Talk 2. Quantum chaos for open systems: Universal spectra of random Lindblad operators

The spectrum of generic superoperators, corresponding to random stochastic operations, displays a universal behaviour: it contains the leading eigenvalue λ1= 1, while all other eigenvalues are restricted to the disk of radius R<1. In the case of generic dynamics in continuous time, we introduce an ensemble of random Lindblad operators, demonstrate its spectral features including the lemon-like shape of the spectrum in the complex plane, and explain them with a non-hermitian random matrix model [2]. We show how such spectra are modified due to superdecoherence, which leads to Kolmogorov operators, which generate Markovian evolution in the simplex of classical probability vectors.       

[2] J. Czartowski, D. Goyeneche, M. Grassl and K. Życzkowski, Iso-entangled mutually unbiased  bases, symmetric quantum measurements