On the effect of exceptional points in the Liouvillian dynamics of a 1D quantum Lorentz gas

摘要

We study the physical influence of exceptional points in the spectrum of the Liouville–von Neumann operator (Liouvillian). The system that we consider in this paper is a weakly coupled 1D quantum perfect Lorentz gas, which has exceptional points on the real axis of the wavenumber space in the Liouvillian spectrum at which two eigenvalues coalesce. In order to clarify how the exceptional points affect the system dynamics, we analyze the spatial time evolution of the Wigner distribution function relying on a complex spectral decomposition of the Liouville–von Neumann equation. We show that the exceptional points represent a threshold between two qualitatively different dynamical regimes; one is a diffusive motion due to pure imaginary eigenvalues of the Liouvillian for wavenumbers on one side of the transition, while the other is a ballistic motion due to the existence of the real part of the eigenvalues for wavenumbers on the other side.