1,662 research outputs found
The Tunneling Hybrid Monte-Carlo algorithm
The hermitian Wilson kernel used in the construction of the domain-wall and
overlap Dirac operators has exceptionally small eigenvalues that make it
expensive to reach high-quality chiral symmetry for domain-wall fermions, or
high precision in the case of the overlap operator. An efficient way of
suppressing such eigenmodes consists of including a positive power of the
determinant of the Wilson kernel in the Boltzmann weight, but doing this also
suppresses tunneling between topological sectors. Here we propose a
modification of the Hybrid Monte-Carlo algorithm which aims to restore
tunneling between topological sectors by excluding the lowest eigenmodes of the
Wilson kernel from the molecular-dynamics evolution, and correcting for this at
the accept/reject step. We discuss the implications of this modification for
the acceptance rate.Comment: improved discussion in appendix B, RevTeX, 19 page
Remark on lattice BRST invariance
A recently claimed resolution to the lattice Gribov problem in the context of
chiral lattice gauge theories is examined. Unfortunately, I find that the old
problem remains.Comment: 4 pages, plain TeX, presentation improved (see acknowledgments
Mobility edge in lattice QCD
We determine the location of the mobility edge in the spectrum of
the hermitian Wilson operator on quenched ensembles. We confirm a theoretical
picture of localization proposed for the Aoki phase diagram. When
we also determine some key properties of the localized eigenmodes with
eigenvalues . Our results lead to simple tests for the
validity of simulations with overlap and domain-wall fermions.Comment: revtex, 4 pages, 1 figure, minor change
Chiral Fermions on the Lattice through Gauge Fixing -- Perturbation Theory
We study the gauge-fixing approach to the construction of lattice chiral
gauge theories in one-loop weak-coupling perturbation theory. We show how
infrared properties of the gauge degrees of freedom determine the nature of the
continuous phase transition at which we take the continuum limit. The fermion
self-energy and the vacuum polarization are calculated, and confirm that, in
the abelian case, this approach can be used to put chiral gauge theories on the
lattice in four dimensions. We comment on the generalization to the nonabelian
case.Comment: 31 pages, 5 figures, two refs. adde
Perturbative study for domain-wall fermions in 4+1 dimensions
We investigate a U(1) chiral gauge model in 4+1 dimensions formulated on the
lattice via the domain-wall method. We calculate an effective action for smooth
background gauge fields at a fermion one loop level. From this calculation we
discuss properties of the resulting 4 dimensional theory, such as gauge
invariance of 2 point functions, gauge anomalies and an anomaly in the fermion
number current.Comment: 39 pages incl. 9 figures, REVTeX+epsf, uuencoded Z-compressed .tar
fil
The Phase Diagram and Spectrum of Gauge-Fixed Abelian Lattice Gauge Theory
We consider a lattice discretization of a covariantly gauge-fixed abelian
gauge theory. The gauge fixing is part of the action defining the theory, and
we study the phase diagram in detail. As there is no BRST symmetry on the
lattice, counterterms are needed, and we construct those explicitly. We show
that the proper adjustment of these counterterms drives the theory to a new
type of phase transition, at which we recover a continuum theory of (free)
photons. We present both numerical and (one-loop) perturbative results, and
show that they are in good agreement near this phase transition. Since
perturbation theory plays an important role, it is important to choose a
discretization of the gauge-fixing action such that lattice perturbation theory
is valid. Indeed, we find numerical evidence that lattice actions not
satisfying this requirement do not lead to the desired continuum limit. While
we do not consider fermions here, we argue that our results, in combination
with previous work, provide very strong evidence that this new phase transition
can be used to define abelian lattice chiral gauge theories.Comment: 42 pages, 30 figure
Before sailing on a domain-wall sea
We discuss the very different roles of the valence-quark and the sea-quark
residual masses ( and ) in dynamical domain-wall fermions
simulations. Focusing on matrix elements of the effective weak hamiltonian
containing a power divergence, we find that can be a source of a
much bigger systematic error. To keep all systematic errors due to residual
masses at the 1% level, we estimate that one needs
and , at a lattice spacing fm. The
practical implications are that (1) optimal use of computer resources calls for
a mixed scheme with different domain-wall fermion actions for the valence and
sea quarks; (2) better domain-wall fermion actions are needed for both the sea
and the valence sectors.Comment: latex, 25 pages. Improved discussion in appendix, including
correction of some technical mistakes; ref. adde
Analysis of Different Types of Regret in Continuous Noisy Optimization
The performance measure of an algorithm is a crucial part of its analysis.
The performance can be determined by the study on the convergence rate of the
algorithm in question. It is necessary to study some (hopefully convergent)
sequence that will measure how "good" is the approximated optimum compared to
the real optimum. The concept of Regret is widely used in the bandit literature
for assessing the performance of an algorithm. The same concept is also used in
the framework of optimization algorithms, sometimes under other names or
without a specific name. And the numerical evaluation of convergence rate of
noisy algorithms often involves approximations of regrets. We discuss here two
types of approximations of Simple Regret used in practice for the evaluation of
algorithms for noisy optimization. We use specific algorithms of different
nature and the noisy sphere function to show the following results. The
approximation of Simple Regret, termed here Approximate Simple Regret, used in
some optimization testbeds, fails to estimate the Simple Regret convergence
rate. We also discuss a recent new approximation of Simple Regret, that we term
Robust Simple Regret, and show its advantages and disadvantages.Comment: Genetic and Evolutionary Computation Conference 2016, Jul 2016,
Denver, United States. 201
Conserved Quantities in Gravity via Noether Symmetry
This paper is devoted to investigate gravity using Noether symmetry
approach. For this purpose, we consider Friedmann Robertson-Walker (FRW)
universe and spherically symmetric spacetimes. The Noether symmetry generators
are evaluated for some specific choice of models in the presence of
gauge term. Further, we calculate the corresponding conserved quantities in
each case. Moreover, the importance and stability criteria of these models are
discussed.Comment: 14 pages, accepted for publication in Chin. Phys. Let
A study of chiral symmetry in quenched QCD using the Overlap-Dirac operator
We compute fermionic observables relevant to the study of chiral symmetry in
quenched QCD using the Overlap-Dirac operator for a wide range of the fermion
mass. We use analytical results to disentangle the contribution from exact zero
modes and simplify our numerical computations. Details concerning the numerical
implementation of the Overlap-Dirac operator are presented.Comment: 24 pages revtex with 5 postscript figures included by eps
- …