25,820 research outputs found
Caustic formation in expanding condensates of cold atoms
We study the evolution of density in an expanding Bose-Einstein condensate
that initially has a spatially varying phase, concentrating on behaviour when
these phase variations are large. In this regime large density fluctuations
develop during expansion. Maxima have a characteristic density that diverges
with the amplitude of phase variations and their formation is analogous to that
of caustics in geometrical optics. We analyse in detail caustic formation in a
quasi-one dimensional condensate, which before expansion is subject to a
periodic or random optical potential, and we discuss the equivalent problem for
a quasi-two dimensional system. We also examine the influence of many-body
correlations in the initial state on caustic formation for a Bose gas expanding
from a strictly one-dimensional trap. In addition, we study a similar
arrangement for non-interacting fermions, showing that Fermi surface
discontinuities in the momentum distribution give rise in that case to sharp
peaks in the spatial derivative of the density. We discuss recent experiments
and argue that fringes reported in time of flight images by Chen and co-workers
[Phys. Rev. A 77, 033632 (2008)] are an example of caustic formation.Comment: 10 pages, 5 figures. Published versio
An associative memory for the on-line recognition and prediction of temporal sequences
This paper presents the design of an associative memory with feedback that is
capable of on-line temporal sequence learning. A framework for on-line sequence
learning has been proposed, and different sequence learning models have been
analysed according to this framework. The network model is an associative
memory with a separate store for the sequence context of a symbol. A sparse
distributed memory is used to gain scalability. The context store combines the
functionality of a neural layer with a shift register. The sensitivity of the
machine to the sequence context is controllable, resulting in different
characteristic behaviours. The model can store and predict on-line sequences of
various types and length. Numerical simulations on the model have been carried
out to determine its properties.Comment: Published in IJCNN 2005, Montreal, Canad
Dark energy: a quantum fossil from the inflationary Universe?
The discovery of dark energy (DE) as the physical cause for the accelerated
expansion of the Universe is the most remarkable experimental finding of modern
cosmology. However, it leads to insurmountable theoretical difficulties from
the point of view of fundamental physics. Inflation, on the other hand,
constitutes another crucial ingredient, which seems necessary to solve other
cosmological conundrums and provides the primeval quantum seeds for structure
formation. One may wonder if there is any deep relationship between these two
paradigms. In this work, we suggest that the existence of the DE in the present
Universe could be linked to the quantum field theoretical mechanism that may
have triggered primordial inflation in the early Universe. This mechanism,
based on quantum conformal symmetry, induces a logarithmic,
asymptotically-free, running of the gravitational coupling. If this evolution
persists in the present Universe, and if matter is conserved, the general
covariance of Einstein's equations demands the existence of dynamical DE in the
form of a running cosmological term whose variation follows a power law of the
redshift.Comment: LaTeX, 14 pages, extended discussion. References added. Accepted in
J. Phys. A: Mathematical and Theoretica
Shape-dependent Depinning of a Domain Wall by a Magnetic Field and a Spin-Polarized Current
The effect of sample shape on the depinning of the domain wall (DW) driven by
an applied magnetic field or a spin-polarized current is studied theoretically.
The shape effect resulting from the modulation of the sample width (geometric
pinning) can essentially affect the DW depinning. We found a good agreement
between the ratios of the critical values of the magnetic field and the
spin-polarized current predicted by the theory and measured in the experiment.Comment: 9 pages, 5 figure
A matrix ensemble with a preferential basis and its application to disordered metals and insulators
URL: http://www-spht.cea.fr/articles/s93/085The standard ensembles of the random matrix theory are invariant under change of basis. For non interacting electrons in disordered systems, this invariance is broken and deviations from the random matrix theory predictions occur, especially for strong disorder. We consider a generalization of the standard ensembles which includes a preferential basis and which gives rise to a ``screening'' of the logarithmic pairwise interaction between energy levels. In the unitary case, we recover a mathematically tractable distribution of energy levels first introduced by Gaudin. This simplified model provides a qualitative description of level statistics in the metal, insulator and at the mobility edge, which only depends on the dimensionless conductance
Importance of cooling in triggering the collapse of hypermassive neutron stars
The inspiral and merger of a binary neutron star (NSNS) can lead to the
formation of a hypermassive neutron star (HMNS). As the HMNS loses thermal
pressure due to neutrino cooling and/or centrifugal support due to
gravitational wave (GW) emission, and/or magnetic breaking of differential
rotation it will collapse to a black hole. To assess the importance of
shock-induced thermal pressure and cooling, we adopt an idealized equation of
state and perform NSNS simulations in full GR through late inspiral, merger,
and HMNS formation, accounting for cooling. We show that thermal pressure
contributes significantly to the support of the HMNS against collapse and that
thermal cooling accelerates its "delayed" collapse. Our simulations demonstrate
explicitly that cooling can induce the catastrophic collapse of a hot
hypermassive neutron star formed following the merger of binary neutron stars.
Thus, cooling physics is important to include in NSNS merger calculations to
accurately determine the lifetime of the HMNS remnant and to extract
information about the NS equation of state, cooling mechanisms, bar
instabilities and B-fields from the GWs emitted during the transient phase
prior to BH formation.Comment: 13 pages, 7 figures, matches published versio
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