1,024 research outputs found
Classical-quantum correspondence in bosonic two-mode conversion systems: polynomial algebras and Kummer shapes
Bosonic quantum conversion systems can be modeled by many-particle
single-mode Hamiltonians describing a conversion of molecules of type A
into molecules of type B and vice versa. These Hamiltonians are analyzed in
terms of generators of a polynomially deformed algebra. In the
mean-field limit of large particle numbers, these systems become classical and
their Hamiltonian dynamics can again be described by polynomial deformations of
a Lie algebra, where quantum commutators are replaced by Poisson brackets. The
Casimir operator restricts the motion to Kummer shapes, deformed Bloch spheres
with cusp singularities depending on and . It is demonstrated that the
many-particle eigenvalues can be recovered from the mean-field dynamics using a
WKB type quantization condition. The many-particle state densities can be
semiclassically approximated by the time-periods of periodic orbits, which show
characteristic steps and singularities related to the fixed points, whose
bifurcation properties are analyzed.Comment: 13 pages, 13 figure
Quasiclassical analysis of Bloch oscillations in non-Hermitian tight-binding lattices
Many features of Bloch oscillations in one-dimensional quantum lattices with
a static force can be described by quasiclassical considerations for example by
means of the acceleration theorem, at least for Hermitian systems. Here the
quasiclassical approach is extended to non-Hermitian lattices, which are of
increasing interest. The analysis is based on a generalised non-Hermitian phase
space dynamics developed recently. Applications to a single-band tight-binding
system demonstrate that many features of the quantum dynamics can be understood
from this classical description qualitatively and even quantitatively. Two
non-Hermitian and -symmetric examples are studied, a Hatano-Nelson lattice
with real coupling constants and a system with purely imaginary couplings, both
for initially localised states in space or in momentum. It is shown that the
time-evolution of the norm of the wave packet and the expectation values of
position and momentum can be described in a classical picture.Comment: 20 pages, 8 figures, typos corrected, slightly extended, accepted for
publication in New Journal of Physics in Focus Issue on Parity-Time Symmetry
in Optics and Photonic
Instant restore after a media failure
Media failures usually leave database systems unavailable for several hours
until recovery is complete, especially in applications with large devices and
high transaction volume. Previous work introduced a technique called
single-pass restore, which increases restore bandwidth and thus substantially
decreases time to repair. Instant restore goes further as it permits read/write
access to any data on a device undergoing restore--even data not yet
restored--by restoring individual data segments on demand. Thus, the restore
process is guided primarily by the needs of applications, and the observed mean
time to repair is effectively reduced from several hours to a few seconds.
This paper presents an implementation and evaluation of instant restore. The
technique is incrementally implemented on a system starting with the
traditional ARIES design for logging and recovery. Experiments show that the
transaction latency perceived after a media failure can be cut down to less
than a second and that the overhead imposed by the technique on normal
processing is minimal. The net effect is that a few "nines" of availability are
added to the system using simple and low-overhead software techniques
Mean-field dynamics of a non-Hermitian Bose-Hubbard dimer
We investigate an -particle Bose-Hubbard dimer with an additional
effective decay term in one of the sites. A mean-field approximation for this
non-Hermitian many-particle system is derived, based on a coherent state
approximation. The resulting nonlinear, non-Hermitian two-level dynamics, in
particular the fixed point structures showing characteristic modifications of
the self-trapping transition, are analyzed. The mean-field dynamics is found to
be in reasonable agreement with the full many-particle evolution.Comment: 4 pages, 3 figures, published versio
Bose-Einstein condensates in accelerated double-periodic optical lattices: Coupling and Crossing of resonances
We study the properties of coupled linear and nonlinear resonances. The
fundamental phenomena and the level crossing scenarios are introduced for a
nonlinear two-level system with one decaying state, describing the dynamics of
a Bose-Einstein condensate in a mean-field approximation (Gross-Pitaevskii or
nonlinear Schroedinger equation). An important application of the discussed
concepts is the dynamics of a condensate in tilted optical lattices. In
particular the properties of resonance eigenstates in double-periodic lattices
are discussed, in the linear case as well as within mean-field theory. The
decay is strongly altered, if an additional period-doubled lattice is
introduced. Our analytic study is supported by numerical computations of
nonlinear resonance states, and future applications of our findings for
experiments with ultracold atoms are discussed.Comment: 12 pages, 17 figure
Non-adiabatic transitions through exceptional points in the band structure of a PT-symmetric lattice
Exceptional points, at which two or more eigenfunctions of a Hamiltonian coalesce, occur in non-Hermitian systems and lead to surprising physical effects. In particular, the behaviour of a system under parameter variation can differ significantly from the familiar Hermitian case in the presence of exceptional points. Here we analytically derive the probability of a non-adiabatic transition in a two-level system driven through two consecutive exceptional points at finite speed. The system is Hermitian far away from the exceptional points. In the adiabatic limit an equal redistribution between the states coalescing in the exceptional point is observed, which can be interpreted as a loss of information when passing through the exceptional point. For finite parameter variation this gets modified. We demonstrate how the transition through the exceptional points can be experimentally addressed in a PT-symmetric lattice using Bloch oscillations
PT-Symmetric Sinusoidal Optical Lattices at the Symmetry-Breaking Threshold
The symmetric potential has
a completely real spectrum for , and begins to develop complex
eigenvalues for . At the symmetry-breaking threshold
some of the eigenvectors become degenerate, giving rise to a Jordan-block
structure for each degenerate eigenvector. In general this is expected to
result in a secular growth in the amplitude of the wave. However, it has been
shown in a recent paper by Longhi, by numerical simulation and by the use of
perturbation theory, that for a broad initial wave packet this growth is
suppressed, and instead a saturation leading to a constant maximum amplitude is
observed. We revisit this problem by explicitly constructing the Bloch
wave-functions and the associated Jordan functions and using the method of
stationary states to find the dependence on the longitudinal distance for a
variety of different initial wave packets. This allows us to show in detail how
the saturation of the linear growth arises from the close connection between
the contributions of the Jordan functions and those of the neighbouring Bloch
waves.Comment: 15 pages, 7 figures Minor corrections, additional reference
Sampling-Based Query Re-Optimization
Despite of decades of work, query optimizers still make mistakes on
"difficult" queries because of bad cardinality estimates, often due to the
interaction of multiple predicates and correlations in the data. In this paper,
we propose a low-cost post-processing step that can take a plan produced by the
optimizer, detect when it is likely to have made such a mistake, and take steps
to fix it. Specifically, our solution is a sampling-based iterative procedure
that requires almost no changes to the original query optimizer or query
evaluation mechanism of the system. We show that this indeed imposes low
overhead and catches cases where three widely used optimizers (PostgreSQL and
two commercial systems) make large errors.Comment: This is the extended version of a paper with the same title and
authors that appears in the Proceedings of the ACM SIGMOD International
Conference on Management of Data (SIGMOD 2016
Optical realization of the two-site Bose-Hubbard model in waveguide lattices
A classical realization of the two-site Bose-Hubbard Hamiltonian, based on
light transport in engineered optical waveguide lattices, is theoretically
proposed. The optical lattice enables a direct visualization of the
Bose-Hubbard dynamics in Fock space.Comment: to be published, J Phys. B (Fast Track Communication
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