204 research outputs found
A new class of integrable diffusion-reaction processes
We consider a process in which there are two types of particles, A and B, on
an infinite one-dimensional lattice. The particles hop to their adjacent sites,
like the totally asymmetric exclusion process (ASEP), and have also the
following interactions: A+B -> B+B and B+A -> B+B, all occur with equal rate.
We study this process by imposing four boundary conditions on ASEP master
equation. It is shown that this model is integrable, in the sense that its
N-particle S-matrix is factorized into a product of two-particle S-matrices
and, more importantly, the two-particle S-matrix satisfy quantum Yang-Baxter
equation. Using coordinate Bethe-ansatz, the N-particle wavefunctions and the
two-particle conditional probabilities are found exactly.
Further, by imposing four reasonable physical conditions on two-species
diffusion-reaction processes (where the most important ones are the equality of
the reaction rates and the conservation of the number of particles in each
reaction), we show that among the 4096 types of the interactions which have
these properties and can be modeled by a master equation and an appropriate set
of boundary conditions, there are only 28 independent interactions which are
integrable. We find all these interactions and also their corresponding wave
functions. Some of these may be new solutions of quantum Yang-Baxter equation.Comment: LaTex,16 pages, some typos are corrected, will be appeared in Phys.
Rev. E (2000
On the solvable multi-species reaction-diffusion processes
A family of one-dimensional multi-species reaction-diffusion processes on a
lattice is introduced. It is shown that these processes are exactly solvable,
provided a nonspectral matrix equation is satisfied. Some general remarks on
the solutions to this equation, and some special solutions are given. The
large-time behavior of the conditional probabilities of such systems are also
investigated.Comment: 13 pages, LaTeX2
Multispecies reaction-diffusion systems
Multispecies reaction-diffusion systems, for which the time evolution
equation of correlation functions become a closed set, are considered. A formal
solution for the average densities is found. Some special interactions and the
exact time dependence of the average densities in these cases are also studied.
For the general case, the large time behaviour of the average densities has
also been obtained.Comment: LaTeX file, 15 pages, to appear in Phys. Rev.
Spin 0 and spin 1/2 particles in a spherically symmetric static gravity and a Coulomb field
A relativistic particle in an attractive Coulomb field as well as a static
and spherically symmetric gravitational field is studied. The gravitational
field is treated perturbatively and the energy levels are obtained for both
spin 0 (Klein-Gordon) and spin 1/2 (Dirac) particles. The results are shown to
coincide with each other as well as the result of the nonrelativistic
(Schrodinger) equation in the nonrelativistic limit.Comment: 12 page
Exactly solvable models through the empty interval method
The most general one dimensional reaction-diffusion model with
nearest-neighbor interactions, which is exactly-solvable through the empty
interval method, has been introduced. Assuming translationally-invariant
initial conditions, the probability that consecutive sites are empty
(), has been exactly obtained. In the thermodynamic limit, the large-time
behavior of the system has also been investigated. Releasing the translational
invariance of the initial conditions, the evolution equation for the
probability that consecutive sites, starting from the site , are empty
() is obtained. In the thermodynamic limit, the large time behavior of
the system is also considered. Finally, the continuum limit of the model is
considered, and the empty-interval probability function is obtained.Comment: 12 pages, LaTeX2
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
Autonomous multispecies reaction-diffusion systems with more-than-two-site interactions
Autonomous multispecies systems with more-than-two-neighbor interactions are
studied. Conditions necessary and sufficient for closedness of the evolution
equations of the -point functions are obtained. The average number of the
particles at each site for one species and three-site interactions, and its
generalization to the more-than-three-site interactions is explicitly obtained.
Generalizations of the Glauber model in different directions, using generalized
rates, generalized number of states at each site, and generalized number of
interacting sites, are also investigated.Comment: 9 pages, LaTeX2
Phase transition in an asymmetric generalization of the zero-temperature Glauber model
An asymmetric generalization of the zero-temperature Glauber model on a
lattice is introduced. The dynamics of the particle-density and specially the
large-time behavior of the system is studied. It is shown that the system
exhibits two kinds of phase transition, a static one and a dynamic one.Comment: LaTeX, 9 pages, to appear in Phys. Rev. E (2001
Phase transition in an asymmetric generalization of the zero-temperature q-state Potts model
An asymmetric generalization of the zero-temperature q-state Potts model on a
one dimensional lattice, with and without boundaries, has been studied. The
dynamics of the particle number, and specially the large time behavior of the
system has been analyzed. In the thermodynamic limit, the system exhibits two
kinds of phase transitions, a static and a dynamic phase transition.Comment: 11 pages, LaTeX2
Exactly solvable models through the empty interval method, for more-than-two-site interactions
Single-species reaction-diffusion systems on a one-dimensional lattice are
considered, in them more than two neighboring sites interact. Constraints on
the interaction rates are obtained, that guarantee the closedness of the time
evolution equation for 's, the probability that consecutive sites
are empty at time . The general method of solving the time evolution
equation is discussed. As an example, a system with next-nearest-neighbor
interaction is studied.Comment: 19 pages, LaTeX2
- …