173 research outputs found
Dynamics of entanglement of bosonic modes on symmetric graphs
We investigate the dynamics of an initially disentangled Gaussian state on a
general finite symmetric graph. As concrete examples we obtain properties of
this dynamics on mean field graphs of arbitrary sizes. In the same way that
chains can be used for transmitting entanglement by their natural dynamics,
these graphs can be used to store entanglement. We also consider two kinds of
regular polyhedron which show interesting features of entanglement sharing.Comment: 14 pages, 11 figures, Accepted for publication in Physics Letters
General Reaction-Diffusion Processes With Separable Equations for Correlation Functions
We consider general multi-species models of reaction diffusion processes and
obtain a set of constraints on the rates which give rise to closed systems of
equations for correlation functions. Our results are valid in any dimension and
on any type of lattice. We also show that under these conditions the evolution
equations for two point functions at different times are also closed. As an
example we introduce a class of two species models which may be useful for the
description of voting processes or the spreading of epidemics.Comment: 17 pages, Latex, No figure
Exact Solution of the Quantum Calogero-Gaudin System and of its q-Deformation
A complete set of commuting observables for the Calogero-Gaudin system is
diagonalized, and the explicit form of the corresponding eigenvalues and
eigenfunctions is derived. We use a purely algebraic procedure exploiting the
co-algebra invariance of the model; with the proper technical modifications
this procedure can be applied to the deformed version of the model, which
is then also exactly solved.Comment: 20 pages Late
Algebraic Bethe Ansatz for the two species ASEP with different hopping rates
An ASEP with two species of particles and different hopping rates is
considered on a ring. Its integrability is proved and the Nested Algebraic
Bethe Ansatz is used to derive the Bethe Equations for states with arbitrary
numbers of particles of each type, generalizing the results of Derrida and
Evans. We present also formulas for the total velocity of particles of a given
type and their limit for large size of the system and finite densities of the
particles.Comment: 14 page
Coarsening of Sand Ripples in Mass Transfer Models with Extinction
Coarsening of sand ripples is studied in a one-dimensional stochastic model,
where neighboring ripples exchange mass with algebraic rates, , and ripples of zero mass are removed from the system. For ripples vanish through rare fluctuations and the average ripples mass grows
as \avem(t) \sim -\gamma^{-1} \ln (t). Temporal correlations decay as
or depending on the symmetry of the mass transfer, and
asymptotically the system is characterized by a product measure. The stationary
ripple mass distribution is obtained exactly. For ripple evolution
is linearly unstable, and the noise in the dynamics is irrelevant. For the problem is solved on the mean field level, but the mean-field theory
does not adequately describe the full behavior of the coarsening. In
particular, it fails to account for the numerically observed universality with
respect to the initial ripple size distribution. The results are not restricted
to sand ripple evolution since the model can be mapped to zero range processes,
urn models, exclusion processes, and cluster-cluster aggregation.Comment: 10 pages, 8 figures, RevTeX4, submitted to Phys. Rev.
Matrix product approach for the asymmetric random average process
We consider the asymmetric random average process which is a one-dimensional
stochastic lattice model with nearest neighbour interaction but continuous and
unbounded state variables. First, the explicit functional representations,
so-called beta densities, of all local interactions leading to steady states of
product measure form are rigorously derived. This also completes an outstanding
proof given in a previous publication. Then, we present an alternative solution
for the processes with factorized stationary states by using a matrix product
ansatz. Due to continuous state variables we obtain a matrix algebra in form of
a functional equation which can be solved exactly.Comment: 17 pages, 1 figur
Classical Dynamical Systems from q-algebras:"cluster" variables and explicit solutions
A general procedure to get the explicit solution of the equations of motion
for N-body classical Hamiltonian systems equipped with coalgebra symmetry is
introduced by defining a set of appropriate collective variables which are
based on the iterations of the coproduct map on the generators of the algebra.
In this way several examples of N-body dynamical systems obtained from
q-Poisson algebras are explicitly solved: the q-deformed version of the sl(2)
Calogero-Gaudin system (q-CG), a q-Poincare' Gaudin system and a system of
Ruijsenaars type arising from the same (non co-boundary) q-deformation of the
(1+1) Poincare' algebra. Also, a unified interpretation of all these systems as
different Poisson-Lie dynamics on the same three dimensional solvable Lie group
is given.Comment: 19 Latex pages, No figure
A systematic construction of completely integrable Hamiltonians from coalgebras
A universal algorithm to construct N-particle (classical and quantum)
completely integrable Hamiltonian systems from representations of coalgebras
with Casimir element is presented. In particular, this construction shows that
quantum deformations can be interpreted as generating structures for integrable
deformations of Hamiltonian systems with coalgebra symmetry. In order to
illustrate this general method, the algebra and the oscillator
algebra are used to derive new classical integrable systems including a
generalization of Gaudin-Calogero systems and oscillator chains. Quantum
deformations are then used to obtain some explicit integrable deformations of
the previous long-range interacting systems and a (non-coboundary) deformation
of the Poincar\'e algebra is shown to provide a new
Ruijsenaars-Schneider-like Hamiltonian.Comment: 26 pages, LaTe
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