1,202 research outputs found
Discrete Breathers
Nonlinear classical Hamiltonian lattices exhibit generic solutions in the
form of discrete breathers. These solutions are time-periodic and (typically
exponentially) localized in space. The lattices exhibit discrete translational
symmetry. Discrete breathers are not confined to certain lattice dimensions.
Necessary ingredients for their occurence are the existence of upper bounds on
the phonon spectrum (of small fluctuations around the groundstate) of the
system as well as the nonlinearity in the differential equations. We will
present existence proofs, formulate necessary existence conditions, and discuss
structural stability of discrete breathers. The following results will be also
discussed: the creation of breathers through tangent bifurcation of band edge
plane waves; dynamical stability; details of the spatial decay; numerical
methods of obtaining breathers; interaction of breathers with phonons and
electrons; movability; influence of the lattice dimension on discrete breather
properties; quantum lattices - quantum breathers. Finally we will formulate a
new conceptual aproach capable of predicting whether discrete breather exist
for a given system or not, without actually solving for the breather. We
discuss potential applications in lattice dynamics of solids (especially
molecular crystals), selective bond excitations in large molecules, dynamical
properties of coupled arrays of Josephson junctions, and localization of
electromagnetic waves in photonic crystals with nonlinear response.Comment: 62 pages, LaTeX, 14 ps figures. Physics Reports, to be published; see
also at http://www.mpipks-dresden.mpg.de/~flach/html/preprints.htm
Black Hole Scattering from Monodromy
We study scattering coefficients in black hole spacetimes using analytic
properties of complexified wave equations. For a concrete example, we analyze
the singularities of the Teukolsky equation and relate the corresponding
monodromies to scattering data. These techniques, valid in full generality,
provide insights into complex-analytic properties of greybody factors and
quasinormal modes. This leads to new perturbative and numerical methods which
are in good agreement with previous results.Comment: 28 pages + appendices, 2 figures. For Mathematica calculation of
Stokes multipliers, download "StokesNotebook" from
https://sites.google.com/site/justblackholes/techy-zon
Dynamics of Lattice Kinks
In this paper we consider two models of soliton dynamics (the sine Gordon and
the \phi^4 equations) on a 1-dimensional lattice. We are interested in
particular in the behavior of their kink-like solutions inside the Peierls-
Nabarro barrier and its variation as a function of the discreteness parameter.
We find explicitly the asymptotic states of the system for any value of the
discreteness parameter and the rates of decay of the initial data to these
asymptotic states. We show that genuinely periodic solutions are possible and
we identify the regimes of the discreteness parameter for which they are
expected to persist. We also prove that quasiperiodic solutions cannot exist.
Our results are verified by numerical simulations.Comment: 50 pages, 10 figures, LaTeX documen
Electron-positron pairs in physics and astrophysics: from heavy nuclei to black holes
From the interaction of physics and astrophysics we are witnessing in these
years a splendid synthesis of theoretical, experimental and observational
results originating from three fundametal physical processes. They were
originally proposed by Dirac, by Breit and Wheeler and by Sauter, Heisenberg,
Euler and Schwinger. The vacuum polarization process in strong electromagnetic
field, pioneered by Sauter, Heisenberg, Euler and Schwinger, introduced the
concept of critical electric field. It has been searched without success for
more than forty years by heavy-ion collisions in many of the leading particle
accelerators worldwide. The novel situation today is that these same processes
can be studied on a much more grandiose scale during the gravitational collapse
leading to the formation of a black hole being observed in Gamma Ray Bursts.
This report is dedicated to the scientific race in act. The theoretical and
experimental work developed in Earth-based laboratories is confronted with the
theoretical interpretation of space-based observations of phenomena originating
on cosmological scales. What has become clear in the last ten years is that all
the three above mentioned processes, duly extended in the general relativistic
framework, are necessary for the understanding of the physics of the
gravitational collapse to a black hole. Vice versa, the natural arena where
these processes can be observed in mutual interaction and on an unprecedented
scale, is indeed the realm of relativistic astrophysics.Comment: to appear in Physics Reports, corrected proof
Applications of Massive Integrable Quantum Field Theories to Problems in Condensed Matter Physics
We review applications of the sine-Gordon model, the O(3) non-linear sigma
model, the U(1) Thirring model, and the O(N) Gross--Neveu model to quasi
one-dimensional quantum magnets, Mott insulators, and carbon nanotubes. We
focus upon the determination of dynamical response functions for these
problems. These quantities are computed by means of form factor expansions of
quantum correlation functions in integrable quantum field theories. This
approach is reviewed here in some detail.Comment: 150 pages, 35 figures, published in the I. Kogan Memorial Volume by
World Scientifi
Resonant nonlinear magneto-optical effects in atoms
In this article, we review the history, current status, physical mechanisms,
experimental methods, and applications of nonlinear magneto-optical effects in
atomic vapors. We begin by describing the pioneering work of Macaluso and
Corbino over a century ago on linear magneto-optical effects (in which the
properties of the medium do not depend on the light power) in the vicinity of
atomic resonances, and contrast these effects with various nonlinear
magneto-optical phenomena that have been studied both theoretically and
experimentally since the late 1960s. In recent years, the field of nonlinear
magneto-optics has experienced a revival of interest that has led to a number
of developments, including the observation of ultra-narrow (1-Hz)
magneto-optical resonances, applications in sensitive magnetometry, nonlinear
magneto-optical tomography, and the possibility of a search for parity- and
time-reversal-invariance violation in atoms.Comment: 51 pages, 23 figures, to appear in Rev. Mod. Phys. in Oct. 2002,
Figure added, typos corrected, text edited for clarit
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