93 research outputs found
Equivalent T-Q relations and exact results for the open TASEP
Starting from the Bethe ansatz solution for the open Totally Asymmetric
Simple Exclusion Process (TASEP), we compute the largest eigenvalue of the
deformed Markovian matrix, in exact agreement with results obtained by the
matrix ansatz. We also compute the eigenvalues of the higher conserved charges.
The key step is to find a simpler equivalent T-Q relation, which is similar to
the one for the TASEP with periodic boundary conditions
Generalized Coordinate Bethe Ansatz for open spin chains with non-diagonal boundaries
We introduce a generalization of the original Coordinate Bethe Ansatz that
allows to treat the case of open spin chains with non-diagonal boundary
matrices. We illustrate it on two cases: the XXX and XXZ chains.
Short review on a joint work with N. Crampe (L2C) and D. Simon (LPMA), see
arXiv:1009.4119, arXiv:1105.4119 and arXiv:1106.3264.Comment: Proceeding of QTS7, Prague, 201
Relational lattices via duality
The natural join and the inner union combine in different ways tables of a
relational database. Tropashko [18] observed that these two operations are the
meet and join in a class of lattices-called the relational lattices- and
proposed lattice theory as an alternative algebraic approach to databases.
Aiming at query optimization, Litak et al. [12] initiated the study of the
equational theory of these lattices. We carry on with this project, making use
of the duality theory developed in [16]. The contributions of this paper are as
follows. Let A be a set of column's names and D be a set of cell values; we
characterize the dual space of the relational lattice R(D, A) by means of a
generalized ultrametric space, whose elements are the functions from A to D,
with the P (A)-valued distance being the Hamming one but lifted to subsets of
A. We use the dual space to present an equational axiomatization of these
lattices that reflects the combinatorial properties of these generalized
ultrametric spaces: symmetry and pairwise completeness. Finally, we argue that
these equations correspond to combinatorial properties of the dual spaces of
lattices, in a technical sense analogous of correspondence theory in modal
logic. In particular, this leads to an exact characterization of the finite
lattices satisfying these equations.Comment: Coalgebraic Methods in Computer Science 2016, Apr 2016, Eindhoven,
Netherland
Matrix product solution to a 2-species TASEP with open integrable boundaries
We present an explicit representation for the matrix product ansatz for some
two-species TASEP with open boundary conditions. The construction relies on the
integrability of the models, a property that constrains the possible rates at
the boundaries. The realisation is built on a tensor product of copies of the
DEHP algebras. Using this explicit construction, we are able to calculate the
partition function of the models. The densities and currents in the stationary
state are also computed. It leads to the phase diagram of the models. Depending
on the values of the boundary rates, we obtain for each species shock waves,
maximal current, or low/high densities phases.Comment: 23 page
Relaxation rate of the reverse biased asymmetric exclusion process
We compute the exact relaxation rate of the partially asymmetric exclusion
process with open boundaries, with boundary rates opposing the preferred
direction of flow in the bulk. This reverse bias introduces a length scale in
the system, at which we find a crossover between exponential and algebraic
relaxation on the coexistence line. Our results follow from a careful analysis
of the Bethe ansatz root structure.Comment: 22 pages, 12 figure
Generalized T-Q relations and the open spin-s XXZ chain with nondiagonal boundary terms
We consider the open spin-s XXZ quantum spin chain with nondiagonal boundary
terms. By exploiting certain functional relations at roots of unity, we derive
a generalized form of T-Q relation involving more than one independent Q(u),
which we use to propose the Bethe-ansatz-type expressions for the eigenvalues
of the transfer matrix. At most two of the boundary parameters are set to be
arbitrary and the bulk anisotropy parameter has values \eta = i\pi/2,
i\pi/4,... We also provide numerical evidence for the completeness of the
Bethe-ansatz-type solutions derived, using s = 1 case as an example.Comment: 23 pages. arXiv admin note: substantial text overlap with
arXiv:0901.3558; v2: published versio
The effect of data analysis strategies in density estimation of mountain ungulates using Distance sampling.
The effect of data analysis strategies in density estimation of mountain ungulates using distance sampling
Distance sampling is being extensively used to estimate the abundance of animal populations. Nevertheless, the great variety of ways in which data can be analyzed may limit comparisons due to the lack of standardization of such protocols. In this study, the influence of analytical procedures for distance sampling data on density estimates and their precision was assessed. We have used data from 21 surveys of mountain ungulates in the Iberian Peninsula, France and the Italian Alps. Data from such surveys were analyzed with the program Distance 6.0. Our analyses show that estimated density can be higher for higher levels of data truncation. We also confirm that the estimates tend to be more precise when data are analyzed without binning and without truncating. We found no evidence of size biased sampling as group size and distances were uncorrelated in most of our surveys. Despite distance sampling being a fairly robust methodology, it can be sensitive to some data analysis strategies
Matrix Coordinate Bethe Ansatz: Applications to XXZ and ASEP models
We present the construction of the full set of eigenvectors of the open ASEP
and XXZ models with special constraints on the boundaries. The method combines
both recent constructions of coordinate Bethe Ansatz and the old method of
matrix Ansatz specific to the ASEP. This "matrix coordinate Bethe Ansatz" can
be viewed as a non-commutative coordinate Bethe Ansatz, the non-commutative
part being related to the algebra appearing inComment: 18 pages; Version to appear in J Phys
Renyi entropy of the totally asymmetric exclusion process
The Renyi entropy is a generalisation of the Shannon entropy that is
sensitive to the fine details of a probability distribution. We present results
for the Renyi entropy of the totally asymmetric exclusion process (TASEP). We
calculate explicitly an entropy whereby the squares of configuration
probabilities are summed, using the matrix product formalism to map the problem
to one involving a six direction lattice walk in the upper quarter plane. We
derive the generating function across the whole phase diagram, using an
obstinate kernel method. This gives the leading behaviour of the Renyi entropy
and corrections in all phases of the TASEP. The leading behaviour is given by
the result for a Bernoulli measure and we conjecture that this holds for all
Renyi entropies. Within the maximal current phase the correction to the leading
behaviour is logarithmic in the system size. Finally, we remark upon a special
property of equilibrium systems whereby discontinuities in the Renyi entropy
arise away from phase transitions, which we refer to as secondary transitions.
We find no such secondary transition for this nonequilibrium system, supporting
the notion that these are specific to equilibrium cases
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