Ground state energy of a non-integer number of particles with delta attractive interactions

Details Ground state energy of a non-integer number of particles with delta attractive interactions Ground state energy of a non-integer number of particles with delta attractive interactions

2000-05-22

arxiv.org/abs/cond-mat/0005355v1

Physica A 279 (2000), 395-407

Physics

Condensed Matter

Statistical Mechanics

11 pages, no figure

Scientific paper

10.1016/S0378-4371(99)00526-9

We show how to define and calculate the ground state energy of a system of quantum particles with delta attractive interactions when the number of particles n$is non-integer. The question is relevant to obtain the probability distribution of the free energy of a directed polymer in a random medium. When one expands the ground state energy in powers of the interaction, all the coefficients of the perturbation series are polynomials in n, allowing to define the perturbation theory for non-integer n. We develop a procedure to calculate all the cumulants of the free energy of the directed polymer and we give explicit, although complicated, expressions of the first three cumulants.

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