Standard mechanisms of metastable decay are tunneling and thermal activation. We show that periodically modulated systems may display a different decay mechanism, quantum activation. Here, decay occurs via diffusion over a quasi-energy barrier. The diffusion is induced by quantum fluctuations. We study quantum activation for nonlinear oscillators and show that the decay rate displays unexpected features. It exhibits scaling behavior near critical parameter values where metastable vibrational states disappear. The results bear on quantum measurements with nonlinear oscillators.

The process of quantum tunneling through a static potential barrier is well described by the theory of Wentzel, Kramers, and Brillouin. When, due to external electric field ξ(t), the barrier is nonstationary the tunneling scenario becomes very delicate. First of all, an electron can absorb a number of quanta of the external field and to tunnel in a more transparent part (with a higher energy) of the barrier. This process is known as photon-assisted tunneling. The probability of this process can be calculated by the method of classical trajectories in complex time. In this case analytical properties of the function ξ(t), which can be sinusoidal or of a pulsed type, in the complex plane of time play a crucial role. In addition to photon-assisted tunneling, which has no conflict with intuition, there is another under-barrier process which is counter-intuitive and is called Euclidean resonance. A new branch of the wave function is created under the barrier due to nonstationary conditions. As a result, the tunneling probability strongly enhances and can be not exponentially small even for almost classical barriers. Remarkable, that an electron loses its energy under the barrier. Classical trajectories in complex time are also applicable to description of Euclidean resonance. Analytical methods and a direct numerical solution of Schroedinger equation are used to study photon-assisted tunneling and Euclidean resonance. The above phenomena can be used for control of tunneling: in scanning tunneling microscopy, for selective destruction of chemical bonds, in nanostructures, etc.

PACS numbers: 74.25.Nf, 74.40.+k, 74.72.Hs

In the first part of the talk I will describe the large scale behavior of general cosmological solutions under a priori bounds of the space time curvature and show how, at large scales, these universes evolve toward "geometrized ones". In the second part I will concentrate on a more accurate and predictive description of the evolution, paying quantitative attention to the gravitational and material energy an their contributions in the universe deceleration. I will do so by studying a Friedman-Lemaitre equation for the volume-averaged cosmological parameters. These results in particular extend the large scale and long time behavior of the standard compact Friedman-Lemaitre-Robertson-Walker models to general non-homogeneous and non-isotropic cosmologies.

The energy relaxation in the spin-polarized disordered electron liquid is studied in the diffusive regime. We derived the quantum kinetic equation in which the kernel of electron-electron collision integral explicitly depends on the electron magnetization. As the consequence, the inelastic scattering rate is found to have non-monotonic dependence on spin-polarization of the electron system. Based on arxiv:0708.0523