950 research outputs found
Optimal Design of Multiple Description Lattice Vector Quantizers
In the design of multiple description lattice vector quantizers (MDLVQ),
index assignment plays a critical role. In addition, one also needs to choose
the Voronoi cell size of the central lattice v, the sublattice index N, and the
number of side descriptions K to minimize the expected MDLVQ distortion, given
the total entropy rate of all side descriptions Rt and description loss
probability p. In this paper we propose a linear-time MDLVQ index assignment
algorithm for any K >= 2 balanced descriptions in any dimensions, based on a
new construction of so-called K-fraction lattice. The algorithm is greedy in
nature but is proven to be asymptotically (N -> infinity) optimal for any K >=
2 balanced descriptions in any dimensions, given Rt and p. The result is
stronger when K = 2: the optimality holds for finite N as well, under some mild
conditions. For K > 2, a local adjustment algorithm is developed to augment the
greedy index assignment, and conjectured to be optimal for finite N.
Our algorithmic study also leads to better understanding of v, N and K in
optimal MDLVQ design. For K = 2 we derive, for the first time, a
non-asymptotical closed form expression of the expected distortion of optimal
MDLVQ in p, Rt, N. For K > 2, we tighten the current asymptotic formula of the
expected distortion, relating the optimal values of N and K to p and Rt more
precisely.Comment: Submitted to IEEE Trans. on Information Theory, Sep 2006 (30 pages, 7
figures
Quantum Simulations of Lattice Gauge Theories using Ultracold Atoms in Optical Lattices
Can high energy physics be simulated by low-energy, non-relativistic,
many-body systems, such as ultracold atoms? Such ultracold atomic systems lack
the type of symmetries and dynamical properties of high energy physics models:
in particular, they manifest neither local gauge invariance nor Lorentz
invariance, which are crucial properties of the quantum field theories which
are the building blocks of the standard model of elementary particles.
However, it turns out, surprisingly, that there are ways to configure atomic
system to manifest both local gauge invariance and Lorentz invariance. In
particular, local gauge invariance can arise either as an effective, low
energy, symmetry, or as an "exact" symmetry, following from the conservation
laws in atomic interactions. Hence, one could hope that such quantum simulators
may lead to new type of (table-top) experiments, that shall be used to study
various QCD phenomena, as the confinement of dynamical quarks, phase
transitions, and other effects, which are inaccessible using the currently
known computational methods.
In this report, we review the Hamiltonian formulation of lattice gauge
theories, and then describe our recent progress in constructing quantum
simulation of Abelian and non-Abelian lattice gauge theories in 1+1 and 2+1
dimensions using ultracold atoms in optical lattices.Comment: A review; 55 pages, 14 figure
Multiple Description Quantization via Gram-Schmidt Orthogonalization
The multiple description (MD) problem has received considerable attention as
a model of information transmission over unreliable channels. A general
framework for designing efficient multiple description quantization schemes is
proposed in this paper. We provide a systematic treatment of the El Gamal-Cover
(EGC) achievable MD rate-distortion region, and show that any point in the EGC
region can be achieved via a successive quantization scheme along with
quantization splitting. For the quadratic Gaussian case, the proposed scheme
has an intrinsic connection with the Gram-Schmidt orthogonalization, which
implies that the whole Gaussian MD rate-distortion region is achievable with a
sequential dithered lattice-based quantization scheme as the dimension of the
(optimal) lattice quantizers becomes large. Moreover, this scheme is shown to
be universal for all i.i.d. smooth sources with performance no worse than that
for an i.i.d. Gaussian source with the same variance and asymptotically optimal
at high resolution. A class of low-complexity MD scalar quantizers in the
proposed general framework also is constructed and is illustrated
geometrically; the performance is analyzed in the high resolution regime, which
exhibits a noticeable improvement over the existing MD scalar quantization
schemes.Comment: 48 pages; submitted to IEEE Transactions on Information Theor
Three dimensional resonating valence bond liquids and their excitations
We show that there are two types of RVB liquid phases present in
three-dimensional quantum dimer models, corresponding to the deconfining phases
of U(1) and Z_2 gauge theories in d=3+1. The former is found on the bipartite
cubic lattice and is the generalization of the critical point in the square
lattice quantum dimer model found originally by Rokhsar and Kivelson. The
