73,930 research outputs found
Ehrenfest Dynamics and Frictionless Cooling Methods
Recently introduced methods which result in shortcuts to adiabaticity,
particularly in the context of frictionless cooling, are rederived and
discussed in the framework of an approach based on Ehrenfest dynamics. This
construction provides physical insights into the emergence of the Ermakov
equation, the choice of its boundary conditions, and the use of minimum
uncertainty states as indicators of the efficiency of the procedure.
Additionally, it facilitates the extension of frictionless cooling to more
general situations of physical relevance, such as optical dipole trapping
schemes. In this context, we discuss frictionless cooling in the short-time
limit, a complementary case to the one considered in the literature, making
explicit the limitations intrinsic to the technique when the full
three-dimensional case is analyzed.Comment: 9 pages, 4 figures, v2: To appear in Physical Review A. (some minor
typos corrected and some references added
Consistency and heterogeneity of individual behavior under uncertainty
By using graphical representations of simple portfolio choice problems,
we generate a very rich data set to study behavior under uncertainty
at the level of the individual subject. We test the data for
consistency with the maximization hypothesis, and we estimate preferences
using a two-parameter utility function based on Faruk Gul
(1991). This specification provides a good interpretation of the data
at the individual level and can account for the highly heterogeneous
behaviors observed in the laboratory. The parameter estimates jointly
describe attitudes toward risk and allow us to characterize the distribution
of risk preferences in the population
Squeezing and robustness of frictionless cooling strategies
Quantum control strategies that provide shortcuts to adiabaticity are
increasingly considered in various contexts including atomic cooling. Recent
studies have emphasized practical issues in order to reduce the gap between the
idealized models and actual ongoing implementations. We rephrase here the
cooling features in terms of a peculiar squeezing effect, and use it to
parametrize the robustness of frictionless cooling techniques with respect to
noise-induced deviations from the ideal time-dependent trajectory for the
trapping frequency. We finally discuss qualitative issues for the experimental
implementation of this scheme using bichromatic optical traps and lattices,
which seem especially suitable for cooling Fermi-Bose mixtures and for
investigating equilibration of negative temperature states, respectively.Comment: 9 pages, 7 figures; To appear in Physical Review
Time-dependent coupled oscillator model for charged particle motion in the presence of a time varyingmagnetic field
The dynamics of time-dependent coupled oscillator model for the charged
particle motion subjected to a time-dependent external magnetic field is
investigated. We used canonical transformation approach for the classical
treatment of the system, whereas unitary transformation approach is used when
managing the system in the framework of quantum mechanics. For both approaches,
the original system is transformed to a much more simple system that is the sum
of two independent harmonic oscillators which have time-dependent frequencies.
We therefore easily identified the wave functions in the transformed system
with the help of invariant operator of the system. The full wave functions in
the original system is derived from the inverse unitary transformation of the
wave functions associated to the transformed system.Comment: 16 page
Anti-correlated time lags in the Z source GX 5-1: Possible evidence for a truncated accretion disk
We investigate the nature of the inner accretion disk in the neutron star
source GX 5-1 by making a detailed study of time lags between X-rays of
different energies. Using the cross-correlation analysis, we found
anti-correlated hard and soft time lags of the order of a few tens to a few
hundred seconds and the corresponding intensity states were mostly the
horizontal branch (HB) and upper normal branch (NB). The model independent and
dependent spectral analysis showed that during these time lags the structure of
accretion disk significantly varied. Both eastern and western approaches were
used to unfold the X-ray continuum and systematic changes were observed in soft
and hard spectral components. These changes along with a systematic shift in
the frequency of quasi-periodic oscillations (QPOs) made it substantially
evident that the geometry of the accretion disk is truncated. Simultaneous
energy spectral and power density spectral study shows that the production of
the horizontal branch oscillations (HBOs) are closely related to the
Comptonizing region rather than the disk component in the accretion disk. We
found that as the HBO frequency decreases from the hard apex to upper HB, the
disk temperature increases along with an increase in the coronal temperature
which is in sharp contrast with the changes found in black hole binaries where
the decrease in QPO frequency is accompanied by a decrease in the disk
temperature and a simultaneous increase in the coronal temperature. We discuss
the results in the context of re-condensation of coronal material in the inner
region of the disk.Comment: 40 pages, 7 figures, accepted for publication in The Astrophysical
Journal Supplement (ApJS
The definability criterions for convex projective polyhedral reflection groups
Following Vinberg, we find the criterions for a subgroup generated by
reflections \Gamma \subset \SL^{\pm}(n+1,\mathbb{R}) and its finite-index
subgroups to be definable over where is an integrally
closed Noetherian ring in the field . We apply the criterions for
groups generated by reflections that act cocompactly on irreducible properly
convex open subdomains of the -dimensional projective sphere. This gives a
method for constructing injective group homomorphisms from such Coxeter groups
to \SL^{\pm}(n+1,\mathbb{Z}). Finally we provide some examples of
\SL^{\pm}(n+1,\mathbb{Z})-representations of such Coxeter groups. In
particular, we consider simplicial reflection groups that are isomorphic to
hyperbolic simplicial groups and classify all the conjugacy classes of the
reflection subgroups in \SL^{\pm}(n+1,\mathbb{R}) that are definable over
. These were known by Goldman, Benoist, and so on previously.Comment: 31 pages, 8 figure
On sums of three squares
Let be the number of representations of a positive integer as a
sum of three squares of integers. We give two distinct proofs of a conjecture
of Wagon concerning the asymptotic value of the mean square of .Comment: 11 pages, minor revisions made; to appear in Internat. J. Number
Theor
Intersecting Brane World from Type I Compactification
We elaborate that general intersecting brane models on orbifolds are obtained
from type I string compactifications and their T-duals. Symmetry breaking and
restoration occur via recombination and parallel separation of branes,
preserving supersymmetry. The Ramond-Ramond tadpole cancelation and the toron
quantization constrain the spectrum as a branching of the adjoints of SO(32),
up to orbifold projections. Since the recombination changes the gauge coupling,
the single gauge coupling of type I could give rise to different coupling below
the unification scale. This is due to the nonlocal properties of the
Dirac-Born-Infeld action. The weak mixing angle sin^2 theta_W = 3/8 is
naturally explained by embedding the quantum numbers to those of SO(10).Comment: 31 pages, 5 figure
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