Extension and approximation of mm-subharmonic functions

Let $\Omega\subset \mathbb C^n$ be a bounded domain, and let $f$ be a real-valued function defined on the whole topological boundary $\partial \Omega$. The aim of this paper is to find a characterization of the functions $f$ which can be extended to the inside to a $m$-subharmonic function under suitable assumptions on $\Omega$. We shall do so by using a function algebraic approach with focus on $m$-subharmonic functions defined on compact sets. We end this note with some remarks on approximation of $m$-subharmonic functions

Gilbert Damping in Conducting Ferromagnets II: Model Tests of the Torque-Correlation Formula

We report on a study of Gilbert damping due to particle-hole pair excitations in conducting ferromagnets. We focus on a toy two-band model and on a four-band spherical model which provides an approximate description of ferromagnetic (Ga,Mn)As. These models are sufficiently simple that disorder-ladder-sum vertex corrections to the long-wavelength spin-spin response function can be summed to all orders. An important objective of this study is to assess the reliability of practical approximate expressions which can be combined with electronic structure calculations to estimate Gilbert damping in more complex systems.Comment: 10 pages, 10 figures. Submitted to Phys. Rev.

Atomic excitation during recollision-free ultrafast multi-electron tunnel ionization

Modern intense ultrafast pulsed lasers generate an electric field of sufficient strength to permit tunnel ionization of the valence electrons in atoms. This process is usually treated as a rapid succession of isolated events, in which the states of the remaining electrons are neglected. Such electronic interactions are predicted to be weak, the exception being recollision excitation and ionization caused by linearly-polarized radiation. In contrast, it has recently been suggested that intense field ionization may be accompanied by a two-stage `shake-up' reaction. Here we report a unique combination of experimental techniques that enables us to accurately measure the tunnel ionization probability for argon exposed to 50 femtosecond laser pulses. Most significantly for the current study, this measurement is independent of the optical focal geometry, equivalent to a homogenous electric field. Furthermore, circularly-polarized radiation negates recollision. The present measurements indicate that tunnel ionization results in simultaneous excitation of one or more remaining electrons through shake-up. From an atomic physics standpoint, it may be possible to induce ionization from specific states, and will influence the development of coherent attosecond XUV radiation sources. Such pulses have vital scientific and economic potential in areas such as high-resolution imaging of in-vivo cells and nanoscale XUV lithography.Comment: 17 pages, 4 figures, original format as accepted by Nature Physic

Nonlinear Sigma Model for Disordered Media: Replica Trick for Non-Perturbative Results and Interactions

In these lectures, given at the NATO ASI at Windsor (2001), applications of the replicas nonlinear sigma model to disordered systems are reviewed. A particular attention is given to two sets of issues. First, obtaining non-perturbative results in the replica limit is discussed, using as examples (i) an oscillatory behaviour of the two-level correlation function and (ii) long-tail asymptotes of different mesoscopic distributions. Second, a new variant of the sigma model for interacting electrons in disordered normal and superconducting systems is presented, with demonstrating how to reduce it, under certain controlled approximations, to known ``phase-only'' actions, including that of the ``dirty bosons'' model.Comment: 25 pages, Proceedings of the NATO ASI "Field Theory of Strongly Correlated Fermions and Bosons in Low - Dimensional Disordered Systems", Windsor, August, 2001; to be published by Kluwe

Stochastic Gravity: Theory and Applications

Whereas semiclassical gravity is based on the semiclassical Einstein equation with sources given by the expectation value of the stress-energy tensor of quantum fields, stochastic semiclassical gravity is based on the Einstein-Langevin equation, which has in addition sources due to the noise kernel.In the first part, we describe the fundamentals of this new theory via two approaches: the axiomatic and the functional. In the second part, we describe three applications of stochastic gravity theory. First, we consider metric perturbations in a Minkowski spacetime: we compute the two-point correlation functions for the linearized Einstein tensor and for the metric perturbations. Second, we discuss structure formation from the stochastic gravity viewpoint. Third, we discuss the backreaction of Hawking radiation in the gravitational background of a quasi-static black hole.Comment: 75 pages, no figures, submitted to Living Reviews in Relativit

Quasistationary Stabilization of the Decay of a Weakly-Bound Level and Its Breakdown in a Strong Laser Field

Although it was pointed out about 10 years ago that an atomic decay rate might decrease as the intensity of a high-frequency laser field increases, there still does not exist any complete understanding of either the physical origin of this interesting nonlinear phenomenon or its dependence on the atomic and field parameters. Essentially, the problem consists in that the phenomenon requires a major modification of the standard picture of photoeffect in a strong laser field. In Reference #1 the origin of this stabilization is related to a particular distortion of an atomic potential by an intense monochromatic high-frequency field. This phenomenon is called adiabatic or quasistationary stabilization (QS). For the case of Rydberg levels, another (interference) mechanism of QS was suggested. Both theories predict an unlimited decrease of the decay rate (or of the width Γ of an atomic level, i.e., of the imaginary part of the complex quasienergy, ε = Re ε – iΓ/2 ) as the laser field amplitude increases. In recent years the idea of “dynamic stabilization” (DS) has become popular. It originates from the pulse form of a laser field rather than from any intrinsic property of the atom in a strong monochromatic field. Within this model the numerous simulations point also to the possibility of a breakdown of stabilization for the case of superintense short laser pulses. However, a recent paper, using the quasistationary quasienergy states (QQES) as an adiabatic basis for the laser pulse has shown that DS has the same (quasistationary) origin as QS. Finally, a number of authors deny the existence of stabilization, in particular, of QS for ionization from a short-range potential and of DS in pulsed fields. Obviously, these controversies and ambiguities are caused by the complexity of the numerical solution of the Cauchy problem for the time-dependent Schrödinger equation in a strong field and by the absence of analyses for exactly solvable analytical models. We analyze the exactly solvable problem of an electron in a three-dimensional, short-range potential and consider the two questions: does a QS-like behavior of the decay rate exist for this model, and, if so, is there an upper intensity limit of the QS regime

Stochastic Gravity: Theory and Applications

Whereas semiclassical gravity is based on the semiclassical Einstein equation with sources given by the expectation value of the stress-energy tensor of quantum fields, stochastic semiclassical gravity is based on the Einstein-Langevin equation, which has in addition sources due to the noise kernel. In the first part, we describe the fundamentals of this new theory via two approaches: the axiomatic and the functional. In the second part, we describe three applications of stochastic gravity theory. First, we consider metric perturbations in a Minkowski spacetime, compute the two-point correlation functions of these perturbations and prove that Minkowski spacetime is a stable solution of semiclassical gravity. Second, we discuss structure formation from the stochastic gravity viewpoint. Third, we discuss the backreaction of Hawking radiation in the gravitational background of a black hole and describe the metric fluctuations near the event horizon of an evaporating black holeComment: 100 pages, no figures; an update of the 2003 review in Living Reviews in Relativity gr-qc/0307032 ; it includes new sections on the Validity of Semiclassical Gravity, the Stability of Minkowski Spacetime, and the Metric Fluctuations of an Evaporating Black Hol