Skip to Main content Skip to Navigation
Journal articles

Spectrum of the totally asymmetric simple exclusion process on a periodic lattice -- first excited states

Sylvain Prolhac 1
1 PhyStat - Physique Statistique des Systèmes Complexes (LPT)
LPT - Laboratoire de Physique Théorique
Abstract : 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 $L^{-3/2}$ 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.
Complete list of metadata

https://hal.archives-ouvertes.fr/hal-01062740
Contributor : Sylvain Prolhac <>
Submitted on : Wednesday, September 10, 2014 - 2:23:39 PM
Last modification on : Thursday, February 27, 2020 - 4:40:05 PM

Links full text

Identifiers

Citation

Sylvain Prolhac. Spectrum of the totally asymmetric simple exclusion process on a periodic lattice -- first excited states. Journal of Physics A: Mathematical and Theoretical, IOP Publishing, 2014, 47, pp.375001. ⟨10.1088/1751-8113/47/37/375001⟩. ⟨hal-01062740⟩

Share

Metrics

Record views

205