The Joint Condensed Matter Seminar (JCMS) series is organised by KTH Royal Insitute of Technology, Nordita, and Stockholm University.
On Monday, October 16th, 2023 from 11 am to 12 am we will host a seminar by Per Moosavi from Stockholm University.
Exact Dirac-Bogoliubov-de Gennes dynamics for inhomogeneous quantum liquids
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.