495 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
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
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