Abstract
The stochastic R matrix for Uq(An(1)) introduced recently gives rise to an integrable zero range process of n classes of particles in one dimension. For n=2 we investigate how finitely many first class particles fixed as defects influence the grand canonical ensemble of the second class particles. By using the matrix product stationary probabilities involving infinite products of q-bosons, exact formulas are derived for the local density and current of the second class particles in the large volume limit.
Highlights
Zero range processes (ZRPs) [19] are stochastic particle systems on lattice modeling various flows in granules, queuing networks, traffic and so forth
The relevant matrix product operators are quite distinct from those in the exclusion type processes in that they involve quantum dilogarithm type infinite products of q-bosons, offering a challenge to extract physics of the model. With this background in mind we present in this paper a modest analysis of stationary properties of the Uq(A(21)) ZRP based on the matrix product formula (1.1)–(1.2)
We present the profiles of the local density and currents in a number of figures for various values of q, μ, ρ and the defect pattern (d1, . . . , ds), where ρ denotes the average density of the second class particles
Summary
Zero range processes (ZRPs) [19] are stochastic particle systems on lattice modeling various flows in granules, queuing networks, traffic and so forth. Once the conditional probability is determined, the local density and current of the second class particles are derived at any site r. They are physical quantities seen from the defects. The evolution equation (2.11) describes a stochastic dynamics of n classes of particles hopping to the right periodically via an extra lane (horizontal arrows in (2.8)) which particles get on or get off when they leave or arrive at a site The rate of such local processes is specified by (2.2), (2.3) and (2.4). It means that larger class particles have the priority to jump out, which precisely reproduces the n class totally asymmetric zero range process explored in [12] after reversing the labeling of the classes 1, 2, . . . , n of the particles
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