341 research outputs found
Exact Solution of a Three-Dimensional Dimer System
We consider a three-dimensional lattice model consisting of layers of vertex
models coupled with interlayer interactions. For a particular non-trivial
interlayer interaction between charge-conserving vertex models and using a
transfer matrix approach, we show that the eigenvalues and eigenvectors of the
transfer matrix are related to those of the two-dimensional vertex model. The
result is applied to analyze the phase transitions in a realistic
three-dimensional dimer system.Comment: 11 pages in REVTex with 2 PS figure
Why spontaneous symmetry breaking disappears in a bridge system with PDE-friendly boundaries
We consider a driven diffusive system with two types of particles, A and B,
coupled at the ends to reservoirs with fixed particle densities. To define
stochastic dynamics that correspond to boundary reservoirs we introduce
projection measures. The stationary state is shown to be approached dynamically
through an infinite reflection of shocks from the boundaries. We argue that
spontaneous symmetry breaking observed in similar systems is due to placing
effective impurities at the boundaries and therefore does not occur in our
system. Monte-Carlo simulations confirm our results.Comment: 24 pages, 7 figure
On the Fibonacci universality classes in nonlinear fluctuating hydrodynamics
We present a lattice gas model that without fine tuning of parameters is
expected to exhibit the so far elusive modified Kardar-Parisi-Zhang (KPZ)
universality class. To this end, we review briefly how non-linear fluctuating
hydrodynamics in one dimension predicts that all dynamical universality classes
in its range of applicability belong to an infinite discrete family which we
call Fibonacci family since their dynamical exponents are the Kepler ratios
of neighbouring Fibonacci numbers , including
diffusion (), KPZ (), and the limiting ratio which is the
golden mean . Then we revisit the case of two
conservation laws to which the modified KPZ model belongs. We also derive
criteria on the macroscopic currents to lead to other non-KPZ universality
classes.Comment: 17 page
Changes of gas metabolism, gas homeostasis and tissue respiration in rats during prolonged hypokinesia
The oxygen uptake and tissue gas homeostasis of restrained albinic rats remained relatively constant during a 60 day experiment. The gas metabolism in some tissues changed, and O2 consumption increased in the liver and decreased in the myocardium. Capacity for physical work was reduced by five times. Hypokinesia for 60 days resulted in a delay in the animals growth
Lattice Statistics in Three Dimensions: Exact Solution of Layered Dimer and Layered Domain Wall Models
Exact analyses are given for two three-dimensional lattice systems: A system
of close-packed dimers placed in layers of honeycomb lattices and a layered
triangular-lattice interacting domain wall model, both with nontrivial
interlayer interactions. We show that both models are equivalent to a 5-vertex
model on the square lattice with interlayer vertex-vertex interactions. Using
the method of Bethe ansatz, a closed-form expression for the free energy is
obtained and analyzed. We deduce the exact phase diagram and determine the
nature of the phase transitions as a function of the strength of the interlayer
interaction.Comment: 22 pages in Revtex, 6 PS files, submitted to PR
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
Ergodicity breaking in one-dimensional reaction-diffusion systems
We investigate one-dimensional driven diffusive systems where particles may
also be created and annihilated in the bulk with sufficiently small rate. In an
open geometry, i.e., coupled to particle reservoirs at the two ends, these
systems can exhibit ergodicity breaking in the thermodynamic limit. The
triggering mechanism is the random motion of a shock in an effective potential.
Based on this physical picture we provide a simple condition for the existence
of a non-ergodic phase in the phase diagram of such systems. In the
thermodynamic limit this phase exhibits two or more stationary states. However,
for finite systems transitions between these states are possible. It is shown
that the mean lifetime of such a metastable state is exponentially large in
system-size. As an example the ASEP with the A0A--AAA reaction kinetics is
analyzed in detail. We present a detailed discussion of the phase diagram of
this particular model which indeed exhibits a phase with broken ergodicity. We
measure the lifetime of the metastable states with a Monte Carlo simulation in
order to confirm our analytical findings.Comment: 25 pages, 14 figures; minor alterations, typos correcte
The Bethe ansatz as a matrix product ansatz
The Bethe ansatz in its several formulations is the common tool for the exact
solution of one dimensional quantum Hamiltonians. This ansatz asserts that the
several eigenfunctions of the Hamiltonians are given in terms of a sum of
permutations of plane waves. We present results that induce us to expect that,
alternatively, the eigenfunctions of all the exact integrable quantum chains
can also be expressed by a matrix product ansatz. In this ansatz the several
components of the eigenfunctions are obtained through the algebraic properties
of properly defined matrices. This ansatz allows an unified formulation of
several exact integrable Hamiltonians. We show how to formulate this ansatz for
a huge family of quantum chains like the anisotropic Heisenberg model,
Fateev-Zamolodchikov model, Izergin-Korepin model, model, Hubbard model,
etc.Comment: 4 pages and no figure
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