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University of Rochester

1. Mallalieu, Mark R. (1959 - ). Semiclassical dynamics of Rydberg electronic wave packets.

Degree: PhD, 2017, University of Rochester

URL: http://hdl.handle.net/1802/32162

This thesis develops theoretical techniques to
clarify the correspondence between Kepler trajectories and Rydberg
wave packet evolution. These methods provide criteria for
determining when classical or nonclassical evolution can be
expected, and lay the foundation for such studies for closely
related systems which display nonintegrable dynamics.
</br>A semiclassical propagator which is the WKB
approximation to the Feynman propagator is applied to describe the
dynamics of circular-orbit wave packets which are initially well
localized in three dimensions. A sum over classical Kepler
trajectories for the wave-packet autocorrelation function is
obtained which is extremely accurate well past the classical regime
of wave-packet evolution. The nonclassical nature of the
wave-packet evolution at long times is associated with the
interference between amplitudes from classical paths at different
energies. The time scale of the wave-packet revivals is related to
the shearing rate of the corresponding classical ensemble.
</br>Electron interferometry between pairs of
radial wave packets created by phasecoherent
laser pulses is
studied. It is shown how the quantal phases that wave packets
acquire after propagation about the Kepler orbits can be measured
with this method. A classical path representation of this
measurement is found using a theory based on the Maslov formulation
of WKB wave functions. The resulting
semiclassical sum is used to
show that the phase the wave packet acquires is a type of Berry's
phase which is related to the Bohr-Sommerfeld action of Kepler
orbits. This method is also used to study the correlated fractional
wave packet states which occur when a wave packet revives into
several replicas of the initial
state.
</br>Closed-form solutions to the semiclassical
sums for the wave-packet autocorrelation functions are derived for
times during fractional revivals. These solutions provide
correspondences between the fractional wave packets and discrete
sets of orbits. These sets have values of action variable which are
multiples of rational fractions, and sometimes contain the Bohr
orbits as a subset. Analytical solutions for the phases of the
fractional wave packets are also obtained and found to be very
accurate.

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APA (6^{th} Edition):

Mallalieu, M. R. (. -. ). (2017). Semiclassical dynamics of Rydberg electronic wave packets. (Doctoral Dissertation). University of Rochester. Retrieved from http://hdl.handle.net/1802/32162

Chicago Manual of Style (16^{th} Edition):

Mallalieu, Mark R (1959 - ). “Semiclassical dynamics of Rydberg electronic wave packets.” 2017. Doctoral Dissertation, University of Rochester. Accessed June 21, 2018. http://hdl.handle.net/1802/32162.

MLA Handbook (7^{th} Edition):

Mallalieu, Mark R (1959 - ). “Semiclassical dynamics of Rydberg electronic wave packets.” 2017. Web. 21 Jun 2018.

Vancouver:

Mallalieu MR(-). Semiclassical dynamics of Rydberg electronic wave packets. [Internet] [Doctoral dissertation]. University of Rochester; 2017. [cited 2018 Jun 21]. Available from: http://hdl.handle.net/1802/32162.

Council of Science Editors:

Mallalieu MR(-). Semiclassical dynamics of Rydberg electronic wave packets. [Doctoral Dissertation]. University of Rochester; 2017. Available from: http://hdl.handle.net/1802/32162