66 research outputs found
Extension and approximation of -subharmonic functions
Let be a bounded domain, and let be a
real-valued function defined on the whole topological boundary . The aim of this paper is to find a characterization of the functions
which can be extended to the inside to a -subharmonic function under
suitable assumptions on . We shall do so by using a function algebraic
approach with focus on -subharmonic functions defined on compact sets. We
end this note with some remarks on approximation of -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
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