Asymmetric exclusion model with several kinds of impurities

Abstract

Abstract.We formulate a new integrable asymmetric exclusion process with N −1 = 0, 1, 2, . . . kinds of impurities and with hierarchically ordered dynamics. The model we proposed displays the full spectrum of the simple asymmetric exclusion model plus new levels. The first excited state belongs to these new levels and displays unusual scaling exponents. We conjecture that, while the simple asymmetric exclusion process without impurities belongs to the KPZ universality class with dynamical exponent 3 2 , our model has a scaling exponent 3 2 +N −1. In order to check the conjecture, we solve numerically the Bethe equation with N = 3 and N = 4 for the totally asymmetric diffusion and found the dynamical exponents 7 2 and 9 2 in these cases.

The spectral gap and the dynamical critical exponent of an exact solvable probabilistic cellular automaton

“…Although the model can be solved by the coordinate Bethe ansatz [37], we are going to formulate a new matrix product ansatz (MPA) [38][39][40] due its simplicity and unifying implementation for arbitrary systems. This new MPA introduced in [38][39][40] can be seen as a matrix product formulation of the coordinate Bethe ansatz and it is suited to describe all eigenvectors of integrable models, including spin chains [38][39][40], stochastic models [41][42][43] and transfer matrices [44][45][46]. According to this ansatz, there is a correspondence between the amplitudes of the eigenvectors and matrix products among matrices obeying special algebraic relations.…”