16,707 research outputs found
Alternatives to the stochastic "noise vector" approach
Several important observables, like the quark condensate and the Taylor
coefficients of the expansion of the QCD pressure with respect to the chemical
potential, are based on the trace of the inverse Dirac operator and of its
powers. Such traces are traditionally estimated with "noise vectors"
sandwiching the operator. We explore alternative approaches based on polynomial
approximations of the inverse Dirac operator.Comment: Eight pages, thirteen figures. Proceedings of the 35th International
Symposium on Lattice Field Theor
A Quantum Random Walk Search Algorithm
Quantum random walks on graphs have been shown to display many interesting
properties, including exponentially fast hitting times when compared with their
classical counterparts. However, it is still unclear how to use these novel
properties to gain an algorithmic speed-up over classical algorithms. In this
paper, we present a quantum search algorithm based on the quantum random walk
architecture that provides such a speed-up. It will be shown that this
algorithm performs an oracle search on a database of items with
calls to the oracle, yielding a speed-up similar to other quantum
search algorithms. It appears that the quantum random walk formulation has
considerable flexibility, presenting interesting opportunities for development
of other, possibly novel quantum algorithms.Comment: 13 pages, 3 figure
Multi-site mean-field theory for cold bosonic atoms in optical lattices
We present a detailed derivation of a multi-site mean-field theory (MSMFT)
used to describe the Mott-insulator to superfluid transition of bosonic atoms
in optical lattices. The approach is based on partitioning the lattice into
small clusters which are decoupled by means of a mean field approximation. This
approximation invokes local superfluid order parameters defined for each of the
boundary sites of the cluster. The resulting MSMFT grand potential has a
non-trivial topology as a function of the various order parameters. An
understanding of this topology provides two different criteria for the
determination of the Mott insulator superfluid phase boundaries. We apply this
formalism to -dimensional hypercubic lattices in one, two and three
dimensions, and demonstrate the improvement in the estimation of the phase
boundaries when MSMFT is utilized for increasingly larger clusters, with the
best quantitative agreement found for . The MSMFT is then used to examine
a linear dimer chain in which the on-site energies within the dimer have an
energy separation of . This system has a complicated phase diagram
within the parameter space of the model, with many distinct Mott phases
separated by superfluid regions.Comment: 30 pages, 23 figures, accepted for publication in Phys. Rev.
High frequency homogenisation for elastic lattices
A complete methodology, based on a two-scale asymptotic approach, that
enables the homogenisation of elastic lattices at non-zero frequencies is
developed. Elastic lattices are distinguished from scalar lattices in that two
or more types of coupled waves exist, even at low frequencies. Such a theory
enables the determination of effective material properties at both low and high
frequencies. The theoretical framework is developed for the propagation of
waves through lattices of arbitrary geometry and dimension. The asymptotic
approach provides a method through which the dispersive properties of lattices
at frequencies near standing waves can be described; the theory accurately
describes both the dispersion curves and the response of the lattice near the
edges of the Brillouin zone. The leading order solution is expressed as a
product between the standing wave solution and long-scale envelope functions
that are eigensolutions of the homogenised partial differential equation. The
general theory is supplemented by a pair of illustrative examples for two
archetypal classes of two-dimensional elastic lattices. The efficiency of the
asymptotic approach in accurately describing several interesting phenomena is
demonstrated, including dynamic anisotropy and Dirac cones.Comment: 24 pages, 7 figure
Accurate determination of the superfluid-insulator transition in the one-dimensional Bose-Hubbard model
The quantum phase transition point between the insulator and the superfluid
phase at unit filling factor of the infinite one-dimensional Bose-Hubbard model
is numerically computed with a high accuracy, better than current state of the
art calculations. The method uses the infinite system version of the time
evolving block decimation algorithm, here tested in a challenging case.Comment: revised version, modified fig.1, a reference added, 5pp. 3fig
Critical properties of an aperiodic model for interacting polymers
We investigate the effects of aperiodic interactions on the critical behavior
of an interacting two-polymer model on hierarchical lattices (equivalent to the
Migadal-Kadanoff approximation for the model on Bravais lattices), via
renormalization-group and tranfer-matrix calculations. The exact
renormalization-group recursion relations always present a symmetric fixed
point, associated with the critical behavior of the underlying uniform model.
If the aperiodic interactions, defined by s ubstitution rules, lead to relevant
geometric fluctuations, this fixed point becomes fully unstable, giving rise to
novel attractors of different nature. We present an explicit example in which
this new attractor is a two-cycle, with critical indices different from the
uniform model. In case of the four-letter Rudin-Shapiro substitution rule, we
find a surprising closed curve whose points are attractors of period two,
associated with a marginal operator. Nevertheless, a scaling analysis indicates
that this attractor may lead to a new critical universality class. In order to
provide an independent confirmation of the scaling results, we turn to a direct
thermodynamic calculation of the specific-heat exponent. The thermodynamic free
energy is obtained from a transfer matrix formalism, which had been previously
introduced for spin systems, and is now extended to the two-polymer model with
aperiodic interactions.Comment: 19 pages, 6 eps figures, to appear in J. Phys A: Math. Ge
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