Quantum transport in non-Hermitian systems
Naomichi Hatano
U. Tokyo

We here discuss how to find the current in non-Hermitian systems. If we use the left- and right-eigenvectors to compute the current expectation value, we find it vanishing because it describes a non-Hermitian closed system. Meanwhile, if we use the right-eigenvector and its bra vector, we can find a finite current because it now describes an open quantum system. The reason why the right-eigenvectors are not orthogonal to each other is because the inner product is taken only in a partial system.