We present an analytical solution of the delocalization transition that is induced by an imaginary vector potential in a disordered chain [N. Hatano and D. R. Nelson, Phys. Rev. Lett. 77, 570 (1996)]. We compute the relation between the real and imaginary parts of the energy in the thermodynamic limit, as well as finite-size effects. The results are in good agreement with numerical simulations for weak disorder (in which the mean free path is large compared to the wavelength).
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Brouwer et al. (1997) studied this question.
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