198 research outputs found
What are spin currents in Heisenberg magnets?
We discuss the proper definition of the spin current operator in Heisenberg
magnets subject to inhomogeneous magnetic fields. We argue that only the
component of the naive "current operator" J_ij S_i x S_j in the plane spanned
by the local order parameters and is related to real transport of
magnetization. Within a mean field approximation or in the classical ground
state the spin current therefore vanishes. Thus, finite spin currents are a
direct manifestation of quantum correlations in the system.Comment: 4 pages, 1 figure, published versio
Spectral gap of the totally asymmetric exclusion process at arbitrary filling
We calculate the spectral gap of the Markov matrix of the totally asymmetric
simple exclusion process (TASEP) on a ring of L sites with N particles. Our
derivation is simple and self-contained and extends a previous calculation that
was valid only for half-filling. We use a special property of the Bethe
equations for TASEP to reformulate them as a one-body problem. Our method is
closely related to the one used to derive exact large deviation functions of
the TASEP
Current Distribution and random matrix ensembles for an integrable asymmetric fragmentation process
We calculate the time-evolution of a discrete-time fragmentation process in
which clusters of particles break up and reassemble and move stochastically
with size-dependent rates. In the continuous-time limit the process turns into
the totally asymmetric simple exclusion process (only pieces of size 1 break
off a given cluster). We express the exact solution of master equation for the
process in terms of a determinant which can be derived using the Bethe ansatz.
From this determinant we compute the distribution of the current across an
arbitrary bond which after appropriate scaling is given by the distribution of
the largest eigenvalue of the Gaussian unitary ensemble of random matrices.
This result confirms universality of the scaling form of the current
distribution in the KPZ universality class and suggests that there is a link
between integrable particle systems and random matrix ensembles.Comment: 11 page
The spin-1/2 XXZ Heisenberg chain, the quantum algebra U_q[sl(2)], and duality transformations for minimal models
The finite-size scaling spectra of the spin-1/2 XXZ Heisenberg chain with
toroidal boundary conditions and an even number of sites provide a projection
mechanism yielding the spectra of models with a central charge c<1 including
the unitary and non-unitary minimal series. Taking into account the
half-integer angular momentum sectors - which correspond to chains with an odd
number of sites - in many cases leads to new spinor operators appearing in the
projected systems. These new sectors in the XXZ chain correspond to a new type
of frustration lines in the projected minimal models. The corresponding new
boundary conditions in the Hamiltonian limit are investigated for the Ising
model and the 3-state Potts model and are shown to be related to duality
transformations which are an additional symmetry at their self-dual critical
point. By different ways of projecting systems we find models with the same
central charge sharing the same operator content and modular invariant
partition function which however differ in the distribution of operators into
sectors and hence in the physical meaning of the operators involved. Related to
the projection mechanism in the continuum there are remarkable symmetry
properties of the finite XXZ chain. The observed degeneracies in the energy and
momentum spectra are shown to be the consequence of intertwining relations
involving U_q[sl(2)] quantum algebra transformations.Comment: This is a preprint version (37 pages, LaTeX) of an article published
back in 1993. It has been made available here because there has been recent
interest in conformal twisted boundary conditions. The "duality-twisted"
boundary conditions discussed in this paper are particular examples of such
boundary conditions for quantum spin chains, so there might be some renewed
interest in these result
A sufficient criterion for integrability of stochastic many-body dynamics and quantum spin chains
We propose a dynamical matrix product ansatz describing the stochastic
dynamics of two species of particles with excluded-volume interaction and the
quantum mechanics of the associated quantum spin chains respectively. Analyzing
consistency of the time-dependent algebra which is obtained from the action of
the corresponding Markov generator, we obtain sufficient conditions on the
hopping rates for identifing the integrable models. From the dynamical algebra
we construct the quadratic algebra of Zamolodchikov type, associativity of
which is a Yang Baxter equation. The Bethe ansatz equations for the spectra are
obtained directly from the dynamical matrix product ansatz.Comment: 19 pages Late
Educational effects of early or later secondary school tracking in Germany
This paper examines educational outcomes of pupils selected to secondary school types by different tracking regimes in a German state: Pupils are alternatively streamed after fourth grade or after sixth grade. Regression results indicate that, estimated on the mean, there are no negative effects of later tracking on educational outcomes in the middle of secondary school. Positive effects are observed for pupils with a less favorable family background. Quantile regressions reveal that the estimated effects of later tracking are positive for the lower quantiles but decrease monotonically over the conditional distribution of test scores
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