2,334 research outputs found
Radiation reaction in curved space-time: local method
Although consensus seems to exist about the validity of equations accounting
for radiation reaction in curved space-time, their previous derivations were
criticized recently as not fully satisfactory: some ambiguities were noticed in
the procedure of integration of the field momentum over the tube surrounding
the world-line. To avoid these problems we suggest a purely local derivation
dealing with the field quantities defined only {\em on the world-line}. We
consider point particle interacting with scalar, vector (electromagnetic) and
linearized gravitational fields in the (generally non-vacuum) curved
space-time. To properly renormalize the self-action in the gravitational case,
we use a manifestly reparameterization-invariant formulation of the theory.
Scalar and vector divergences are shown to cancel for a certain ratio of the
corresponding charges. We also report on a modest progress in extending the
results for the gravitational radiation reaction to the case of non-vacuum
background.Comment: 10 pages, ws-procs9x6, published in "Gravitation and Astrophysics",
Proceedings of the VII Asia-Pacific International Conference National Central
University, Taiwan 23 - 26 November 2005, ed. J.M. Nester, C.-M. Chen, J.-P.
Hsu. World Scientific, 2006, pp. 345-35
Non-perturbative corrections to the one-loop free energy induced by a massive scalar field on a stationary slowly varying in space gravitational background
The explicit expressions for the one-loop non-perturbative corrections to the
gravitational effective action induced by a scalar field on a stationary
gravitational background are obtained both at zero and finite temperatures. The
perturbative and non-perturbative contributions to the one-loop effective
action are explicitly separated. It is proved that, after a suitable
renormalization, the perturbative part of the effective action at zero
temperature can be expressed in a covariant form solely in terms of the metric
and its derivatives. This part coincides with the known large mass expansion of
the one-loop effective action. The non-perturbative part of the renormalized
one-loop effective action at zero temperature is proved to depend explicitly on
the Killing vector defining the vacuum state of quantum fields. This part
cannot be expressed in a covariant way through the metric and its derivatives
alone. The implications of this result for the structure and symmetries of the
effective action for gravity are discussed.Comment: 46 pp; some misprints corrected, elucidations adde
Hidden dynamics in models of discontinuity and switching
AbstractSharp switches in behaviour, like impacts, stick–slip motion, or electrical relays, can be modelled by differential equations with discontinuities. A discontinuity approximates fine details of a switching process that lie beyond a bulk empirical model. The theory of piecewise-smooth dynamics describes what happens assuming we can solve the system of equations across its discontinuity. What this typically neglects is that effects which are vanishingly small outside the discontinuity can have an arbitrarily large effect at the discontinuity itself. Here we show that such behaviour can be incorporated within the standard theory through nonlinear terms, and these introduce multiple sliding modes. We show that the nonlinear terms persist in more precise models, for example when the discontinuity is smoothed out. The nonlinear sliding can be eliminated, however, if the model contains an irremovable level of unknown error, which provides a criterion for systems to obey the standard Filippov laws for sliding dynamics at a discontinuity
How to play a disc brake
We consider a gyroscopic system under the action of small dissipative and
non-conservative positional forces, which has its origin in the models of
rotating bodies of revolution being in frictional contact. The spectrum of the
unperturbed gyroscopic system forms a "spectral mesh" in the plane "frequency
-gyroscopic parameter" with double semi-simple purely imaginary eigenvalues at
zero value of the gyroscopic parameter. It is shown that dissipative forces
lead to the splitting of the semi-simple eigenvalue with the creation of the
so-called "bubble of instability" - a ring in the three-dimensional space of
the gyroscopic parameter and real and imaginary parts of eigenvalues, which
corresponds to complex eigenvalues. In case of full dissipation with a
positive-definite damping matrix the eigenvalues of the ring have negative real
parts making the bubble a latent source of instability because it can "emerge"
to the region of eigenvalues with positive real parts due to action of both
indefinite damping and non-conservative positional forces. In the paper, the
instability mechanism is analytically described with the use of the
perturbation theory of multiple eigenvalues. As an example stability of a
rotating circular string constrained by a stationary load system is studied in
detail. The theory developed seems to give a first clear explanation of the
mechanism of self-excited vibrations in the rotating structures in frictional
contact, that is responsible for such well-known phenomena of acoustics of
friction as the squealing disc brake and the singing wine glass.Comment: 25 pages, 9 figures, Presented at BIRS 07w5068 Workshop "Geometric
Mechanics: Continuous and discrete, finite and infinite dimensional", August
12-17, 2007, Banff, Canad
Semiclassical Calculation of Multiparticle Scattering Cross Sections in Classicalizing Theories
It has been suggested in arXiv:1010.1415 that certain derivatively coupled
non-renormalizable scalar field theories might restore the perturbative
unitarity of high energy hard scatterings by classicalization, i.e. formation
of multiparticle states of soft quanta. Here we apply the semiclassical method
of calculating the multiparticle production rates to the scalar
Dirac-Born-Infeld (DBI) theory which is suggested to classicalize. We find that
the semiclassical method is applicable for the energies in the final state
above the cutoff scale of the theory L_*^{-1}. We encounter that the cross
section of the process two to N ceases to be exponentially suppressed for the
particle number in the final state N smaller than a critical particle number
N_{crit} ~ (E L_*)^{4/3}. It coincides with the typical particle number
produced in two-particle collisions at high energies predicted by
classicalization arguments.Comment: 17 pages, 4 figures, v2. Minor changes to match the published versio
Wannier functions for quasi-periodic finite-gap potentials
In this paper we consider Wannier functions of quasi-periodic g-gap () potentials and investigate their main properties. In particular, we discuss
the problem of averaging underlying the definition of Wannier functions for
both periodic and quasi-periodic potentials and express Bloch functions and
quasi-momenta in terms of hyperelliptic functions. Using this approach
we derive a power series expansion of the Wannier function for quasi-periodic
potentials valid at and an asymptotic expansion valid at large
distance. These functions are important for a number of applied problems
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