1,276 research outputs found
Finite-size left-passage probability in percolation
We obtain an exact finite-size expression for the probability that a
percolation hull will touch the boundary, on a strip of finite width. Our
calculation is based on the q-deformed Knizhnik--Zamolodchikov approach, and
the results are expressed in terms of symplectic characters. In the large size
limit, we recover the scaling behaviour predicted by Schramm's left-passage
formula. We also derive a general relation between the left-passage probability
in the Fortuin--Kasteleyn cluster model and the magnetisation profile in the
open XXZ chain with diagonal, complex boundary terms.Comment: 21 pages, 8 figure
Exact Ground State and Finite Size Scaling in a Supersymmetric Lattice Model
We study a model of strongly correlated fermions in one dimension with
extended N=2 supersymmetry. The model is related to the spin XXZ
Heisenberg chain at anisotropy with a real magnetic field on the
boundary. We exploit the combinatorial properties of the ground state to
determine its exact wave function on finite lattices with up to 30 sites. We
compute several correlation functions of the fermionic and spin fields. We
discuss the continuum limit by constructing lattice observables with well
defined finite size scaling behavior. For the fermionic model with periodic
boundary conditions we give the emptiness formation probability in closed form.Comment: 4 pages, 4 eps figure
Bethe Ansatz solution of a decagonal rectangle triangle random tiling
A random tiling of rectangles and triangles displaying a decagonal phase is
solved by Bethe Ansatz. Analogously to the solutions of the dodecagonal square
triangle and the octagonal rectangle triangle tiling an exact expression for
the maximum of the entropy is found.Comment: 17 pages, 4 figures, some remarks added and typos correcte
Raise and Peel Models of fluctuating interfaces and combinatorics of Pascal's hexagon
The raise and peel model of a one-dimensional fluctuating interface (model A)
is extended by considering one source (model B) or two sources (model C) at the
boundaries. The Hamiltonians describing the three processes have, in the
thermodynamic limit, spectra given by conformal field theory. The probability
of the different configurations in the stationary states of the three models
are not only related but have interesting combinatorial properties. We show
that by extending Pascal's triangle (which gives solutions to linear relations
in terms of integer numbers), to an hexagon, one obtains integer solutions of
bilinear relations. These solutions give not only the weights of the various
configurations in the three models but also give an insight to the connections
between the probability distributions in the stationary states of the three
models. Interestingly enough, Pascal's hexagon also gives solutions to a
Hirota's difference equation.Comment: 33 pages, an abstract and an introduction are rewritten, few
references are adde
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
Construction of a Coordinate Bethe Ansatz for the asymmetric simple exclusion process with open boundaries
The asymmetric simple exclusion process with open boundaries, which is a very
simple model of out-of-equilibrium statistical physics, is known to be
integrable. In particular, its spectrum can be described in terms of Bethe
roots. The large deviation function of the current can be obtained as well by
diagonalizing a modified transition matrix, that is still integrable: the
spectrum of this new matrix can be also described in terms of Bethe roots for
special values of the parameters. However, due to the algebraic framework used
to write the Bethe equations in the previous works, the nature of the
excitations and the full structure of the eigenvectors were still unknown. This
paper explains why the eigenvectors of the modified transition matrix are
physically relevant, gives an explicit expression for the eigenvectors and
applies it to the study of atypical currents. It also shows how the coordinate
Bethe Ansatz developped for the excitations leads to a simple derivation of the
Bethe equations and of the validity conditions of this Ansatz. All the results
obtained by de Gier and Essler are recovered and the approach gives a physical
interpretation of the exceptional points The overlap of this approach with
other tools such as the matrix Ansatz is also discussed. The method that is
presented here may be not specific to the asymmetric exclusion process and may
be applied to other models with open boundaries to find similar exceptional
points.Comment: references added, one new subsection and corrected typo
Membrane topology of the 60 kDa Oxa1p-homologue from Escherichia coli
We have characterized the membrane topology of a 60-kDa inner membrane protein from Escherichia coli that is homologous to the recently identified Oxa1p protein in Saccharomyces cerevisiae mitochondria implicated in the assembly of mitochondrial inner membrane proteins. Hydrophobicity and alkaline phosphatase fusion analyses suggest a membrane topology with six transmembrane segments, including an N-terminal signal-anchor sequence not present in mitochondrial Oxa1p. In contrast to partial N-terminal fusion protein constructs, the full-length protein folds into a protease-resistant conformation, suggesting that important folding determinants are present in the C-terminal part of the molecule
Exact expressions for correlations in the ground state of the dense O(1) loop model
Conjectures for analytical expressions for correlations in the dense O
loop model on semi infinite square lattices are given. We have obtained these
results for four types of boundary conditions. Periodic and reflecting boundary
conditions have been considered before. We give many new conjectures for these
two cases and review some of the existing results. We also consider boundaries
on which loops can end. We call such boundaries ''open''. We have obtained
expressions for correlations when both boundaries are open, and one is open and
the other one is reflecting. Also, we formulate a conjecture relating the
ground state of the model with open boundaries to Fully Packed Loop models on a
finite square grid. We also review earlier obtained results about this relation
for the three other types of boundary conditions. Finally, we construct a
mapping between the ground state of the dense O loop model and the XXZ
spin chain for the different types of boundary conditions.Comment: 25 pages, version accepted by JSTA
Slowest relaxation mode of the partially asymmetric exclusion process with open boundaries
We analyze the Bethe ansatz equations describing the complete spectrum of the
transition matrix of the partially asymmetric exclusion process on a finite
lattice and with the most general open boundary conditions. We extend results
obtained recently for totally asymmetric diffusion [J. de Gier and F.H.L.
Essler, J. Stat. Mech. P12011 (2006)] to the case of partial symmetry. We
determine the finite-size scaling of the spectral gap, which characterizes the
approach to stationarity at large times, in the low and high density regimes
and on the coexistence line. We observe boundary induced crossovers and discuss
possible interpretations of our results in terms of effective domain wall
theories.Comment: 30 pages, 9 figures, typeset for pdflatex; revised versio
Structure of the two-boundary XXZ model with non-diagonal boundary terms
We study the integrable XXZ model with general non-diagonal boundary terms at
both ends. The Hamiltonian is considered in terms of a two boundary extension
of the Temperley-Lieb algebra.
We use a basis that diagonalizes a conserved charge in the one-boundary case.
The action of the second boundary generator on this space is computed. For the
L-site chain and generic values of the parameters we have an irreducible space
of dimension 2^L. However at certain critical points there exists a smaller
irreducible subspace that is invariant under the action of all the bulk and
boundary generators. These are precisely the points at which Bethe Ansatz
equations have been formulated. We compute the dimension of the invariant
subspace at each critical point and show that it agrees with the splitting of
eigenvalues, found numerically, between the two Bethe Ansatz equations.Comment: 9 pages Latex. Minor correction
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