Abstract:The rate of entropy production in a classical dynamical system is characterized by the Kolmogorov-Sinai entropy rate h KS 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 S A of a Gaussian state grows linearly for large times in unstable systems, with a rate Λ A ≤ h KS determined by the Lyapunov exponents and the choice of the subsystem A. 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 Λ A appears in the entanglement growth of chaotic quantum systems prepared in a semiclassical state.

Our previous results on the nonperturbative calculations of the mean current and of the energymomentum tensor in QED with the T-constant electric field are generalized to arbitrary dimensions. The renormalized mean values are found, and the vacuum polarization contributions and particle creation contributions to these mean values are isolated in the large T limit; we also relate the vacuum polarization contributions to the one-loop effective Euler-Heisenberg Lagrangian. Peculiarities in odd dimensions are considered in detail. We adapt general results obtained in 2 þ 1 dimensions to the conditions which are realized in the Dirac model for graphene. We study the quantum electronic and energy transport in the graphene at low carrier density and low temperatures when quantum interference effects are important. Our description of the quantum transport in the graphene is based on the so-called generalized Furry picture in QED where the strong external field is taken into account nonperturbatively; this approach is not restricted to a semiclassical approximation for carriers and does not use any statistical assumptions inherent in the Boltzmann transport theory. In addition, we consider the evolution of the mean electromagnetic field in the graphene, taking into account the backreaction of the matter field to the applied external field. We find solutions of the corresponding Dirac-Maxwell set of equations and with their help we calculate the effective mean electromagnetic field and effective mean values of the current and the energy-momentum tensor. The nonlinear and linear I-V characteristics experimentally observed in both low-and high-mobility graphene samples are quite well explained in the framework of the proposed approach, their peculiarities being essentially due to the carrier creation from the vacuum by the applied electric field.

We derive a formula for the entanglement entropy of squeezed states on a lattice in terms of the complex structure J. The analysis involves the identification of squeezed states with group-theoretical coherent states of the symplectic group and the relation between the coset Sp(2N, R)/Isot(J 0 ) and the space of complex structures. We present two applications of the new formula: (i) we derive the area law for the ground state of a scalar field on a generic lattice in the limit of small speed of sound, (ii) we compute the rate of growth of the entanglement entropy in the presence of an instability and show that it is asymptotically bounded from above by the Kolmogorov-Sinai rate. *

Abstract. Recent cosmic microwave background (CMB) observations put strong constraints on the spatial curvature via estimation of the parameter Ω k assuming an almost scale invariant primordial power spectrum. We study the evolution of the background geometry and gauge-invariant scalar perturbations in an inflationary closed FLRW model and calculate the primordial power spectrum. We find that the inflationary dynamics is modified due to the presence of spatial curvature, leading to corrections to the nearly scale invariant power spectrum at the end of inflation. When evolved to the surface of last scattering, the resulting temperature anisotropy spectrum (C TT ) shows deficit of power at low multipoles ( < 20). By comparing our results with the recent Planck data we discuss the role of spatial curvature in accounting for CMB anomalies and in the estimation of the parameter Ω k . Since the curvature effects are limited to low multipoles, the Planck estimation of cosmological parameters remains robust under inclusion of positive spatial curvature.