19,048 research outputs found
Non-ergodic states induced by impurity levels in quantum spin chains
The semi-infinite XY spin chain with an impurity at the boundary has been
chosen as a prototype of interacting many-body systems to test for non-ergodic
behavior. The model is exactly solvable in analytic way in the thermodynamic
limit, where energy eigenstates and the spectrum are obtained in closed form.
In addition of a continuous band, localized states may split off from the
continuum, for some values of the impurity parameters. In the next step, after
the preparation of an arbitrary non-equilibrium state, we observe the time
evolution of the site magnetization. Relaxation properties are described by the
long-time behavior, which is estimated using the stationary phase method.
Absence of localized states defines an ergodic region in parameter space, where
the system relaxes to a homogeneous magnetization. Out of this region, impurity
levels split from the band, and localization phenomena may lead to
non-ergodicity.Comment: 10 pages, 5 figures. arXiv admin note: substantial text overlap with
arXiv:1703.0344
Criteria for Bayesian model choice with application to variable selection
In objective Bayesian model selection, no single criterion has emerged as
dominant in defining objective prior distributions. Indeed, many criteria have
been separately proposed and utilized to propose differing prior choices. We
first formalize the most general and compelling of the various criteria that
have been suggested, together with a new criterion. We then illustrate the
potential of these criteria in determining objective model selection priors by
considering their application to the problem of variable selection in normal
linear models. This results in a new model selection objective prior with a
number of compelling properties.Comment: Published in at http://dx.doi.org/10.1214/12-AOS1013 the Annals of
Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical
Statistics (http://www.imstat.org
Multifractality of quantum wave functions in the presence of perturbations
We present a comprehensive study of the destruction of quantum
multifractality in the presence of perturbations. We study diverse
representative models displaying multifractality, including a pseudointegrable
system, the Anderson model and a random matrix model. We apply several types of
natural perturbations which can be relevant for experimental implementations.
We construct an analytical theory for certain cases, and perform extensive
large-scale numerical simulations in other cases. The data are analyzed through
refined methods including double scaling analysis. Our results confirm the
recent conjecture that multifractality breaks down following two scenarios. In
the first one, multifractality is preserved unchanged below a certain
characteristic length which decreases with perturbation strength. In the second
one, multifractality is affected at all scales and disappears uniformly for a
strong enough perturbation. Our refined analysis shows that subtle variants of
these scenarios can be present in certain cases. This study could guide
experimental implementations in order to observe quantum multifractality in
real systems.Comment: 20 pages, 27 figure
Two scenarios for quantum multifractality breakdown
We expose two scenarios for the breakdown of quantum multifractality under
the effect of perturbations. In the first scenario, multifractality survives
below a certain scale of the quantum fluctuations. In the other one, the
fluctuations of the wave functions are changed at every scale and each
multifractal dimension smoothly goes to the ergodic value. We use as generic
examples a one-dimensional dynamical system and the three-dimensional Anderson
model at the metal-insulator transition. Based on our results, we conjecture
that the sensitivity of quantum multifractality to perturbation is universal in
the sense that it follows one of these two scenarios depending on the
perturbation. We also discuss the experimental implications.Comment: 5 pages, 4 figures, minor modifications, published versio
A Prym-Narasimhan-Ramanan construction of principal bundle fixed points
Let be a compact Riemann surface and be a connected reductive complex
Lie group with centre . Consider the moduli space of polystable
principal holomorphic -bundles on . There is an action of the group
of isomorphism classes of -bundles over on induced
by the multiplication Let be a finite subgroup of
. Our goal is to find a Prym--Narasimhan--Ramanan-type construction
to describe the fixed points of under the action of . A main
ingredient in this construction is the theory of twisted equivariant bundles on
an \'etale cover of developed in arXiv:2208.0902(2).Comment: 52 pages. In this version we have substantially restructured the
content of the pape
Constraining the neutrino magnetic dipole moment from white dwarf pulsations
Pulsating white dwarf stars can be used as astrophysical laboratories to
constrain the properties of weakly interacting particles. Comparing the cooling
rates of these stars with the expected values from theoretical models allows us
to search for additional sources of cooling due to the emission of axions,
neutralinos, or neutrinos with magnetic dipole moment. In this work, we derive
an upper bound to the neutrino magnetic dipole moment using an estimate of the
rate of period change of the pulsating DB white dwarf star PG 1351+489. By
comparing the theoretical rate of change of period expected for this star with
the rate of change of period with time of PG 1351+489, we assess the possible
existence of additional cooling by neutrinos with magnetic dipole moment. Our
models suggest the existence of some additional cooling in this pulsating DB
white dwarf, consistent with a non-zero magnetic dipole moment. Our upper limit
for the neutrino magnetic dipole moment is somewhat less restrictive than, but
still compatible with, other limits inferred from the white dwarf luminosity
function or from the color-magnitude diagram of the Globular cluster M5.
Further improvements of the measurement of the rate of period change of the
dominant pulsation mode of PG 1351+489 will be necessary to confirm our bound.Comment: 18 pages, 10 figures, 3 tables. Accepted for publication in Journal
of Cosmology and Astroparticle Physic
- …