The Bose Gas and Asymmetric Simple Exclusion Process on the Half-Line
arXiv:1205.4054 · doi:10.1007/s10955-012-0686-4
Abstract
In this paper we find explicit formulas for: (1) Green's function for a system of one-dimensional bosons interacting via a delta-function potential with particles confined to the positive half-line; and (2) the transition probability for the one-dimensional asymmetric simple exclusion process (ASEP) with particles confined to the nonnegative integers. These are both for systems with a finite number of particles. The formulas are analogous to ones obtained earlier for the Bose gas and ASEP on the line and integers, respectively. We use coordinate Bethe Ansatz appropriately modified to account for confinement of the particles to the half-line. As in the earlier work, the proof for the ASEP is less straightforward than for the Bose gas.
arXiv comment14 Pages
References in corpus (5)
Cited by in corpus (14)
- Stochastic six-vertex model in a half-quadrant and half-line open ASEP
- Spectral theory for the q-Boson particle system
- Directed random polymers via nested contour integrals
- Half-space Macdonald processes
- Half-space stationary Kardar-Parisi-Zhang equation
- Replica Bethe Ansatz solution to the Kardar-Parisi-Zhang equation on the half-line
- Delta-Bose gas on a half-line and the KPZ equation: boundary bound states and unbinding transitions
- Integral formulas of ASEP and -TAZRP on a ring
- The asymmetric simple exclusion process with an open boundary
- Boundary current fluctuations for the half space ASEP and six vertex model
- Something interacting and solvable in 1d
- The semi-infinite q-boson system with boundary interaction
- Markov duality and Bethe ansatz formula for half-line open ASEP
- Integral formula for the propagator of the one-dimensional Hubbard model