Current statistics in the q-boson zero range process

@article{Trofimova2020CurrentSI,
  title={Current statistics in the q-boson zero range process},
  author={A. A. Trofimova and A. M. Povolotsky},
  journal={Journal of Physics A: Mathematical and Theoretical},
  year={2020},
  volume={53}
}
We obtain exact formulas of the first two cumulants of particle current in the q-boson zero range process on a ring via exact perturbative solution of the TQ-equation. The result is represented as an infinite sum of double contour integrals. We perform the asymptotic analysis of the large system size limit N → ∞ of the expressions obtained. For |q| ≠ 1 the leading terms of the second cumulant reproduce the N 3/2 scaling expected for models in the Kardar–Parisi–Zhang universality class. The… 

References

SHOWING 1-10 OF 88 REFERENCES
Integral Formulas of ASEP and q-TAZRP on a Ring
In this paper, we obtain the transition probability formulas for the Asymmetric Simple Exclusion Process (ASEP) and the $q$-deformed Totally Asymmetric Zero Range Process ($q$-TAZRP) on the ring by
Scaling of the active zone in the Eden process on percolation networks and the ballistic deposition model
The interface of the Eden clusters on percolation networks and the ballistic deposition model is studied by Monte Carlo simulations, using a simple definition for the surface thickness. The width of
A q-deformed completely integrable Bose gas model
The authors construct the Hamiltonian of a new quantum integrable 'q-boson' lattice model in 1+1 dimensions which has q-bosons as dynamical variables and solve it for its energy eigenstates and
Origins of scale invariance in growth processes
Abstract This review describes recent progress in the understanding of the emergence of scale invariance in far-from-equilibrium growth. The first section is devoted to ‘solvable’ needle models which
Exact solution of a 1d asymmetric exclusion model using a matrix formulation
Several recent works have shown that the one-dimensional fully asymmetric exclusion model, which describes a system of particles hopping in a preferred direction with hard core interactions, can be
Exact diffusion constant for one-dimensional asymmetric exclusion models
The one-dimensional fully asymmetric exclusion model, which describes a system of particles hopping in a preferred direction with hard core interactions, is considered on a ring of size N. The steady
EXACT ANALYSIS OF AN INTERACTING BOSE GAS. I. THE GENERAL SOLUTION AND THE GROUND STATE
A gas of one-dimensional Bose particles interacting via a repulsive delta-function potential has been solved exactly. All the eigenfunctions can be found explicitly and the energies are given by the
Self-Affinity for the Growing Interface of Bacterial Colonies
We have investigated experimentally the self-affinity of bacterial colonies. We examined roughness exponent α for one-dimensional growing interfaces of colonies which belong to regions B and D in t...
...
...