132 research outputs found
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
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
Statistical Theory of Asteroid Escape Rates
Transition states in phase space are identified and shown to regulate the rate of escape of asteroids temporarily captured in circumplanetary orbits. The transition states, similar to those occurring in chemical reaction dynamics, are then used to develop a statistical semianalytical theory for the rate of escape of asteroids temporarily captured by Mars. Theory and numerical simulations are found to agree to better than 1%. These calculations suggest that further development of transition state theory in celestial mechanics, as an alternative to large-scale numerical simulations, will be a fruitful approach to mass transport calculations
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
Stochastic Transition States: Reaction Geometry amidst Noise
Classical transition state theory (TST) is the cornerstone of reaction rate
theory. It postulates a partition of phase space into reactant and product
regions, which are separated by a dividing surface that reactive trajectories
must cross. In order not to overestimate the reaction rate, the dynamics must
be free of recrossings of the dividing surface. This no-recrossing rule is
difficult (and sometimes impossible) to enforce, however, when a chemical
reaction takes place in a fluctuating environment such as a liquid.
High-accuracy approximations to the rate are well known when the solvent forces
are treated using stochastic representations, though again, exact no-recrossing
surfaces have not been available. To generalize the exact limit of TST to
reactive systems driven by noise, we introduce a time-dependent dividing
surface that is stochastically moving in phase space such that it is crossed
once and only once by each transition path
Eigenvalues of the Schrödinger equation for a periodic potential with nonperiodic boundary conditions: A uniform semiclassical analysis
A uniform semiclassical expression for the eigenvalues of a one dimensional periodic Schrödinger equation with nonperiodic boundary conditions has been derived. The potential energy function can have any number of symmetric or asymmetric barriers and wells. The treatment is uniform in that the classical turning points can come close together, coalesce, and move into the complex plane as the energy passes through a barrier maximum. A detailed application is made to Mathieu functions of integer order; the equations themselves include the case of fractional order. Approximate semiclassical expressions are derived for the widths of the energy bands and the energy gaps of the periodic Mathieu equation when these quantities are small. The semiclassical results give a physical interpretation to formulas present in the mathematical literature and to the decrease in the splitting of a sequence of avoided crossings with increasing quantum numbers in coupled oscillator systems. Numerical calculations are reported to illustrate the high accuracy of the semiclassical formulas
Transition State Theory For Laser-Driven Reactions
Recent developments in transition state theory brought about by dynamical systems theory are extended to time-dependent systems such as laser-driven reactions. Using time-dependent normal form theory, the authors construct a reaction coordinate with regular dynamics inside the transition region. The conservation of the associated action enables one to extract time-dependent invariant manifolds that act as separatrices between reactive and nonreactive trajectories and thus make it possible to predict the ultimate fate of a trajectory. They illustrate the power of our approach on a driven Henon-Heiles system, which serves as a simple example of a reactive system with several open channels. The present generalization of transition state theory to driven systems will allow one to study processes such as the control of chemical reactions through laser pulses
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