Physical Aspect of Exceptional Point in the Liouvillian Dynamics for a Quantum Lorentz Gas

Physical aspect of the exceptional point in the spectrum of the Liouville-von Neumann operator (Liouvillian) is discussed. The example we study in this paper is the weakly-coupled one-dimensional quantum perfect Lorentz gas. The effective Liouvillian for the system derived by applying the Brillouin-Wigner-Feshbach formalism takes non-Hermitian form due to resonance singularity, thus its spectra take complex values. We find that the complex spectra has two second order exceptional points in the wavenumber space. As a physical effect of the exceptional points, we show that the time evolution of the Wigner distribution function is described by the telegraph equation. The time evolution described by the telegraph equation shows a shifting motion in space. We also show that mechanism of the shifting motion completely changes at the exceptional points.