591 research outputs found
Derivation of a Matrix Product Representation for the Asymmetric Exclusion Process from Algebraic Bethe Ansatz
We derive, using the algebraic Bethe Ansatz, a generalized Matrix Product
Ansatz for the asymmetric exclusion process (ASEP) on a one-dimensional
periodic lattice. In this Matrix Product Ansatz, the components of the
eigenvectors of the ASEP Markov matrix can be expressed as traces of products
of non-commuting operators. We derive the relations between the operators
involved and show that they generate a quadratic algebra. Our construction
provides explicit finite dimensional representations for the generators of this
algebra.Comment: 16 page
Generalization of the matrix product ansatz for integrable chains
We present a general formulation of the matrix product ansatz for exactly
integrable chains on periodic lattices. This new formulation extends the matrix
product ansatz present on our previous articles (F. C. Alcaraz and M. J. Lazo
J. Phys. A: Math. Gen. 37 (2004) L1-L7 and J. Phys. A: Math. Gen. 37 (2004)
4149-4182.)Comment: 5 pages. to appear in J. Phys. A: Math. Ge
Asymmetric exclusion model with several kinds of impurities
We formulate a new integrable asymmetric exclusion process with
kinds of impurities and with hierarchically ordered dynamics.
The model we proposed displays the full spectrum of the simple asymmetric
exclusion model plus new levels. The first excited state belongs to these new
levels and displays unusual scaling exponents. We conjecture that, while the
simple asymmetric exclusion process without impurities belongs to the KPZ
universality class with dynamical exponent 3/2, our model has a scaling
exponent . In order to check the conjecture, we solve numerically the
Bethe equation with N=3 and N=4 for the totally asymmetric diffusion and found
the dynamical exponents 7/2 and 9/2 in these cases.Comment: to appear in JSTA
The asymmetric simple exclusion process: an integrable model for non-equilibrium statistical mechanics
The asymmetric simple exclusion process (ASEP) plays the role of a paradigm
in non-equilibrium statistical mechanics. We review exact results for the ASEP
obtained by Bethe ansatz and put emphasis on the algebraic properties of this
model. The Bethe equations for the eigenvalues of the Markov matrix of the ASEP
are derived from the algebraic Bethe ansatz. Using these equations we explain
how to calculate the spectral gap of the model and how global spectral
properties such as the existence of multiplets can be predicted. An extension
of the Bethe ansatz leads to an analytic expression for the large deviation
function of the current in the ASEP that satisfies the Gallavotti-Cohen
relation. Finally, we describe some variants of the ASEP that are also solvable
by Bethe ansatz.
Keywords: ASEP, integrable models, Bethe ansatz, large deviations.Comment: 24 pages, 5 figures, published in the "special issue on recent
advances in low-dimensional quantum field theories", P. Dorey, G. Dunne and
J. Feinberg editor
Hidden symmetries in the asymmetric exclusion process
We present a spectral study of the evolution matrix of the totally asymmetric
exclusion process on a ring at half filling. The natural symmetries
(translation, charge conjugation combined with reflection) predict only two
fold degeneracies. However, we have found that degeneracies of higher order
also exist and, as the system size increases, higher and higher orders appear.
These degeneracies become generic in the limit of very large systems. This
behaviour can be explained by the Bethe Ansatz and suggests the presence of
hidden symmetries in the model.
Keywords: ASEP, Markov matrix, symmetries, spectral degeneracies, Bethe
Ansatz.Comment: 16 page
Carrier Thermal Conductivity: Analysis and Application to Submicron-Device Simulation
Within a correlation-function (CF) formalism, the kinetic coefficientsof charge carriers in semiconductors are studied under different conditions. For the case of linear response in equilibrium, thetransitions from the non-degenerate to the degenerate regimes as wellas from ballistic to diffusive conditions are discussed within ananalytical model. Generalizing the method to high-field transport innondegenerate semiconductors, the CFs are determined by Monte Carlo (MC) calculations for bulk silicon from which the appropriate thermalconductivity has been
obtained and included into the hydrodynamic code HEIELDS. For an n+nn+ submicron structure the temperatureand velocity profiles of the carriers have been calculated with HFIELDS
Changes in private health service utilisation and access to the Italian National Health Service between 2006 and 2019: A cross-sectional comparative study
Objectives: Previous research highlighted that in the early 2000s a significant share of the Italian population used and paid out of pocket for private healthcare services even when they could potentially have received the same treatments from the National Health Service (NHS). The decrease in public investments in healthcare and the increase in health needs due to the population ageing may have modified the use of private health services and equity of access to the Italian NHS. This study aims to investigate the change in the prevalence of individuals who have fully paid out of pocket for accessing healthcare services in Italy between 2006 and 2019 and the main reasons behind this choice. Design: Cross-sectional comparative study. Participants and comparison: Two representative samples of the Italian population were collected in 2006 and 2019. Outcome measures: Prevalence of access to fully paid out-of-pocket private health services; type of service of the last fully paid out-of-pocket access; main reasons for the last fully paid out-of-pocket access. Results: We found an increase in the prevalence of people who declared having fully paid out of pocket at least one access to health services during their lifetime from 79.0% in 2006 to 91.9% in 2019 (adjusted OR 2.66; 95% CI 1.98 to 3.58). 'To avoid waiting times' was the main reason and it was significantly more frequent in 2019 compared with 2006 (adjusted OR 1.75; 95% CI 1.45 to 2.11). Conclusions: This comparative study, conducted the year before the outbreak of the COVID-19 pandemic, highlighted an increase in the prevalence of Italian residents who have fully paid out of pocket for access to health services to overcome long waiting times. Our findings may indicate a reduced access and possible worsening of the equity of access to the public and universalistic Italian NHS between 2006 and 2019
Percolation Transition in the random antiferromagnetic spin-1 chain
We give a physical description in terms of percolation theory of the phase
transition that occurs when the disorder increases in the random
antiferromagnetic spin-1 chain between a gapless phase with topological order
and a random singlet phase. We study the statistical properties of the
percolation clusters by numerical simulations, and we compute exact exponents
characterizing the transition by a real-space renormalization group
calculation.Comment: 9 pages, 4 encapsulated Postscript figures, REVTeX 3.
Some Exact Results for the Exclusion Process
The asymmetric simple exclusion process (ASEP) is a paradigm for
non-equilibrium physics that appears as a building block to model various
low-dimensional transport phenomena, ranging from intracellular traffic to
quantum dots. We review some recent results obtained for the system on a
periodic ring by using the Bethe Ansatz. We show that this method allows to
derive analytically many properties of the dynamics of the model such as the
spectral gap and the generating function of the current. We also discuss the
solution of a generalized exclusion process with -species of particles and
explain how a geometric construction inspired from queuing theory sheds light
on the Matrix Product Representation technique that has been very fruitful to
derive exact results for the ASEP.Comment: 21 pages; Proceedings of STATPHYS24 (Cairns, Australia, July 2010
Bethe Ansatz calculation of the spectral gap of the asymmetric exclusion process
We present a new derivation of the spectral gap of the totally asymmetric
exclusion process on a half-filled ring of size L by using the Bethe Ansatz. We
show that, in the large L limit, the Bethe equations reduce to a simple
transcendental equation involving the polylogarithm, a classical special
function. By solving that equation, the gap and the dynamical exponent are
readily obtained. Our method can be extended to a system with an arbitrary
density of particles.
Keywords: ASEP, Bethe Ansatz, Dynamical Exponent, Spectral Gap
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