Quantum fate of classical solitons

Math Physics Seminar
Monday, October 28, 2019 - 4:00pm for 1 hour (actually 50 minutes)
Skiles 005
Michael Pustilnik – School of Physics, Georgia Tech – pustilnik@gatech.edu
Federico Bonetto
This talk will focus on one-dimensional interacting quantum systems near the classical limit described by the Korteweg–de Vries (KdV) equation. Classical excitations in this regime are the well-known solitons, i.e., localized disturbances with particle-like properties, and delocalized waves of density, or phonons. It turns out, however, that the semiclassical description inevitably breaks down at long wavelengths. In this limit, quantum effects become dominant, the system is best described in terms of weakly interacting fermions, and classical solitons and phonons reach their ultimate quantum fate of being demoted to fermionic particles and holes.
We will give simple heuristic arguments in support of this claim and present the exact solution for the spectra of elementary excitations. The results are universally applicable to all quantum one-dimensional systems with a well-defined classical limit described by the KdV equation. This includes identical bosons with a weak short-range repulsion and identical particles, either bosons or fermions, with a strong long-range repulsion.