Quantum Chains with GLq(2)GL_q(2) Symmetry

Usually quantum chains with quantum group symmetry are associated with representations of quantized universal algebras $U_q(g)$ . Here we propose a method for constructing quantum chains with $C_q(G)$ global symmetry , where $C_q(G)$ is the algebra of functions on the quantum group. In particular we will construct a quantum chain with $GL_q(2)$ symmetry which interpolates between two classical Ising chains.It is shown that the Hamiltonian of this chain satisfies in the generalised braid group algebra.Comment: 7 pages,latex,this is the completely revised version of my paper which is submitted for publicatio

Coulomb gas representation of quantum Hall effect on Riemann surfaces

Using the correlation function of chiral vertex operators of the Coulomb gas model, we find the Laughlin wavefunctions of quantum Hall effect, with filling factor $\nu =1/m$, on Riemann sufaces with Poincare metric. The same is done for quasihole wavefunctions. We also discuss their plasma analogy.Comment: 10 pages, LaTex, the paper is completely rewritten, It will be appeared in : Jour. Phys. A 32 (1999

Class of solvable reaction-diffusion processes on Cayley tree

Considering the most general one-species reaction-diffusion processes on a Cayley tree, it has been shown that there exist two integrable models. In the first model, the reactions are the various creation processes, i.e. $\circ\circ\to\bullet\circ$, $\circ\circ\to\bullet\bullet$ and $\circ\bullet\to\bullet\bullet$, and in the second model, only the diffusion process $\bullet\circ\to\circ\bullet$ exists. For the first model, the probabilities $P_l(m;t)$, of finding $m$ particles on $l$-th shell of Cayley tree, have been found exactly, and for the second model, the functions $P_l(1;t)$ have been calculated. It has been shown that these are the only integrable models, if one restricts himself to $L+1$-shell probabilities $P(m_0,m_1,...,m_L;t)$s.Comment: 9 pages, to be appeared in Physica

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

Laughlin states on the Poincare half-plane and its quantum group symmetry

We find the Laughlin states of the electrons on the Poincare half-plane in different representations. In each case we show that there exist a quantum group $su_q(2)$ symmetry such that the Laughlin states are a representation of it. We calculate the corresponding filling factor by using the plasma analogy of the FQHE.Comment: 9 pages,Late

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

Non-local 2D Generalized Yang-Mills theories on arbitrary surfaces with boundary

The non-local generalized two dimensional Yang Mills theories on an arbitrary orientable and non-orientable surfaces with boundaries is studied. We obtain the effective action of these theories for the case which the gauge group is near the identity, $U\simeq I$. Furthermore, by obtaining the effective action at the large-N limit, it is shown that the phase structure of these theories is the same as that obtain for these theories on orientable and non-orientable surface without boundaries. It is seen that the $\phi^2$ model of these theories on an arbitrary orientable and non-orientable surfaces with boundaries have third order phase transition only on $g=0$ and $r=1$ surfaces, with modified area $\tilde{A}+{\cal A}/2$ for orientable and $\bar{A}+\mathcal{A}$ for non-orientable surfaces respectivly.Comment: 10 pages, no figures, late

Remarks on generalized Gauss-Bonnet dark energy

The modified gravity with F(R,G) Lagrangian, G is the Gauss-Bonnet invariant, is considered. It is shown that the phantom-divide-line crossing and the deceleration to acceleration transition generally occur in these models. Our results coincide with the known results of f(R)-gravity and f(G)-gravity models. The contribution of quantum effects to these transitions is calculated, and it is shown that in some special cases where there are no transitions in classical level, quantum contributions can induce transitions. The quantum effects are described via the account of conformal anomaly.Comment: 11 pages, LaTeX, a paragraph added, to be appeared in Phys. Rev.

Quantum Hall Effect Wave Functions as Cyclic Representations of U_q(sl(2))

Quantum Hall effect wave functions corresponding to the filling factors 1/2p+1, 2/2p+1, ..., 2p/2p+1, 1, are shown to form a basis of irreducible cyclic representation of the quantum algebra U_q(sl(2)) at q^{2p+1}=1. Thus, the wave functions \Psi_{P/Q} possessing filling factors P/Q<1 where Q is odd and P, Q are relatively prime integers are classified in terms of U_q(sl(2)).Comment: Version to appear in Jour. Phys.