815 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
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
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
Quantum-classical correspondence for a non-Hermitian Bose-Hubbard dimer
We investigate the many-particle and mean-field correspondence for a
non-Hermitian N-particle Bose-Hubbard dimer where a complex onsite energy
describes an effective decay from one of the modes. Recently a generalized
mean-field approximation for this non-Hermitian many-particle system yielding
an alternative complex nonlinear Schr\"odinger equation was introduced. Here we
give details of this mean-field approximation and show that the resulting
dynamics can be expressed in a generalized canonical form that includes a
metric gradient flow. The interplay of nonlinearity and non-Hermiticity
introduces a qualitatively new behavior to the mean-field dynamics: The
presence of the non-Hermiticity promotes the self-trapping transition, while
damping the self-trapping oscillations, and the nonlinearity introduces a
strong sensitivity to the initial conditions in the decay of the normalization.
Here we present a complete characterization of the mean-field dynamics and the
fixed point structure. We also investigate the full many-particle dynamics,
which shows a rich variety of breakdown and revival as well as tunneling
phenomena on top of the mean-field structure.Comment: 17 pages, 17 figures; bibliography updated, typos corrected,
published versio
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