JCMS: Exact Dirac-Bogoliubov-de Gennes dynamics for inhomogeneous quantum liquids

by Per Moosavi (Stockholm University)

Monday 16 Oct 2023, 11:00 → 12:00 Europe/Stockholm

Albano 3: 6228 - Mega (22 seats) (Albano Building 3)

I will discuss a pair of coupled partial differential equations identified as Bogoliubov-de Gennes equations but with Dirac operators and show that they appear naturally in the effective dynamics of inhomogeneous 1D quantum many-body systems. The equations feature an effective local gap that opens up due to the inhomogeneities, coupling right- and left-moving degrees of freedom, leading to scattering, and so far were not solved in general. I show that one can obtain analytical solutions using ordered exponentials, generalizing earlier results for quantum wires and conformal interfaces, and yielding detailed and even explicit results for the dynamics. The main physical motivation comes from inhomogeneous Tomonaga-Luttinger liquids, but the equations also arise in descriptions of superconductor-normal-metal interfaces, the Su-Schrieffer-Heeger model for polymer chains, and a toy model for coupled fractional quantum Hall edges.