9,868 research outputs found
Yang-Baxter algebra and generation of quantum integrable models
An operator deformed quantum algebra is discovered exploiting the quantum
Yang-Baxter equation with trigonometric R-matrix. This novel Hopf algebra along
with its limit appear to be the most general Yang-Baxter algebra
underlying quantum integrable systems. Three different directions of
application of this algebra in integrable systems depending on different sets
of values of deforming operators are identified. Fixed values on the whole
lattice yield subalgebras linked to standard quantum integrable models, while
the associated Lax operators generate and classify them in an unified way.
Variable values construct a new series of quantum integrable inhomogeneous
models. Fixed but different values at different lattice sites can produce a
novel class of integrable hybrid models including integrable matter-radiation
models and quantum field models with defects, in particular, a new quantum
integrable sine-Gordon model with defect.Comment: 13 pages, revised and bit expanded with additional explanations,
accepted for publication in Theor. Math. Phy
Exact correlations in a single file system with a driven tracer
We study the effect of a single driven tracer particle in a bath of other
particles performing the random average process on an infinite line using a
stochastic hydrodynamics approach. We consider arbitrary fixed as well as
random initial conditions and compute the two-point correlations. For quenched
uniform and annealed steady state initial conditions we show that in the large
time limit the fluctuations and the correlations of the positions of the
particles grow subdiffusively as and have well defined scaling forms
under proper rescaling of the labels. We compute the corresponding scaling
functions exactly for these specific initial configurations and verify them
numerically. We also consider a non translationally invariant initial condition
with linearly increasing gaps where we show that the fluctuations and
correlations grow superdiffusively as at large times.Comment: 7 pages, 4 figures, supplementary material appended. To appear in EP
Classical integrable lattice models through quantum group related formalism
We translate effectively our earlier quantum constructions to the classical
language and using Yang-Baxterisation of the Faddeev-Reshetikhin-Takhtajan
algebra are able to construct Lax operators and associated -matrices of
classical integrable models. Thus new as well as known lattice systems of
different classes are generated including new types of collective integrable
models and canonical models with nonstandard matrices.Comment: 7 pages; Talk presented at NEEDS'93 (Gallipoli,Italy
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