Abstract
In this paper we give a closed form expression for the 1/ d corrections to the leading d → ∞ approximation for the ground-state energy of an n-body quantum mechanical problem in a general potential (where d is the number of spatial dimensions). We then extend the results to the problem of directed polymers in a random medium where the limit n → 0 has to be taken in the corresponding n-body problem. In this case the effective two-body potential measures the strength of correlations of the quenched disorder. In the n → 0 limit a replica-symmetry-breaking solution to the saddle-point equations turns out to be the correct solutionin the strong-coupling regime, and we obtain the 1/ d corrections to the corresponding energy which constitute the gaussian fluctuations about this solution as well as provide information about its basin of stability.
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