Green Function for the Nonlinear Luttinger Liquid from Nonlinear Steepest Descent

Condensed Matter Seminars

Speaker: Tom Price (Cambridge University, UK)
Date & Time: March 8, 2016, 2:00 - 3:00
Location: Hennings 318
Local Contact: George Sawatzky
Intended Audience: Graduate

We discuss the time dependent Green function of the nonlinear Luttinger liquid, using the Fractional Quantum Hall edge as an example. The Green function can be written as a Fredholm determinant, whose long time asymptotics we find by solving an associated Riemann–Hilbert problem using the method of nonlinear steepest descent. The results agree exactly with the mobile impurity model, which has a simple interpretation as a factorization of the solution to the asymptotic Riemann–Hilbert problem.