5,091 research outputs found
A general spectral transformation simultaneously including a Fourier transformation and a Laplace transformation
A general spectral transformation is proposed and described. Its spectrum can be interpreted as a Fourier spectrum or a Laplace spectrum. The laws and functions of the method are discussed in comparison with the known transformations, and a sample application is shown
Theory of quantum Loschmidt echoes
In this paper we review our recent work on the theoretical approach to
quantum Loschmidt echoes, i.e. various properties of the so called echo
dynamics -- the composition of forward and backward time evolutions generated
by two slightly different Hamiltonians, such as the state autocorrelation
function (fidelity) and the purity of a reduced density matrix traced over a
subsystem (purity fidelity). Our main theoretical result is a linear response
formalism, expressing the fidelity and purity fidelity in terms of integrated
time autocorrelation function of the generator of the perturbation.
Surprisingly, this relation predicts that the decay of fidelity is the slower
the faster the decay of correlations. In particular for a static
(time-independent) perturbation, and for non-ergodic and non-mixing dynamics
where asymptotic decay of correlations is absent, a qualitatively different and
faster decay of fidelity is predicted on a time scale 1/delta as opposed to
mixing dynamics where the fidelity is found to decay exponentially on a
time-scale 1/delta^2, where delta is a strength of perturbation. A detailed
discussion of a semi-classical regime of small effective values of Planck
constant is given where classical correlation functions can be used to predict
quantum fidelity decay. Note that the correct and intuitively expected
classical stability behavior is recovered in the classical limit, as the
perturbation and classical limits do not commute. The theoretical results are
demonstrated numerically for two models, the quantized kicked top and the
multi-level Jaynes Cummings model. Our method can for example be applied to the
stability analysis of quantum computation and quantum information processing.Comment: 29 pages, 11 figures ; Maribor 2002 proceeding
Diffusive high-temperature transport in the one-dimensional Hubbard model
We consider charge and spin transport in the one-dimensional Hubbard model at
infinite temperature, half-filling and zero magnetization. Implementing
matrix-product-operator simulations of the non-equilibrium steady states of
boundary-driven open Hubbard chains for up to 100 sites we find clear evidence
of diffusive transport for any (non-zero and finite) value of the interaction
U.Comment: 6 pages RevTeX + 8 eps figures; revised and extended versio
Transport properties of a boundary-driven one-dimensional gas of spinless fermions
We analytically study a system of spinless fermions driven at the boundary
with an oscillating chemical potential. Various transport regimes can be
observed: at zero driving frequency the particle current through the system is
independent of the system's length; at the phase-transition frequency, being
equal to the bandwidth, the current decays as n^{-alpha} with the chain length
n, alpha being either 2 or 3; below the transition the scaling of the current
is n^{-1/2}, indicating anomalous transport, while it is exponentially small
exp{(-n/2xi)} above the transition. Therefore, by a simple change of frequency
of the a.c. driving one can vary transport from ballistic, anomalous, to
insulating.Comment: 9 pages, 10 figure
Using RDF to Model the Structure and Process of Systems
Many systems can be described in terms of networks of discrete elements and
their various relationships to one another. A semantic network, or
multi-relational network, is a directed labeled graph consisting of a
heterogeneous set of entities connected by a heterogeneous set of
relationships. Semantic networks serve as a promising general-purpose modeling
substrate for complex systems. Various standardized formats and tools are now
available to support practical, large-scale semantic network models. First, the
Resource Description Framework (RDF) offers a standardized semantic network
data model that can be further formalized by ontology modeling languages such
as RDF Schema (RDFS) and the Web Ontology Language (OWL). Second, the recent
introduction of highly performant triple-stores (i.e. semantic network
databases) allows semantic network models on the order of edges to be
efficiently stored and manipulated. RDF and its related technologies are
currently used extensively in the domains of computer science, digital library
science, and the biological sciences. This article will provide an introduction
to RDF/RDFS/OWL and an examination of its suitability to model discrete element
complex systems.Comment: International Conference on Complex Systems, Boston MA, October 200
Combining Full-Shape and BAO Analyses of Galaxy Power Spectra: A 1.6% CMB-independent constraint on H0
We present cosmological constraints from a joint analysis of the pre- and
post-reconstruction galaxy power spectrum multipoles from the final data
release of the Baryon Oscillation Spectroscopic Survey (BOSS). Geometric
constraints are obtained from the positions of BAO peaks in reconstructed
spectra, analyzed in combination with the unreconstructed spectra in a
full-shape (FS) likelihood using a joint covariance matrix, giving stronger
parameter constraints than FS-only or BAO-only analyses. We introduce a new
method for obtaining constraints from reconstructed spectra based on a
correlated theoretical error, which is shown to be simple, robust, and
applicable to any flavor of density-field reconstruction. Assuming CDM
with massive neutrinos, we analyze data from two redshift bins
and obtain constraints on the Hubble
constant , using only a single prior on the current baryon density
from Big Bang Nucleosynthesis (BBN) and no knowledge of the power
spectrum slope . This gives , with the inclusion of BAO
data sharpening the measurement by , representing one of the strongest
current constraints on independent of cosmic microwave background data.
Restricting to the best-fit slope from Planck (but without additional
priors on the spectral shape), we obtain a measurement of . We find strong constraints on the
cosmological parameters from a joint analysis of the FS, BAO, and Planck data.
This sets new bounds on the sum of neutrino masses (at confidence) and the effective number of
relativistic degrees of freedom , though
contours are not appreciably narrowed by the inclusion of BAO data.Comment: 42 pages, 12 figures, accepted by JCAP, likelihoods available at
https://github.com/Michalychforever/lss_montepython (minor typo corrected
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