2,196 research outputs found
Linear growth of the entanglement entropy and the Kolmogorov-Sinai rate
The rate of entropy production in a classical dynamical system is
characterized by the Kolmogorov-Sinai entropy rate given by
the sum of all positive Lyapunov exponents of the system. We prove a quantum
version of this result valid for bosonic systems with unstable quadratic
Hamiltonian. The derivation takes into account the case of time-dependent
Hamiltonians with Floquet instabilities. We show that the entanglement entropy
of a Gaussian state grows linearly for large times in unstable systems,
with a rate determined by the Lyapunov exponents and
the choice of the subsystem . We apply our results to the analysis of
entanglement production in unstable quadratic potentials and due to periodic
quantum quenches in many-body quantum systems. Our results are relevant for
quantum field theory, for which we present three applications: a scalar field
in a symmetry-breaking potential, parametric resonance during post-inflationary
reheating and cosmological perturbations during inflation. Finally, we
conjecture that the same rate appears in the entanglement growth of
chaotic quantum systems prepared in a semiclassical state.Comment: 50+17 Pages, 11 figure
Localizability in de Sitter space
An analogue of the Newton-Wigner position operator is defined for a massive
neutral scalar field in de Sitter space. The one-particle subspace of the
theory, consisting of positive-energy solutions of the Klein-Gordon equation
selected by the Hadamard condition, is identified with an irreducible
representation of de Sitter group. Postulates of localizability analogous to
those written by Wightman for fields in Minkowski space are formulated on it,
and a unique solution is shown to exist. A simple expression for the
time-evolution of the operator is presented.Comment: Presentation improved; references adde
- …