latter exists on the non-bipartite face-centred cubic lattice and generalizes
the RVB phase found earlier by us on the triangular lattice. We discuss the
excitation spectrum and the nature of the ordering in both cases. Both phases
exhibit gapped spinons. In the U(1) case we find a collective, linearly
dispersing, transverse excitation, which is the photon of the low energy
Maxwell Lagrangian and we identify the ordering as quantum order in Wen's
sense. In the Z_2 case all collective excitations are gapped and, as in d=2,
the low energy description of this topologically ordered state is the purely
topological BF action. As a byproduct of this analysis, we unearth a further
gapless excitation, the pi0n, in the square lattice quantum dimer model at its
critical point.Comment: 9 pages, 2 figure
Artificial Staggered Magnetic Field for Ultracold Atoms in Optical Lattices
A time-dependent optical lattice with staggered particle current in the
tight-binding regime was considered that can be described by a time-independent
effective lattice model with an artificial staggered magnetic field. The low
energy description of a single-component fermion in this lattice at
half-filling is provided by two copies of ideal two-dimensional massless Dirac
fermions. The Dirac cones are generally anisotropic and can be tuned by the
external staggered flux \p. For bosons, the staggered flux modifies the
single-particle spectrum such that in the weak coupling limit, depending on the
flux \p, distinct superfluid phases are realized. Their properties are
discussed, the nature of the phase transitions between them is establised, and
Bogoliubov theory is used to determine their excitation spectra. Then the
generalized superfluid-Mott-insulator transition is studied in the presence of
the staggered flux and the complete phase diagram is established. Finally, the
momentum distribution of the distinct superfluid phases is obtained, which
provides a clear experimental signature of each phase in ballistic expansion
experiments.Comment: 14 pages, 5 figure
Lattice Gauge Theories at the Energy Frontier
This White Paper has been prepared as a planning document for the Division of
High Energy Physics of the U. S. Department of Energy. Recent progress in
lattice-based studies of physics beyond the standard model is summarized, and
major current goals of USQCD research in this area are presented. Challenges
and opportunities associated with the recently discovered 126 GeV Higgs-like
particle are highlighted. Computational resources needed for reaching important
goals are described. The document was finalized on February 11, 2013 with
references that are not aimed to be complete, or account for an accurate
historical record of the field.Comment: Submitted for the Snowmass 2013 e-Proceedings with 44 pages, 10
figures, and 3 table
Non-standard Hubbard models in optical lattices: a review
Originally, the Hubbard model has been derived for describing the behaviour
of strongly-correlated electrons in solids. However, since over a decade now,
variations of it are also routinely being implemented with ultracold atoms in
optical lattices. We review some of the rich literature on this subject, with a
focus on more recent non-standard forms of the Hubbard model. After an
introduction to standard (fermionic and bosonic) Hubbard models, we discuss
briefly common models for mixtures, as well as the so called extended
Bose-Hubbard models, that include interactions between neighboring sites,
next-neighboring sites, and so on. The main part of the review discusses the
importance of additional terms appearing when refining the tight-binding
approximation on the original physical Hamiltonian. Even when restricting the
models to the lowest Bloch band is justified, the standard approach neglects
the density-induced tunneling (which has the same origin as the usual on-site
interaction). The importance of these contributions is discussed for both
contact and dipolar interactions. For sufficiently strong interactions, also
the effects related to higher Bloch bands become important even for deep
optical lattices. Different approaches that aim at incorporating these effects,
mainly via dressing the basis Wannier functions with interactions, leading to
effective, density-dependent Hubbard-type models, are reviewed. We discuss also
examples of Hubbard-like models that explicitly involve higher -orbitals, as
well as models that couple dynamically spin and orbital degrees of freedom.
Finally, we review mean-field nonlinear-Schr\"odinger models of the Salerno
type that share with the non-standard Hubbard models the nonlinear coupling
between the adjacent sites. In that part, discrete solitons are the main
subject of the consideration. We conclude by listing some future open problems.Comment: expanded version 47pp, accepted in Rep. Prog. Phy
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