2010/01/07 by Victor Dotsenko, Boris Klumov · 2 citations
Mathematics · Physics and Astronomy · #Analytic continuation #Ansatz #Bethe ansatz #Boson #Eigenfunction #Function (biology) #Limit (mathematics) #Partition function (quantum field theory) #Quantum many-body systems #Random Matrices and Applications #Replica #Statistical mechanics #Theoretical and Computational Physics #cond-mat.dis-nn #cond-mat.stat-mech
paper · pdf · doi:10.1088/1742-5468/2010/03/p03022
published as J. Stat. Mech. (2010) P03022 · 32 pages, 1 figure
arxiv created 2010/01/07 · openalex publication_date 2010/03/24 · arxiv updated 2015/05/14 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05
We study the statistical properties of one-dimensional directed polymers in a short-range random potential by mapping the replicated problem to a many-body quantum boson system with attractive interactions. We find the full set of eigenvalues and eigenfunctions of the many-body system and perform the summation over the entire spectrum of excited states. The analytic continuation of the obtained exact expression for the replica partition function from integer to non-integer replica parameter N turns out to be ambiguous. Performing the analytic continuation simply by assuming that the parameter N can take arbitrary complex values, and going to the thermodynamic limit of the original directed polymer problem, we obtain the explicit universal expression for the probability distribution function of free energy fluctuations.