Abstract
We find the exact solution for the stationary state measure of the partially asymmetric exclusion process on a ring with multiple species of particles. The solution is in the form of a matrix product representation where the matrices for a system of N species are defined recursively in terms of the matrices for a system of N - 1 species. A complete proof is given, based on the quadratic relations verified by these matrices. This matrix product construction is interpreted in terms of the action of a transfer matrix.
| Original language | English |
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| Article number | 165004 |
| Journal | Journal of Physics A: Mathematical and Theoretical |
| Volume | 42 |
| Issue number | 16 |
| DOIs | |
| Publication status | Published - 1 Jan 2009 |
| Externally published | Yes |