144 research outputs found
Classification of the solutions of constant rational semi-dynamical reflection equations
We propose a classification of the solutions K to the semi-dynamical
reflection equation with constant rational structure matrices associated to
rational scalar Ruijsenaars-Schneider model. Four sets of solutions are
identified and simple analytic transformations generate all solutions from
these sets.Comment: 12 pages, no figure. Dedicated to Daniel Arnaudo
C^{(2)}_{N+1} Ruijsenaars-Schneider models
We define the notion of C^{(2)}_{N+1} Ruijsenaars-Schneider models and
construct their Lax formulation. They are obtained by a particular folding of
the A_{2N+1} systems. Their commuting Hamiltonians are linear combinations of
Koornwinder-van Diejen ``external fields'' Ruijsenaars-Schneider models, for
specific values of the exponential one-body couplings but with the most general
2 double-poles structure as opposed to the formerly studied BC_N case.
Extensions to the elliptic potentials are briefly discussed.Comment: 15 pages, LaTeX, no figure
String field actions from W-infinity
Starting from as a fundamental symmetry and using the coadjoint
orbit method, we derive an action for one dimensional strings. It is shown that
on the simplest nontrivial orbit this gives the single scalar collective field
theory. On higher orbits one finds generalized KdV type field theories with
increasing number of components. Here the tachyon is coupled to higher tensor
fields.Comment: 18 page
Commuting quantum traces: the case of reflection algebras
We formulate a systematic construction of commuting quantum traces for
reflection algebras. This is achieved by introducing two sets of generalized
reflection equations with associated consistent fusion procedures. Products of
their solutions yield commuting quantum traces.Comment: 16 pages, Late
Construction of dynamical quadratic algebras
We propose a dynamical extension of the quantum quadratic exchange algebras
introduced by Freidel and Maillet. It admits two distinct fusion structures. A
simple example is provided by the scalar Ruijsenaars-Schneider model.Comment: LaTeX, 13 pages, no figures Important changes. Changed the title.
Added an example and a theorem on fusion on the quantum space. To appear in
LM
Did the ever dead outnumber the living and when? A birth-and-death approach
This paper is an attempt to formalize analytically the question raised in
"World Population Explained: Do Dead People Outnumber Living, Or Vice Versa?"
Huffington Post, \cite{HJ}. We start developing simple deterministic Malthusian
growth models of the problem (with birth and death rates either constant or
time-dependent) before running into both linear birth and death Markov chain
models and age-structured models
Integrable quantum spin chains and their classical continuous counterparts
We present certain classical continuum long wave-length limits of prototype
integrable quantum spin chains, and define the corresponding construction of
classical continuum Lax operators. We also provide two specific examples, i.e.
the isotropic and anisotropic Heisenberg models.Comment: 15 pages Latex. Proceedings contribution to the Corfu Summer
Institute on Elementary Particle Physics and Gravity - Workshop on Non
Commutative Field Theory and Gravity, 8-12 September 2010, Corfu, Greec
Scattering in Twisted Yangians
We study the bulk and boundary scattering of the sl(N) twisted Yangian spin
chain via the solution of the Bethe ansatz equations in the thermodynamic
limit. Explicit expressions for the scattering amplitudes are obtained and the
factorization of the bulk scattering is shown. The issue of defects in twisted
Yangians is also briefly discussed.Comment: 10 pages, Latex. Based on a talk presented by AD, in "Integrable
systems and quantum symmetries", Prague, June 2015. Related results are also
presented in: arXiv:1410.5991, arXiv:1412.648
Classification of Non-Affine Non-Hecke Dynamical R-Matrices
A complete classification of non-affine dynamical quantum -matrices
obeying the -Gervais-Neveu-Felder equation is
obtained without assuming either Hecke or weak Hecke conditions. More general
dynamical dependences are observed. It is shown that any solution is built upon
elementary blocks, which individually satisfy the weak Hecke condition. Each
solution is in particular characterized by an arbitrary partition of the set of indices into classes,
being the class of the index , and an arbitrary family of
signs
on this partition. The weak Hecke-type -matrices exhibit the analytical
behaviour , where is a
particular trigonometric or rational function, , and
denotes the family of dynamical coordinates
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