arXiv subjects
Publications and source records attributed to Masoud Alimohammadi.
For the quintom models with arbitrary potential $V=V(ϕ,σ)$, the asymptotic value of equation of state parameter w is obtained by a new method. In this method, w of stable attractors are calculated by using the ratio (d ln V)/(d ln a) in asymptotic region. All the known results, have been obtained by other methods, are reproduced by this method as specific examples.
By considering the master equation of asymmetric exclusion process on a one-dimensional lattice, we obtain the most general boundary condition of the multi-species exclusion processes in which the number of particles is constant in time. This boundary condition introduces the various interactions to the particles, including ones which have been studied yet and the new ones. In these new models, the particles have simultaneously diffusion, the two-particle interactions $A_αA_β\to A_γA_δ$, and the $n$-particle extended drop-push interaction. The constraints on reaction rates are obtained and in two-species case, they are solved to obtain a solvable model. The conditional probabilities of this model are calculated.
Multi-species reaction-diffusion systems, with nearest-neighbor 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 $t$. The constraints are solved for the single-species left-right-symmetric systems. Also, examples of multi-species system for which the evolution equations of $E^{\mathbf a}_n(t)$'s are closed, are given.
Using the auxiliary field representation of the simplicial chiral models on a (d-1)-dimensional simplex, the simplicial chiral models are generalized through replacing the term Tr$(AA^{\d})$ in the Lagrangian of these models by an arbitrary class function of $AA^{\d}$; $V(AA^{\d})$. This is the same method used in defining the generalized two-dimensional Yang-Mills theories (gYM_2) from ordinary YM_2. We call these models, the ``generalized simplicial chiral models''. Using the results of the one-link integral over a U(N) matrix, the large-N saddle-point equations for eigenvalue density function $\ro (z)$ in the weak ($\b >\b_c$) and strong ($\b <\b_c$) regions are computed. In d=2, where the model is in some sense related to the gYM_2 theory, the saddle-point equations are solved for $\ro (z)$ in the two regions, and the explicit value of critical point $\b_c$ is calculated for $V(B)$=Tr$B^n$ $(B=AA^{\d})$. For $V(B$)=Tr$B^2$,Tr$B^3$, and Tr$B^4$, the critical behaviour of the model at d=2 is studied, and by calculating the internal energy, it is shown that these models have a third order phase transition.
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.
Using the conformal embedding on the torus, we can express some characters of $SU(3)_3$ in terms of $SO(8)_1$ characters. Then with the help of crossing symmetry, modular transformation and factorization properties of Green functions, we will calculate a class of correlators of $SU(3)_3$ on arbitrary Riemann surfaces. This method can apply to all $k>1$ WZW models which can be conformally embedded in some $k=1$ WZW models.