Entanglement and Chaos: Linear entropy production at instabilities

Dahlem Center for Complex Systems, Freie Universit├Ąt Berlin

The rate of entropy production in a classical dynamical system is characterized by the Kolmogorov-Sinai entropy rate given by the sum over all positive Lyapunov exponents of the system. I will prove a quantum version of this result valid for bosonic systems with unstable quadratic Hamiltonian: the entanglement entropy of squeezed coherent states grows linearly for large times, with a rate determined by the Lyapunov exponents and the choice of the subsystem. I will discuss its application to quantum field theory and explain our conjecture on what this result implies for quantum chaos and thermalization in systems with periodic orbits.