1,457 research outputs found
Quantum dynamics of Bose-Hubbard Hamiltonians beyond Hartree-Fock-Bogoliubov: The Bogoliubov backreaction approximation
e formulate a method for studying the quantum field dynamics of ultracold
Bose gases confined within optical lattice potentials, within the lowest
Bloch-band Bose-Hubbard model. Our formalism extends the two-sites results of
Phys. Rev. Lett. {\bf86}, 000568 (2001) to the general case of lattice
sites. The methodology is based on mapping the Bose-Hubbard Hamiltonian to an
pseudospin problem and truncating the resulting hierarchy of dynamical
equations for correlation functions, up to pair-correlations between
generators. Agreement with few-site exact many-particle calculations is
consistently better than the corresponding Hartree-Fock-Bogoliubov
approximation. Moreover, our approximation compares favorably with a more
elaborate two-particle irreducible effective action formalism, at a fraction of
the analytic and numerical effort.Comment: 8 pages, 7 figure
Holstein model and Peierls instability in 1D boson-fermion lattice gases
We study an ultracold bose-fermi mixture in a one dimensional optical
lattice. When boson atoms are heavier then fermion atoms the system is
described by an adiabatic Holstein model, exhibiting a Peierls instability for
commensurate fermion filling factors. A Bosonic density wave with a wavenumber
of twice the Fermi wavenumber will appear in the quasi one-dimensional system.Comment: 5 pages, 4 figure
Parametric LTL on Markov Chains
This paper is concerned with the verification of finite Markov chains against
parametrized LTL (pLTL) formulas. In pLTL, the until-modality is equipped with
a bound that contains variables; e.g., asserts that
holds within time steps, where is a variable on natural
numbers. The central problem studied in this paper is to determine the set of
parameter valuations for which the probability to
satisfy pLTL-formula in a Markov chain meets a given threshold , where is a comparison on reals and a probability. As for pLTL
determining the emptiness of is undecidable, we consider
several logic fragments. We consider parametric reachability properties, a
sub-logic of pLTL restricted to next and , parametric B\"uchi
properties and finally, a maximal subclass of pLTL for which emptiness of is decidable.Comment: TCS Track B 201
The statistical strength of experiments to reject local realism with photon pairs and inefficient detectors
Because of the fundamental importance of Bell's theorem, a loophole-free
demonstration of a violation of local realism (LR) is highly desirable. Here,
we study violations of LR involving photon pairs. We quantify the experimental
evidence against LR by using measures of statistical strength related to the
Kullback-Leibler (KL) divergence, as suggested by van Dam et al. [W. van Dam,
R. Gill and P. Grunwald, IEEE Trans. Inf. Theory. 51, 2812 (2005)].
Specifically, we analyze a test of LR with entangled states created from two
independent polarized photons passing through a polarizing beam splitter. We
numerically study the detection efficiency required to achieve a specified
statistical strength for the rejection of LR depending on whether photon
counters or detectors are used. Based on our results, we find that a test of LR
free of the detection loophole requires photon counters with efficiencies of at
least 89.71%, or photon detectors with efficiencies of at least 91.11%. For
comparison, we also perform this analysis with ideal unbalanced Bell states,
which are known to allow rejection of LR with detector efficiencies above 2/3.Comment: 18 pages, 3 figures, minor changes (add more references, replace the
old plots, etc.)
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