429 research outputs found
Derivation of theories: structures of the derived system in terms of those of the original system in classical mechanics
We present the technique of derivation of a theory to obtain an
-degrees-of-freedom theory from an -degrees-of-freedom theory and
show that one can calculate all of the quantities of the derived theory from
those of the original one. Specifically, we show that one can use this
technique to construct, from an integrable system, other integrable systems
with more degrees of freedom.Comment: LaTex, 10 page
Models solvable through the empty-interval method
The most general one dimensional reaction-diffusion model with
nearest-neighbor interactions solvable through the empty interval method, and
without any restriction on the particle-generation from two adjacent empty
sites is studied. It is shown that turning on the reactions which generate
particles from two adjacent empty sites, results in a gap in the spectrum of
the evolution operator (or equivalently a finite relaxation time).Comment: 8 page
Exactly solvable reaction diffusion models on a Cayley tree
The most general reaction-diffusion model on a Cayley tree with
nearest-neighbor interactions is introduced, which can be solved exactly
through the empty-interval method. The stationary solutions of such models, as
well as their dynamics, are discussed. Concerning the dynamics, the spectrum of
the evolution Hamiltonian is found and shown to be discrete, hence there is a
finite relaxation time in the evolution of the system towards its stationary
state.Comment: 9 pages, 2 figure
Autonomous models solvable through the full interval method
The most general exclusion single species one dimensional reaction-diffusion
models with nearest-neighbor interactions which are both autonomous and can be
solved exactly through full interval method are introduced. Using a generating
function method, the general solution for, , the probability that
consecutive sites be full, is obtained. Some other correlation functions of
number operators at nonadjacent sites are also explicitly obtained. It is shown
that for a special choice of initial conditions some correlation functions of
number operators called full intervals remain uncorrelated
A pseudo-conformal representation of the Virasoro algebra
Generalizing the concept of primary fields, we find a new representation of
the Virasoro algebra, which we call it a pseudo-conformal representation. In
special cases, this representation reduces to ordinary- or
logarithmic-conformal field theory. There are, however, other cases in which
the Green functions differ from those of ordinary- or logarithmic-conformal
field theories. This representation is parametrized by two matrices. We
classify these two matrices, and calculate some of the correlators for a simple
example.Comment: LaTex, 5 page
Exactly solvable models through the generalized empty interval method: multi-species and more-than-two-site interactions
Multi-species reaction-diffusion systems, with more-than-two-site interaction
on a one-dimensional lattice are considered. Necessary and sufficient
constraints on the interaction rates are obtained, that guarantee the
closedness of the time evolution equation for 's, the
expectation value of the product of certain linear combination of the number
operators on consecutive sites at time .Comment: 10 pages, LaTe
The universal R-matrix for the Jordanian deformation of sl(2), and the contracted forms of so(4)
We introduce a universal R matrix for the Jordanian deformation of \U{
\sl(2)}. Using \Uh{\so(4)}=\Uh{\sl(2)} \oplus {\rm U}_{-h}(\sl(2)), we
obtain the universal R matrix for \Uh{\so(4)}. Applying the graded
contractions on the universal R matrix of \Uh{\so(4)}, we show that there
exist three distinct R matrices for all of the contracted algebras. It is shown
that \Uh{\sl(2)}, \Uh{\so(4)}, and all of these contracted algebras are
triangular.Comment: LaTeX, 8 page
Dynamical phase transition in one-dimensional kinetic Ising model with nonuniform coupling constants
An extension of the Kinetic Ising model with nonuniform coupling constants on
a one-dimensional lattice with boundaries is investigated, and the relaxation
of such a system towards its equilibrium is studied. Using a transfer matrix
method, it is shown that there are cases where the system exhibits a dynamical
phase transition. There may be two phases, the fast phase and the slow phase.
For some region of the parameter space, the relaxation time is independent of
the reaction rates at the boundaries. Changing continuously the reaction rates
at the boundaries, however, there is a point where the relaxation times begins
changing, as a continuous (nonconstant) function of the reaction rates at the
boundaries, so that at this point there is a jump in the derivative of the
relaxation time with respect to the reaction rates at the boundaries.Comment: 17 page
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