1212.4241 (Jie Ren et al.)

Braid Group and Topological Phase Transition in Nonequilibrium
Stochastic Dynamics    [PDF]

Jie Ren, N. A. Sinitsyn

We show that distinct topological phases of a band structure of a non-Hermitian Hamiltonian can be classified with elements of the braid group. As an example we consider a non-Hermitian evolution of the statistics of stochastic transports. We show that topologically nontrivial phases have detectable properties, including the emergence of decaying oscillations of certain statistical characteristics, and discontinuities in the steady state statistics of currents.

View original: http://arxiv.org/abs/1212.4241