2,136 research outputs found
Integrable multiparametric quantum spin chains
Using Reshetikhin's construction for multiparametric quantum algebras we
obtain the associated multiparametric quantum spin chains. We show that under
certain restrictions these models can be mapped to quantum spin chains with
twisted boundary conditions. We illustrate how this general formalism applies
to construct multiparametric versions of the supersymmetric t-J and U models.Comment: 17 pages, RevTe
Integrable Hamiltonians with symmetry from the Fateev-Zamolodchikov model
A special case of the Fateev-Zamolodchikov model is studied resulting in a
solution of the Yang-Baxter equation with two spectral parameters. Integrable
models from this solution are shown to have the symmetry of the Drinfeld double
of a dihedral group. Viewing this solution as a descendant of the zero-field
six-vertex model allows for the construction of functional relations and Bethe
ansatz equations
Exact solution of the simplest super-orthosymplectic invariant magnet
We present the exact solution of the invariant magnet by the Bethe
ansatz approach. The associated Bethe ansatz equation exhibit a new feature by
presenting an explicit and distinct phase behaviour in even and odd sectors of
the theory. The ground state, the low-lying excitations and the critical
properties are discussed by exploiting the Bethe ansatz solution.Comment: 8 pages, UFSCARF-TH-1
Open t-J chain with boundary impurities
We study integrable boundary conditions for the supersymmetric t-J model of
correlated electrons which arise when combining static scattering potentials
with dynamical impurities carrying an internal degree of freedom. The latter
differ from the bulk sites by allowing for double occupation of the local
orbitals. The spectrum of the resulting Hamiltonians is obtained by means of
the algebraic Bethe Ansatz.Comment: LaTeX2e, 9p
Reference instruments based on spectrometric measurement with Lucas Cells
The Bundesamt fĂŒr Strahlenschutz (Berlin, Germany) and the Paul Scherrer Institute (Villigen, Switzerland) both operate accredited calibration laboratories for radon gas activity concentration. Both the institutions use Lucas Cells as detector in their reference instrumentation due to the low dependence of this detector type on variations in environmental conditions. As a further measure to improve the quality of the reference activity concentration, a spectrometric method of data evaluation has been applied. The electric pulses from the photomultiplier tube coupled to the Lucas Cells are subjected to a pulse height analysis. The stored pulse height spectra are analysed retrospectively to compensate for fluctuations in the electric parameters of the instrumentation during a measurement. The reference instrumentation of both the laboratories is described with the respective spectrum evaluation procedures. The methods of obtaining traceability to the primary calibration laboratories of Germany and Switzerland and data of performance tests are presente
Integrable mixing of A_{n-1} type vertex models
Given a family of monodromy matrices {T_u; u=0,1,...,K-1} corresponding to
integrable anisotropic vertex models of A_{(n_u)-1}-type, we build up a related
mixed vertex model by means of glueing the lattices on which they are defined,
in such a way that integrability property is preserved. Algebraically, the
glueing process is implemented through one dimensional representations of
rectangular matrix algebras A(R_p,R_q), namely, the `glueing matrices' zeta_u.
Here R_n indicates the Yang-Baxter operator associated to the standard Hopf
algebra deformation of the simple Lie algebra A_{n-1}. We show there exists a
pseudovacuum subspace with respect to which algebraic Bethe ansatz can be
applied. For each pseudovacuum vector we have a set of nested Bethe ansatz
equations identical to the ones corresponding to an A_{m-1} quasi-periodic
model, with m equal to the minimal range of involved glueing matrices.Comment: REVTeX 28 pages. Here we complete the proof of integrability for
mixed vertex models as defined in the first versio
Kinetic theory of age-structured stochastic birth-death processes
Classical age-structured mass-action models such as the McKendrick-von Foerster equation have been extensively studied but are unable to describe stochastic fluctuations or population-size-dependent birth and death rates. Stochastic theories that treat semi-Markov age-dependent processes using, e.g., the Bellman-Harris equation do not resolve a population's age structure and are unable to quantify population-size dependencies. Conversely, current theories that include size-dependent population dynamics (e.g., mathematical models that include carrying capacity such as the logistic equation) cannot be easily extended to take into account age-dependent birth and death rates. In this paper, we present a systematic derivation of a new, fully stochastic kinetic theory for interacting age-structured populations. By defining multiparticle probability density functions, we derive a hierarchy of kinetic equations for the stochastic evolution of an aging population undergoing birth and death. We show that the fully stochastic age-dependent birth-death process precludes factorization of the corresponding probability densities, which then must be solved by using a Bogoliubov-âBornâ-Greenâ-Kirkwood-âYvon-like hierarchy. Explicit solutions are derived in three limits: no birth, no death, and steady state. These are then compared with their corresponding mean-field results. Our results generalize both deterministic models and existing master equation approaches by providing an intuitive and efficient way to simultaneously model age- and population-dependent stochastic dynamics applicable to the study of demography, stem cell dynamics, and disease evolution
Exactly solvable models for triatomic-molecular Bose-Einstein Condensates
We construct a family of triatomic models for heteronuclear and homonuclear
molecular Bose-Einstein condensates. We show that these new generalized models
are exactly solvable through the algebraic Bethe ansatz method and derive their
corresponding Bethe ansatz equations and energies.Comment: 11 page
Jacobson generators of the quantum superalgebra and Fock representations
As an alternative to Chevalley generators, we introduce Jacobson generators
for the quantum superalgebra . The expressions of all
Cartan-Weyl elements of in terms of these Jacobson generators
become very simple. We determine and prove certain triple relations between the
Jacobson generators, necessary for a complete set of supercommutation relations
between the Cartan-Weyl elements. Fock representations are defined, and a
substantial part of this paper is devoted to the computation of the action of
Jacobson generators on basis vectors of these Fock spaces. It is also
determined when these Fock representations are unitary. Finally, Dyson and
Holstein-Primakoff realizations are given, not only for the Jacobson
generators, but for all Cartan-Weyl elements of .Comment: 27 pages, LaTeX; to be published in J. Math. Phy
Matrix difference equations for the supersymmetric Lie algebra sl(2,1) and the `off-shell' Bethe ansatz
Based on the rational R-matrix of the supersymmetric sl(2,1) matrix
difference equations are solved by means of a generalization of the nested
algebraic Bethe ansatz. These solutions are shown to be of highest-weight with
respect to the underlying graded Lie algebra structure.Comment: 10 pages, LaTex, references and acknowledgements added, spl(2,1) now
called sl(2,1
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