264 research outputs found
Echo spectroscopy and Atom Optics Billiards
We discuss a recently demonstrated type of microwave spectroscopy of trapped
ultra-cold atoms known as "echo spectroscopy" [M.F. Andersen et. al., Phys.
Rev. Lett., in press (2002)]. Echo spectroscopy can serve as an extremely
sensitive experimental tool for investigating quantum dynamics of trapped atoms
even when a large number of states are thermally populated. We show numerical
results for the stability of eigenstates of an atom-optics billiard of the
Bunimovich type, and discuss its behavior under different types of
perturbations. Finally, we propose to use special geometrical constructions to
make a dephasing free dipole trap
Belief heterogeneity and survival in incomplete markets
In complete markets economies (Sandroni [16]), or in economies with Pareto optimal outcomes (Blume and Easley [10]), the market selection hypothesis holds, as long as traders have identical discount factors. Traders who survive must have beliefs that merge with the truth. We show that in incomplete markets, regardless of tradersâ discount factors, the market selects for a range of beliefs, at least some of which do not merge with the truth. We also show that impatient traders with incorrect beliefs can survive and that these incorrect beliefs impact prices. These beliefs may be chosen so that they are far from the truth
Introduction to Isolated Horizons in Numerical Relativity
We present a coordinate-independent method for extracting mass (M) and
angular momentum (J) of a black hole in numerical simulations. This method,
based on the isolated horizon framework, is applicable both at late times when
the black hole has reached equilibrium, and at early times when the black holes
are widely separated. We show how J and M can be determined in numerical
simulations in terms of only those quantities which are intrinsic to the
apparent horizon. We also present a numerical method for finding the rotational
symmetry vector field (required to calculate J) on the horizon.Comment: 14 pages, revtex4, 7 figures. Final PRD versio
Single and double qubit gates by manipulating degeneracy
A novel mechanism is proposed for single and double qubit state manipulations
in quantum computation with four-fold degenerate energy levels. The principle
is based on starting with a four fold degeneracy, lifting it stepwise
adiabatically by a set of control parameters and performing the quantum gate
operations on non-degenerate states. A particular realization of the proposed
mechanism is suggested by using inductively coupled rf-squid loops in the
macroscopic quantum tunnelling regime where the energy eigen levels are
directly connected with the measurable flux states. The one qubit and two qubit
controlled operations are demonstrated explicitly. The appearance of the flux
states also allows precise read-in and read-out operations by the measurement
of flux.Comment: 6 pages + 5 figures (separately included
Estimate of average freeze-out volume in multifragmentation events
An estimate of the average freeze-out volume for multifragmentation events is
presented. Values of volumes are obtained by means of a simulation using the
experimental charged product partitions measured by the 4pi multidetector INDRA
for 129Xe central collisions on Sn at 32 AMeV incident energy. The input
parameters of the simulation are tuned by means of the comparison between the
experimental and simulated velocity (or energy) spectra of particles and
fragments.Comment: To be published in Phys. Lett. B 12 pages, 5 figure
Arbitrary rotation and entanglement of flux SQUID qubits
We propose a new approach for the arbitrary rotation of a three-level SQUID
qubit and describe a new strategy for the creation of coherence transfer and
entangled states between two three-level SQUID qubits. The former is succeeded
by exploring the coupled-uncoupled states of the system when irradiated with
two microwave pulses, and the latter is succeeded by placing the SQUID qubits
into a microwave cavity and used adiabatic passage methods for their
manipulation.Comment: Accepted for publication in Phys. Rev.
Hamiltonian 2-forms in Kahler geometry, III Extremal metrics and stability
This paper concerns the explicit construction of extremal Kaehler metrics on
total spaces of projective bundles, which have been studied in many places. We
present a unified approach, motivated by the theory of hamiltonian 2-forms (as
introduced and studied in previous papers in the series) but this paper is
largely independent of that theory.
We obtain a characterization, on a large family of projective bundles, of
those `admissible' Kaehler classes (i.e., the ones compatible with the bundle
structure in a way we make precise) which contain an extremal Kaehler metric.
In many cases, such as on geometrically ruled surfaces, every Kaehler class is
admissible. In particular, our results complete the classification of extremal
Kaehler metrics on geometrically ruled surfaces, answering several
long-standing questions.
We also find that our characterization agrees with a notion of K-stability
for admissible Kaehler classes. Our examples and nonexistence results therefore
provide a fertile testing ground for the rapidly developing theory of stability
for projective varieties, and we discuss some of the ramifications. In
particular we obtain examples of projective varieties which are destabilized by
a non-algebraic degeneration.Comment: 40 pages, sequel to math.DG/0401320 and math.DG/0202280, but largely
self-contained; partially replaces and extends math.DG/050151
Hodge Theory on Metric Spaces
Hodge theory is a beautiful synthesis of geometry, topology, and analysis,
which has been developed in the setting of Riemannian manifolds. On the other
hand, spaces of images, which are important in the mathematical foundations of
vision and pattern recognition, do not fit this framework. This motivates us to
develop a version of Hodge theory on metric spaces with a probability measure.
We believe that this constitutes a step towards understanding the geometry of
vision.
The appendix by Anthony Baker provides a separable, compact metric space with
infinite dimensional \alpha-scale homology.Comment: appendix by Anthony W. Baker, 48 pages, AMS-LaTeX. v2: final version,
to appear in Foundations of Computational Mathematics. Minor changes and
addition
Thermally-induced expansion in the 8 GeV/c + Au reaction
Fragment kinetic energy spectra for reactions induced by 8.0 GeV/c
beams incident on a Au target have been analyzed in
order to deduce the possible existence and influence of thermal expansion. The
average fragment kinetic energies are observed to increase systematically with
fragment charge but are nearly independent of excitation energy. Comparison of
the data with statistical multifragmentation models indicates the onset of
extra collective thermal expansion near an excitation energy of E*/A
5 MeV. However, this effect is weak relative to the radial
expansion observed in heavy-ion-induced reactions, consistent with the
interpretation that the latter expansion may be driven primarily by dynamical
effects such as compression/decompression.Comment: 12 pages including 4 postscript figure
Fragment properties of fragmenting heavy nuclei produced in central and semi-peripheral collisions
Fragment properties of hot fragmenting sources of similar sizes produced in
central and semi-peripheral collisions are compared in the excitation energy
range 5-10 AMeV. For semi-peripheral collisions a method for selecting compact
quasi-projectiles sources in velocity space similar to those of fused systems
(central collisions) is proposed. The two major results are related to
collective energy. The weak radial collective energy observed for
quasi-projectile sources is shown to originate from thermal pressure only. The
larger fragment multiplicity observed for fused systems and their more
symmetric fragmentation are related to the extra radial collective energy due
to expansion following a compression phase during central collisions. A first
attempt to locate where the different sources break in the phase diagram is
proposed.Comment: 23 pages submitted to NP
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