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ABSTRACT:
We consider the problem of directed walks (or polymers) in a
random potential with both real and imaginary parts. The correlations
of the potential are of short range. The problem is solved using a
variational approximation which is expected to become exact in the
limit of a large embedding dimension. A rich phase diagram is found
which contains five phases. In addition to the simple high temperature
phase, there are four ordered phases with different degrees of
replica symmetry breaking. Three of the phases are dominated by
interference (quantum) effects, and in two phases a pairing interaction
between replicas plays an important role.
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