The Bethe ansatz in practice: an application to a minimal model in nonequilibrium statistical physics

Integrable systems are, loosely speaking, models that can be solved exactly using certain standard methods. For quantum and stochastic 1D lattice models, this method is the Bethe ansatz. Despite this, in physics, integrability techniques have a reputation of being excessively formal and opaque. Indeed, even when a formal exact solution is given, it can be a nontrivial task to translate this into meaningful statements regarding physical observables. In an effort to challenge this stigma, in this seminar, I will present a classic calculation, in which the Bethe ansatz is used to directly calculate physical observables for a toy model of nonequilibrium statistical mechanics. Specifically, I will calculate the long time current statistics in a totally asymmetric simple exclusion process -- the ``Ising model of nonequilibrium statistical physics".

Ref: arXiv:cond-mat/9809044