| Abstract: | Non-Hermitian extension of quantum mechanics has been attracting much attention recently. In most cases, the scalar potential is made complex. I here present studies of complex vector potential, particularly in systems with quantum localization under randomness, including quantum walk in random media. I first show for a non-Hermitian extension of the tight-binding model with a random potential that the Anderson localization is destroyed when we increase the imaginary vector potential. When an eigenfunction gets delocalized, the eigenvalue becomes complex exactly at the same time. We can thus detect the localization by watching the evolution of the eigenvalue distribution due to tuning of the imaginary vector potential. I next show that the same delocalization transition occurs in a non-Hermitian extension of the discrete-time quantum walk with a random coin operator. In this model, the non-Hermitian gauge field in the shift operator is shown to be equivalent to a PT-symmetric scalar potential in the coin operator. |