2-d Gravity as a Limit of the SL(2,R) Black Hole

The transformation of the $SL(2,R)/U(1)$ black hole under a boost of the subgroup U(1) is studied. It is found that the tachyon vertex operators of the black hole go into those of the $c=1$ conformal field theory coupled to gravity. The discrete states of the black hole also tend to the discrete states of the 2-d gravity theory. The fate of the extra discrete states of the black hole under boost are discussed.Comment: LaTeX file, 14 page

Nilpotent Gauging of SL(2,R)WZNWWZNW models, and Liouville Field

We consider the gauging of $SL(2,R)$ WZNW model by its nilpotent subgroup E(1). The resulting space-time of the corresponding sigma model is seen to collapse to a one dimensional field theory of Liouville. Gauging the diagonal subgroup $E(1) \times U(1)$ of $SL(2,R) \times U(1)$ theory yields an extremal three dimensional black string. We show that these solutions are obtained from the two dimensional black hole of Witten and the three dimensional black string of Horne and Horowitz by boosting the gauge group.Comment: 17 pages, late

A family of discrete-time exactly-solvable exclusion processes on a one-dimensional lattice

A two-parameter family of discrete-time exactly-solvable exclusion processes on a one-dimensional lattice is introduced, which contains the asymmetric simple exclusion process and the drop-push model as particular cases. The process is rewritten in terms of boundary conditions, and the conditional probabilities are calculated using the Bethe-ansatz. This is the discrete-time version of the continuous-time processes already investigated in [1-3]. The drift- and diffusion-rates of the particles are also calculated for the two-particle sector.Comment: 10 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

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 $E^{\mathbf a}_n(t)$'s, the expectation value of the product of certain linear combination of the number operators on $n$ consecutive sites at time $t$.Comment: 10 pages, LaTe

Non-Douglas-Kazakov phase transition of two-dimensional generalized Yang-Mills theories

In two-dimensional Yang-Mills and generalized Yang-Mills theories for large gauge groups, there is a dominant representation determining the thermodynamic limit of the system. This representation is characterized by a density the value of which should everywhere be between zero and one. This density itself is determined through a saddle-point analysis. For some values of the parameter space, this density exceeds one in some places. So one should modify it to obtain an acceptable density. This leads to the well-known Douglas-Kazakov phase transition. In generalized Yang-Mills theories, there are also regions in the parameter space where somewhere this density becomes negative. Here too, one should modify the density so that it remains nonnegative. This leads to another phase transition, different from the Douglas-Kazakov one. Here the general structure of this phase transition is studied, and it is shown that the order of this transition is typically three. Using carefully-chosen parameters, however, it is possible to construct models with phase-transition orders not equal to three. A class of these non-typical models are also studied.Comment: 11 pages, accepted for publication in Eur. Phys. J.

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 $n$ consecutive sites are empty ($E_n$), 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 $n$ consecutive sites, starting from the site $k$, are empty ($E_{k,n}$) 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

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

Neutrino oscillation in a space-time with torsion

Using the Einstein-Cartan-Dirac theory, we study the effect of torsion on neutrino oscillation. We see that torsion cannot induce neutrino oscillation, but affects it whenever oscillation exists for other reasons. We show that the torsion effect on neutrino oscillation is as important as the neutrino mass effect, whenever the ratio of neutrino number density to neutrino energy is $\sim 10^{69}$ cm$^{-3}$ /eV, or the number density of the matter is $\sim 10^{69}$ cm$^{-3}$.Comment: 7 pages, LaTex,Some typos corrected Journal: Int. J. Mod. Phys. A (1999) (will be appeared

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.