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ABSTRACT:
Directed Feyman paths in 1+1 dimensions that acquire random phases,
encountered in the study of electron and light propagation in disordered
media, are examined by means of the replica trick. Two models are
considered -- one with short-range correlations, the other with very
long-range correlations. The large and small (finite) n behavior
of the resulting 2n-body quantum Hamiltonians with competing interactions
is calculated. The difficulties that arise in extrapolating the
results to n -> 0 and the possibility of replica symmetry breaking
are discussed.
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