85 research outputs found
Orbiting Resonances and Bound States in Molecular Scattering
A family of orbiting resonances in molecular scattering is globally described
by using a single pole moving in the complex angular momentum plane. The
extrapolation of this pole at negative energies gives the location of the bound
states. Then a single pole trajectory, that connects a rotational band of bound
states and orbiting resonances, is obtained. These complex angular momentum
singularities are derived through a geometrical theory of the orbiting. The
downward crossing of the phase-shifts through pi/2, due to the repulsive region
of the molecular potential, is estimated by using a simple hard-core model.
Some remarks about the difference between diffracted rays and orbiting are also
given.Comment: 18 pages, 3 figures, to appear in Physical Review
Diffusive limit for a quantum linear Boltzmann dynamics
In this article, I study the diffusive behavior for a quantum test particle
interacting with a dilute background gas. The model I begin with is a reduced
picture for the test particle dynamics given by a quantum linear Boltzmann
equation in which the gas particle scattering is assumed to occur through a
hard-sphere interaction. The state of the particle is represented by a density
matrix that evolves according to a translation-covariant Lindblad equation. The
main result is a proof that the particle's position distribution converges to a
Gaussian under diffusive rescaling.Comment: 51 pages. I have restructured Sections 2-4 from the previous version
and corrected an error in the proof of Proposition 7.
Three disks in a row: A two-dimensional scattering analog of the double-well problem
We investigate the scattering off three nonoverlapping disks equidistantly
spaced along a line in the two-dimensional plane with the radii of the outer
disks equal and the radius of the inner disk varied. This system is a
two-dimensional scattering analog to the double-well-potential (bound state)
problem in one dimension. In both systems the symmetry splittings between
symmetric and antisymmetric states or resonances, respectively, have to be
traced back to tunneling effects, as semiclassically the geometrical periodic
orbits have no contact with the vertical symmetry axis. We construct the
leading semiclassical ``creeping'' orbits that are responsible for the symmetry
splitting of the resonances in this system. The collinear three-disk-system is
not only one of the simplest but also one of the most effective systems for
detecting creeping phenomena. While in symmetrically placed n-disk systems
creeping corrections affect the subleading resonances, they here alone
determine the symmetry splitting of the 3-disk resonances in the semiclassical
calculation. It should therefore be considered as a paradigm for the study of
creeping effects. PACS numbers: 03.65.Sq, 03.20.+i, 05.45.+bComment: replaced with published version (minor misprints corrected and
references updated); 23 pages, LaTeX plus 8 Postscript figures, uses
epsfig.sty, espf.sty, and epsf.te
Causality and dispersion relations and the role of the S-matrix in the ongoing research
The adaptation of the Kramers-Kronig dispersion relations to the causal
localization structure of QFT led to an important project in particle physics,
the only one with a successful closure. The same cannot be said about the
subsequent attempts to formulate particle physics as a pure S-matrix project.
The feasibility of a pure S-matrix approach are critically analyzed and their
serious shortcomings are highlighted. Whereas the conceptual/mathematical
demands of renormalized perturbation theory are modest and misunderstandings
could easily be corrected, the correct understanding about the origin of the
crossing property requires the use of the mathematical theory of modular
localization and its relation to the thermal KMS condition. These new concepts,
which combine localization, vacuum polarization and thermal properties under
the roof of modular theory, will be explained and their potential use in a new
constructive (nonperturbative) approach to QFT will be indicated. The S-matrix
still plays a predominant role but, different from Heisenberg's and
Mandelstam's proposals, the new project is not a pure S-matrix approach. The
S-matrix plays a new role as a "relative modular invariant"..Comment: 47 pages expansion of arguments and addition of references,
corrections of misprints and bad formulation
Fluctuations, dissipation and the dynamical Casimir effect
Vacuum fluctuations provide a fundamental source of dissipation for systems
coupled to quantum fields by radiation pressure. In the dynamical Casimir
effect, accelerating neutral bodies in free space give rise to the emission of
real photons while experiencing a damping force which plays the role of a
radiation reaction force. Analog models where non-stationary conditions for the
electromagnetic field simulate the presence of moving plates are currently
under experimental investigation. A dissipative force might also appear in the
case of uniform relative motion between two bodies, thus leading to a new kind
of friction mechanism without mechanical contact. In this paper, we review
recent advances on the dynamical Casimir and non-contact friction effects,
highlighting their common physical origin.Comment: 39 pages, 4 figures. Review paper to appear in Lecture Notes in
Physics, Volume on Casimir Physics, edited by Diego Dalvit, Peter Milonni,
David Roberts, and Felipe da Rosa. Minor changes, a reference adde
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