2014/04/30 by Sylvain Prolhac · 2 citations
Mathematics · Physics and Astronomy · #Random Matrices and Applications #Stochastic processes and statistical mechanics #Theoretical and Computational Physics #cond-mat.stat-mech #math-ph #math.MP
paper · pdf · doi:10.1088/1751-8113/47/37/375001
published as J. Phys. A: Math. Theor. 47 (2014) 375001 · 31 pages, 10 figures
arxiv created 2014/08/13 · openalex publication_date 2014/08/29 · arxiv updated 2014/09/02 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/30
We consider the spectrum of the totally asymmetric simple exclusion process on a periodic lattice of L sites. The first eigenstates have an eigenvalue with real part scaling as for large L with finite density of particles. Bethe ansatz shows that these eigenstates are characterized by four finite sets of positive half-integers, or equivalently by two integer partitions. Each corresponding eigenvalue is found to be equal to the value at its saddle point of a function indexed by the four sets. Our derivation of the large L asymptotics relies on a version of the Euler–Maclaurin formula with square root singularities at both ends of the summation range.