given by a transcendental equation. In the limit of
continuous trading, closed form of the wealth distribution is calculated
analytically.Comment: 8 pages 5 figure
Melvin solution with a dilaton potential
We find new Melvin-like solutions in Einstein-Maxwell-dilaton gravity with a
Liouville-type dilaton potential. The properties of the corresponding solution
in Freedman-Schwarz gauged supergravity model are extensively studied. We show
that this configuration is regular and geodesically complete but do not
preserve any supersymmetry. An exact solution describing travelling waves in
this Melvin-type background is also presented.Comment: 12 pages, LaTeX, no figure
Pair of accelerated black holes in an anti-de Sitter background: the AdS C-metric
The anti-de Sitter C-metric (AdS C-metric) is characterized by a quite
interesting new feature when compared with the C-metric in flat or de Sitter
backgrounds. Indeed, contrarily to what happens in these two last exact
solutions, the AdS C-metric only describes a pair of accelerated black holes if
the acceleration parameter satisfies A>1/L, where L is the cosmological length.
The two black holes cannot interact gravitationally and their acceleration is
totally provided by the pressure exerted by a strut that pushes the black holes
apart. Our analysis is based on the study of the causal structure, on the
description of the solution in the AdS 4-hyperboloid in a 5D Minkowski
embedding spacetime, and on the physics of the strut. We also analyze the cases
A=1/L and A<1/L that represent a single accelerated black hole in the AdS
background.Comment: 20 pages, 15 figures (RevTeX4). Published version: typo in fig. 5
corrected, references adde
Chaotic Scattering Theory, Thermodynamic Formalism, and Transport Coefficients
The foundations of the chaotic scattering theory for transport and
reaction-rate coefficients for classical many-body systems are considered here
in some detail. The thermodynamic formalism of Sinai, Bowen, and Ruelle is
employed to obtain an expression for the escape-rate for a phase space
trajectory to leave a finite open region of phase space for the first time.
This expression relates the escape rate to the difference between the sum of
the positive Lyapunov exponents and the K-S entropy for the fractal set of
trajectories which are trapped forever in the open region. This result is well
known for systems of a few degrees of freedom and is here extended to systems
of many degrees of freedom. The formalism is applied to smooth hyperbolic
systems, to cellular-automata lattice gases, and to hard sphere sytems. In the
latter case, the goemetric constructions of Sinai {\it et al} for billiard
systems are used to describe the relevant chaotic scattering phenomena. Some
applications of this formalism to non-hyperbolic systems are also discussed.Comment: 35 pages, compressed file, follow directions in header for ps file.
Figures are available on request from [email protected]
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