195 research outputs found
Quantization with operators appropriate to shapes of trajectories and classical perturbation theory
Quantization is discussed for molecular systems having a zeroth order pair of doubly degenerate
normal modes. Algebraic quantization is employed using quantum operators appropriate to the
shape of the classical trajectories or wave functions, together with Birkhoff-Gustavson
perturbation theory and the W eyl correspondence for operators. The results are compared with a
previous algebraic quantization made with operators not appropriate to the trajectory shape.
Analogous results are given for a uniform semiclassical quantization based on Mathieu functions of fractional order. The relative sensitivities of these two methods (AQ and US) to the use of operators and coordinates related to and not related to the trajectory shape is discussed. The
arguments are illustrated using principally a Hamiltonian for which many previous results are available
Circularly Polarized Molecular High Harmonic Generation Using a Bicircular Laser
We investigate the process of circularly polarized high harmonic generation
in molecules using a bicircular laser field. In this context, we show that
molecules offer a very robust framework for the production of circularly
polarized harmonics, provided their symmetry is compatible with that of the
laser field. Using a discrete time-dependent symmetry analysis, we show how all
the features (harmonic order and polarization) of spectra can be explained and
predicted. The symmetry analysis is generic and can easily be applied to other
target and/or field configurations
Uniform semiclassical theory of avoided crossings
A voided crossings influence spectra and intramolecular redistribution of energy. A semiclassical theory
of these avoided crossings shows that when primitive semiclassical eigenvalues are plotted vs a parameter
in the Hamiltonian they cross instead of avoiding each other. The trajectories for each are connected by a
classically forbidden path. To obtain the avoided crossing behavior, a uniform semiclassical theory of
avoided crossings is presented in this article for the case where that behavior is generated by a classical
resonance. A low order perturbation theory expression is used as the basis for a functional form for the
treatment. The parameters in the expression are evaluated from canonical invariants (phase integrals)
obtained from classical trajectory data. The results are compared with quantum mechanical results for
the splitting, and reasonable agreement is obtained. Other advantages of the uniform method are
described
Theoretical studies of mode-specificity in intramolecular energy transfer
Issued as Interim reports [nos. 1-3], and Final report, Project no. G-41-63
Quantum-classical correspondence in circularly polarized high harmonic generation
Using numerical simulations, we show that atomic high order harmonic
generation, HHG, with a circularly polarized laser field offers an ideal
framework for quantum-classical correspondence in strong field physics. With an
appropriate initialization of the system, corresponding to a superposition of
ground and excited state(s), simulated HHG spectra display a narrow strip of
strong harmonic radiation preceded by a gap of missing harmonics in the lower
part of the spectrum. In specific regions of the spectra, HHG tends to lock to
circularly polarized harmonic emission. All these properties are shown to be
closely related to a set of key classical periodic orbits that organize the
recollision dynamics in an intense, circularly polarized field
Production of trans-Neptunian binaries through chaos-assisted capture
The recent discovery of binary objects in the Kuiper-belt opens an invaluable
window into past and present conditions in the trans-Neptunian part of the
Solar System. For example, knowledge of how these objects formed can be used to
impose constraints on planetary formation theories. We have recently proposed a
binary-object formation model based on the notion of chaos-assisted capture.
Here we present a more detailed analysis with calculations performed in the
spatial (three-dimensional) three- and four-body Hill approximations. It is
assumed that the potential binary partners are initially following heliocentric
Keplerian orbits and that their relative motion becomes perturbed as these
objects undergo close encounters. First, the mass, velocity, and orbital
element distribu- tions which favour binary formation are identified in the
circular and elliptical Hill limits. We then consider intruder scattering in
the circular Hill four-body problem and find that the chaos-assisted capture
mechanism is consistent with observed, apparently randomly distributed, binary
mutual orbit inclinations. It also predicts asymmetric distributions of
retrograde versus prograde orbits. The time-delay induced by chaos on particle
transport through the Hill sphere is analogous to the formation of a resonance
in a chemical reaction. Implications for binary formation rates are considered
and the 'fine-tuning' problem recently identified by Noll et al. (2007) is also
addressed.Comment: submitted to MNRA
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