Squeezed vacua in systems with instabilities

Primordial Universe and Gravity (PUG) Discussions, Pennsylvania State University

We study the asymptotic behavior of the entanglement entropy when we evolve an arbitrary squeezed vacuum with an unstable quadratic Hamiltonian. Unstable refers here to negative eigenvalues in the potential term leading to a Hamiltonian that is not bounded from below. We show that the entanglement entropy of squeezed vacua is well approximated by their Renyi entropy, for which we present a new geometric representation as volume in the classical phase space of the subsystem. This allows us to prove that the entanglement entropy of any region grows linearly for large times. In particular, we show how the rate of growth depends on the interplay between subsystem and unstable directions of the potential, but is completely independent of the initial squeezed vacuum. We explain a general algorithm to determine the leading asymptotic behavior.