2000/05/01 by Éric Brunet-Gouet, Eric Brunet, Bernard Derrida · 3 citations
Mathematics · Physics and Astronomy · #Cold Atom Physics and Bose-Einstein Condensates #Computer science #Cumulant #Energy (signal processing) #Ground state #Integer (computer science) #Mathematics #Perturbation (astronomy) #Perturbation theory (quantum mechanics) #Physics #Quantum mechanics #Statistical physics #Statistics #Stochastic processes and statistical mechanics #Theoretical and Computational Physics #cond-mat.dis-nn #cond-mat.stat-mech
paper · pdf · doi:10.1016/s0378-4371(99)00526-9
published as Physica A 279 (2000), 395-407 · 11 pages, no figure
openalex publication_date 2000/05/01 · arxiv created 2000/05/22 · arxiv updated 2009/11/30 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/06
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 nis 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.