Microscopic description of irreversibility in 1D quantum Lorentz gas by complex spectral analysis of the Liouville-von Neumann operator

Kazuki Kanki (Osaka Prefecture University)

We reexamined the solution by Hashimoto et al. [1,2] to the complex eigenvalue problem of the Liouville-von Neumann operator (Liouvillian) for weakly coupled 1D quantum perfect Lorentz gas. The theory extends the phenomenological Boltzmann equation to microscopic space-time scale by taking account of the eigenvalue dependence (nolinearity) and the wave-number dependence of the effective Liouvillian. We corrected the nonlinear eigenvalue equation of the effective Liouvillian into a form which does not diverge at the exceptional points of the Boltzmann equation. As a result, we found exceptional points in the nonliear eigenvalue problem of the effective Liouvillian. We have elucidated the nature of the approximations in our treatment, and will discuss how to develop the theory further.

[1] K. Hashimoto, K. Kanki, S. Tanaka, and T. Petrosky, Phys. Rev. E 93, 022132 (2016).
[2] T. Petrosky, K. Hashimoto, K. Kanki, and S. Tanaka, Chaos 27, 104616 (2017).