Non-Hermitian delocalization from Hermitian Hamiltonians - art. no. 041103

Here we show that using Galilean transformations the non-Hermitian delocali zation phenomenon, which is relevant in different fields, such as bacteria population (e.g., Bacillus subtilis), vortex pinning in superconductors, an d stability solutions of hydrodynamical problems discovered by Hatano and N elson [Phys. Rev. Lett. 77, 5706 (1996)], can be obtained from solutions of the time-dependent Schrodinger equation with a Hermitian Hamiltonian. Usin g our approach, one avoids the numerical complications and instabilities wh ich result form the calculations of left and right eigenfunctions of the no n-Hermitian Hamiltonian which are associated with the non-Hermitian delocal ization phenomenon. One also avoids the need to replace the non-Hermitian H amiltonian (H) over cap by a supermatrix with twice the dimension of (H) ov er cap, where the complex frequencies serve as variational parameters rathe r than eigenvalues of (H) over cap.