Properties of the current in non-Hermitian lattice models

Qihang Liu (Peking U.)

Non-Hermitian lattice models described by the Schrödinger equation i∂_t ψ=Hψ exhibit various exotic properties, such as the exceptional point. With gain and loss on some sites, we may find currents flowing in the system. Here, we present a definition of current for non-Hermitian systems with gain and loss terms, and the continuity equation of the current. We compute the current distribution for several lattice models including chains under open and periodic boundary conditions. When the eigenvalues are real, the current is time independent, which results in a steady flow. In particular, we show an interesting distribution of the stationary current for a periodic chain with one gain term and one loss term. The behavior of these models is expected to have potential to some applications in photonics.