11,284 research outputs found
Collective Dynamics of Bose--Einstein Condensates in Optical Cavities
Recent experiments on Bose--Einstein condensates in optical cavities have
reported a quantum phase transition to a coherent state of the matter-light
system -- superradiance. The time dependent nature of these experiments demands
consideration of collective dynamics. Here we establish a rich phase diagram,
accessible by quench experiments, with distinct regimes of dynamics separated
by non-equilibrium phase transitions. We include the key effects of cavity
leakage and the back-reaction of the cavity field on the condensate. Proximity
to some of these phase boundaries results in critical slowing down of the decay
of many-body oscillations. Notably, this slow decay can be assisted by large
cavity losses. Predictions include the frequency of collective oscillations, a
variety of multi-phase co-existence regions, and persistent optomechanical
oscillations described by a damped driven pendulum. These findings open new
directions to study collective dynamics and non-equilibrium phase transitions
in matter-light systems.Comment: 5 pages, 5 figure
Efficient analysis and representation of geophysical processes using localized spherical basis functions
While many geological and geophysical processes such as the melting of
icecaps, the magnetic expression of bodies emplaced in the Earth's crust, or
the surface displacement remaining after large earthquakes are spatially
localized, many of these naturally admit spectral representations, or they may
need to be extracted from data collected globally, e.g. by satellites that
circumnavigate the Earth. Wavelets are often used to study such nonstationary
processes. On the sphere, however, many of the known constructions are somewhat
limited. And in particular, the notion of `dilation' is hard to reconcile with
the concept of a geological region with fixed boundaries being responsible for
generating the signals to be analyzed. Here, we build on our previous work on
localized spherical analysis using an approach that is firmly rooted in
spherical harmonics. We construct, by quadratic optimization, a set of
bandlimited functions that have the majority of their energy concentrated in an
arbitrary subdomain of the unit sphere. The `spherical Slepian basis' that
results provides a convenient way for the analysis and representation of
geophysical signals, as we show by example. We highlight the connections to
sparsity by showing that many geophysical processes are sparse in the Slepian
basis.Comment: To appear in the Proceedings of the SPIE, as part of the Wavelets
XIII conference in San Diego, August 200
The Stellar Content Near the Galactic Center
High angular resolution J, H, K, and L' images are used to investigate the
stellar content within 6 arcsec of SgrA*. The data, which are complete to K ~
16, are the deepest multicolor observations of the region published to date.Comment: 34 pages, including 12 figure
A repulsive atomic gas in a harmonic trap on the border of itinerant ferromagnetism
Alongside superfluidity, itinerant (Stoner) ferromagnetism remains one of the
most well-characterized phases of correlated Fermi systems. A recent experiment
has reported the first evidence for novel phase behavior on the repulsive side
of the Feshbach resonance in a two-component ultracold Fermi gas. By adapting
recent theoretical studies to the atomic trap geometry, we show that an
adiabatic ferromagnetic transition would take place at a weaker interaction
strength than is observed in experiment. This discrepancy motivates a simple
non-equilibrium theory that takes account of the dynamics of magnetic defects
and three-body losses. The formalism developed displays good quantitative
agreement with experiment.Comment: 4 pages, 2 figure
Quantum Phase Transitions in Bosonic Heteronuclear Pairing Hamiltonians
We explore the phase diagram of two-component bosons with Feshbach resonant
pairing interactions in an optical lattice. It has been shown in previous work
to exhibit a rich variety of phases and phase transitions, including a
paradigmatic Ising quantum phase transition within the second Mott lobe. We
discuss the evolution of the phase diagram with system parameters and relate
this to the predictions of Landau theory. We extend our exact diagonalization
studies of the one-dimensional bosonic Hamiltonian and confirm additional Ising
critical exponents for the longitudinal and transverse magnetic
susceptibilities within the second Mott lobe. The numerical results for the
ground state energy and transverse magnetization are in good agreement with
exact solutions of the Ising model in the thermodynamic limit. We also provide
details of the low-energy spectrum, as well as density fluctuations and
superfluid fractions in the grand canonical ensemble.Comment: 11 pages, 14 figures. To appear in Phys. Rev.
Feshbach Resonance in Optical Lattices and the Quantum Ising Model
Motivated by experiments on heteronuclear Feshbach resonances in Bose
mixtures, we investigate s-wave pairing of two species of bosons in an optical
lattice. The zero temperature phase diagram supports a rich array of superfluid
and Mott phases and a network of quantum critical points. This topology reveals
an underlying structure that is succinctly captured by a two-component Landau
theory. Within the second Mott lobe we establish a quantum phase transition
described by the paradigmatic longitudinal and transverse field Ising model.
This is confirmed by exact diagonalization of the 1D bosonic Hamiltonian. We
also find this transition in the homonuclear case.Comment: 5 pages, 4 figure
Theory of quantum paraelectrics and the metaelectric transition
We present a microscopic model of the quantum paraelectric-ferroelectric
phase transition with a focus on the influence of coupled fluctuating phonon
modes. These may drive the continuous phase transition first order through a
metaelectric transition and furthermore stimulate the emergence of a textured
phase that preempts the transition. We discuss two further consequences of
fluctuations, firstly for the heat capacity, and secondly we show that the
inverse paraelectric susceptibility displays T^2 quantum critical behavior, and
can also adopt a characteristic minimum with temperature. Finally, we discuss
the observable consequences of our results.Comment: 5 pages, 2 figure
A hill-sliding strategy for initialization of Gaussian clusters in the multidimensional space
A hill sliding technique was devised to extract Gaussian clusters from the multivariate probability density estimate of sample data for the first step of iterative unsupervised classification. Each cluster was assumed to posses a unimodal normal distribution. A clustering function proposed distinguished elements of a cluster under formation from the rest in the feature space. Initial clusters were extracted one by one according to the hill sliding tactics. A dimensionless cluster compactness parameter was proposed as a universal measure of cluster goodness and used satisfactorily in test runs with LANDSAT multispectral scanner data. The normalized divergence, defined by the cluster divergence divided by the entropy of the entire sample data, was utilized as a general separability measure between clusters. An overall clustering objective function was set forth in terms of cluster covariance matrices, from which the cluster compactness measure could be deduced. Minimal improvement of initial data partitioning was evaluated by this objective function in eliminating scattered sparse data points. The hill sliding clustering technique developed herein has the potential applicability to decomposition any multivariate mixture distribution into a number of unimodal distributions when an appropriate distribution function to the data set is employed
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