3,254 research outputs found
The Exact Solution of the Asymmetric Exclusion Problem With Particles of Arbitrary Size: Matrix Product Ansatz
The exact solution of the asymmetric exclusion problem and several of its
generalizations is obtained by a matrix product {\it ansatz}. Due to the
similarity of the master equation and the Schr\"odinger equation at imaginary
times the solution of these problems reduces to the diagonalization of a one
dimensional quantum Hamiltonian. We present initially the solution of the
problem when an arbitrary mixture of molecules, each of then having an
arbitrary size () in units of lattice spacing, diffuses
asymmetrically on the lattice. The solution of the more general problem where
we have | the diffusion of particles belonging to distinct class of
particles (), with hierarchical order, and arbitrary sizes is also
solved. Our matrix product {\it ansatz} asserts that the amplitudes of an
arbitrary eigenfunction of the associated quantum Hamiltonian can be expressed
by a product of matrices. The algebraic properties of the matrices defining the
{\it ansatz} depend on the particular associated Hamiltonian. The absence of
contradictions in the algebraic relations defining the algebra ensures the
exact integrability of the model. In the case of particles distributed in
classes, the associativity of the above algebra implies the Yang-Baxter
relations of the exact integrable model.Comment: 42 pages, 1 figur
Exact solutions of exactly integrable quantum chains by a matrix product ansatz
Most of the exact solutions of quantum one-dimensional Hamiltonians are
obtained thanks to the success of the Bethe ansatz on its several formulations.
According to this ansatz the amplitudes of the eigenfunctions of the
Hamiltonian are given by a sum of permutations of appropriate plane waves. In
this paper, alternatively, we present a matrix product ansatz that asserts that
those amplitudes are given in terms of a matrix product. The eigenvalue
equation for the Hamiltonian define the algebraic properties of the matrices
defining the amplitudes. The existence of a consistent algebra imply the exact
integrability of the model. The matrix product ansatz we propose allow an
unified and simple formulation of several exact integrable Hamiltonians. In
order to introduce and illustrate this ansatz we present the exact solutions of
several quantum chains with one and two global conservation laws and periodic
boundaries such as the XXZ chain, spin-1 Fateev-Zamolodchikov model,
Izergin-Korepin model, Sutherland model, t-J model, Hubbard model, etc.
Formulation of the matrix product ansatz for quantum chains with open ends is
also possible. As an illustration we present the exact solution of an extended
XXZ chain with -magnetic fields at the surface and arbitrary hard-core
exclusion among the spins.Comment: 57 pages, no figure
Role of tip size, orientation, and structural relaxations in first-principles studies of magnetic exchange force microscopy and spin-polarized scanning tunneling microscopy
Using first-principles calculations based on density functional theory (DFT),
we investigate the exchange interaction between a magnetic tip and a magnetic
sample which is detected in magnetic exchange force microscopy (MExFM) and also
occurs in spin-polarized scanning tunneling microscopy (SP-STM) experiments. As
a model tip-sample system, we choose Fe tips and one monolayer Fe on W(001)
which exhibits a checkerboard antiferromagnetic structure and has been
previously studied with both SP-STM and MExFM. We calculate the exchange forces
and energies as a function of tip-sample distance using different tip models
ranging from single Fe atoms to Fe pyramids consisting of up to 14 atoms. We
find that modelling the tip by a single Fe atom leads to qualitatively
different tip-sample interactions than using clusters consisting of several
atoms. Increasing the cluster size changes the calculated forces quantitatively
enhancing the detectable exchange forces. Rotating the tip with respect to the
surface unit cell has only a small influence on the tip-sample forces.
Interestingly, the exchange forces on the tip atoms in the nearest and
next-nearest layers from the apex atom are non-negligible and can be opposite
to that on the apex atom for a small tip. In addition, the apex atom interacts
not only with the surface atoms underneath but also with nearest-neighbors in
the surface. We find that structural relaxations of tip and sample due to their
interaction depend sensitively on the magnetic alignment of the two systems. As
a result the onset of significant exchange forces is shifted towards larger
tip-sample separations which facilitates their measurement in MExFM. At small
tip-sample separations, structural relaxations of tip apex and surface atoms
can either enhance or reduce the magnetic contrast measured in SP-STMComment: 14 pages, 13 figure
Generalization of the matrix product ansatz for integrable chains
We present a general formulation of the matrix product ansatz for exactly
integrable chains on periodic lattices. This new formulation extends the matrix
product ansatz present on our previous articles (F. C. Alcaraz and M. J. Lazo
J. Phys. A: Math. Gen. 37 (2004) L1-L7 and J. Phys. A: Math. Gen. 37 (2004)
4149-4182.)Comment: 5 pages. to appear in J. Phys. A: Math. Ge
Spin-glass phase transition and behavior of nonlinear susceptibility in the Sherrington-Kirkpatrick model with random fields
The behavior of the nonlinear susceptibility and its relation to the
spin-glass transition temperature , in the presence of random fields, are
investigated. To accomplish this task, the Sherrington-Kirkpatrick model is
studied through the replica formalism, within a one-step
replica-symmetry-breaking procedure. In addition, the dependence of the
Almeida-Thouless eigenvalue (replicon) on the random fields
is analyzed. Particularly, in absence of random fields, the temperature
can be traced by a divergence in the spin-glass susceptibility ,
which presents a term inversely proportional to the replicon . As a result of a relation between and , the
latter also presents a divergence at , which comes as a direct consequence
of at . However, our results show that, in the
presence of random fields, presents a rounded maximum at a temperature
, which does not coincide with the spin-glass transition temperature
(i.e., for a given applied random field). Thus, the maximum
value of at reflects the effects of the random fields in the
paramagnetic phase, instead of the non-trivial ergodicity breaking associated
with the spin-glass phase transition. It is also shown that still
maintains a dependence on the replicon , although in a more
complicated way, as compared with the case without random fields. These results
are discussed in view of recent observations in the LiHoYF
compound.Comment: accepted for publication in PR
Audiovisual narratives about the case Spain’s stolen babies
The critical discourse analysis is the tool used in this article, to study how audiovisual media have constructed mental representation about the historical facts occurred in Spain between the final stage of the Spanish Civil War (1936–1939) and the late 1980s: the theft of newborn babies. The State has failed in an attempt to establish policies that support truth, justice and reparation as it has been recalled by United Nations experts to the Government of Spain, and the reports and documentaries have become vehicles to capture and recover memories. Our objective is to analyze how this collective awareness has been realized and the contribution of reports and documentaries. Our results show that the Spanish television channels silence the Francoist context to depict the thefts as the product of economical mobs focused on child trafficking. The international channels, however, put the origin of the dictatorship at the center of the discourse
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