| Abstract: | We investigate particle transport in a tight-binding system where particles can be lost through a periodic array of absorbing sites. The dynamics in the corresponding non-Hermitian system reveal a topologically-protected quantization of average particle displacements. The phenomenon is associated with the winding of the system’s eigenstates around a dark state that avoids all decaying sites of the lattice. Here I will describe the new topological classification that results from the physical requirement that all particles must eventually escape from the system. Phases are separated by the emergence of dark eigenstates whose energies have vanishing imaginary parts, analogous to but distinct from the real energy gap closings which separate equilibrium phases of bulk insulators. I will discuss some physical realizations and consequences of this model, in particular for nuclear spin pumping in quantum dots. If time permits, I will show how the model can be adapted to incorporate counting fields, which give access to the full counting statistics of the particle displacement distribution. Higher moments reveal a hierarchy of dynamical phase transitions of increasing order as the dimension of the lattice is increased. |
