1,145 research outputs found
A refined Razumov-Stroganov conjecture II
We extend a previous conjecture [cond-mat/0407477] relating the
Perron-Frobenius eigenvector of the monodromy matrix of the O(1) loop model to
refined numbers of alternating sign matrices. By considering the O(1) loop
model on a semi-infinite cylinder with dislocations, we obtain the generating
function for alternating sign matrices with prescribed positions of 1's on
their top and bottom rows. This seems to indicate a deep correspondence between
observables in both models.Comment: 21 pages, 10 figures (3 in text), uses lanlmac, hyperbasics and epsf
macro
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
Exactly solvable quantum spin ladders associated with the orthogonal and symplectic Lie algebras
We extend the results of spin ladder models associated with the Lie algebras
to the case of the orthogonal and symplectic algebras $o(2^n),\
sp(2^n)$ where n is the number of legs for the system. Two classes of models
are found whose symmetry, either orthogonal or symplectic, has an explicit n
dependence. Integrability of these models is shown for an arbitrary coupling of
XX type rung interactions and applied magnetic field term.Comment: 7 pages, Late
Bethe Ansatz Solution of the Asymmetric Exclusion Process with Open Boundaries
We derive the Bethe ansatz equations describing the complete spectrum of the
transition matrix of the partially asymmetric exclusion process with the most
general open boundary conditions. For totally asymmetric diffusion we calculate
the spectral gap, which characterizes the approach to stationarity at large
times. We observe boundary induced crossovers in and between massive, diffusive
and KPZ scaling regimes.Comment: 4 pages, 2 figures, published versio
Limit shapes for the asymmetric five vertex model
We compute the free energy and surface tension function for the five-vertex
model, a model of non-intersecting monotone lattice paths on the grid in which
each corner gets a positive weight. We give a variational principle for limit
shapes in this setting, and show that the resulting Euler-Lagrange equation can
be integrated, giving explicit limit shapes parameterized by analytic
functions.Comment: 37 pages, 21 figure
Refined Razumov-Stroganov conjectures for open boundaries
Recently it has been conjectured that the ground-state of a Markovian
Hamiltonian, with one boundary operator, acting in a link pattern space is
related to vertically and horizontally symmetric alternating-sign matrices
(equivalently fully-packed loop configurations (FPL) on a grid with special
boundaries).We extend this conjecture by introducing an arbitrary boundary
parameter. We show that the parameter dependent ground state is related to
refined vertically symmetric alternating-sign matrices i.e. with prescribed
configurations (respectively, prescribed FPL configurations) in the next to
central row.
We also conjecture a relation between the ground-state of a Markovian
Hamiltonian with two boundary operators and arbitrary coefficients and some
doubly refined (dependence on two parameters) FPL configurations. Our
conjectures might be useful in the study of ground-states of the O(1) and XXZ
models, as well as the stationary states of Raise and Peel models.Comment: 11 pages LaTeX, 8 postscript figure
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
It was twenty years ago today: revisiting time-of-day choice in The Netherlands
Time-of-day (TOD) choice can be considered as a fifth stage in the modelling of transport behaviour, additional to the conventional four stages. Twenty years ago in The Netherlands, a stated preference (SP) study was designed for investigating the choice of time-of-day (departure time) and transport mode. A nested logit time period and mode choice model, largely based on this SP data set, was included as one of the components of The Netherlands national transport model (LMS). A new TOD SP survey has now been developed to obtain up-to-date information for the next re-estimation round of the LMS. The fieldwork was carried out in in 2019, followed by the re-estimation of the nested logit model of period and mode choice on the new SP data. The context for the SP is that of a tour (round trip) carried out by the respondent as car driver or by train, also distinguishing by travel purpose (commuting, business, education and other). This means that we are asking questions both about the outward leg of the tour and the inward leg. Both car drivers and train users are asked to participate in two SP experiments on TOD and mode choice: the first focussing on the trade-off between congestion or crowding and the departure/arrival times; the second also with differentiation in costs between peak and off-peak. Our tentative conclusion is that TOD choice seems to have become (relatively to mode choice) more flexible in the past two decades, in line with the trends towards more flexibility in scheduling activities over the day and a 24 hours economy. Moreover, we now estimate nest coefficients for both car drivers and train users (until now the assumption that had to be made in the LMS was that the nest coefficients for train followed those for car)
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