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 $N-1=0,1,2,...$ 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 $3/2+N-1$. 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 $N$-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