arXiv subjects

M. R. Haggerty

Publications and source records attributed to M. R. Haggerty.

5 recordsLinked to original sources

arXiv2000

Localization of Eigenfunctions in the Stadium Billiard

We present a systematic survey of scarring and symmetry effects in the stadium billiard. The localization of individual eigenfunctions in Husimi phase space is studied first, and it is demonstrated that on average there is more localization than can be accounted for on the basis of random-matrix theory, even after removal of bouncing-ball states and visible scars. A major point of the paper is that symmetry considerations, including parity and time-reversal symmetries, enter to influence the total amount of localization. The properties of the local density of states spectrum are also investigated, as a function of phase space location. Aside from the bouncing-ball region of phase space, excess localization of the spectrum is found on short periodic orbits and along certain symmetry-related lines; the origin of all these sources of localization is discussed quantitatively and comparison is made with analytical predictions. Scarring is observed to be present in all the energy ranges considered. In light of these results the excess localization in individual eigenstates is interpreted as being primarily due to symmetry effects; another source of excess localization, scarring by multiple unstable periodic orbits, is smaller by a factor of $\sqrt{\hbar}$.

nlin.CD↗

arXiv2000

Influence of diffraction on the spectrum and wavefunctions of an open system

In this paper, we demonstrate the existence and significance of diffractive orbits in an open microwave billiard, both experimentally and theoretically. Orbits that diffract off of a sharp edge of the system are found to have a strong influence on the transmission spectrum of the system, especially in the regime where there are no stable classical orbits. On resonance, the wavefunctions are influenced by both classical and diffractive orbits. Off resonance, the wavefunctions are determined by the constructive interference of multiple transient, nonperiodic orbits. Experimental, numerical, and semiclassical results are presented.

nlin.CD↗

arXiv1999

Diffractive orbits in an open microwave billiard

We demonstrate the existence and significance of diffractive orbits in an open microwave billiard, both experimentally and theoretically. Orbits that diffract off of a sharp edge strongly influence the conduction spectrum of this resonator, especially in the regime where there are no stable classical orbits. On resonance, the wavefunctions are influenced by both classical and diffractive orbits. Off resonance, the wavefunctions are determined by the constructive interference of multiple transient, nonperiodic orbits. Experimental, numerical, and semiclassical results are presented.

quant-ph↗

arXiv1997

Symmetry breaking in crossed magnetic and electric fields

We present the first observations of cylindrical symmetry breaking in highly excited diamagnetic hydrogen with a small crossed electric field, and we give a semiclassical interpretation of this effect. As the small perpendicular electric field is added, the recurrence strengths of closed orbits decrease smoothly to a minimum, and revive again. This phenomenon, caused by interference among the electron waves that return to the nucleus, can be computed from the azimuthal dependence of the classical closed orbits.

physics.atom-ph↗

arXiv1995

Semiclassical quantization using Bogomolny's quantum surface of section

The efficacy and accuracy of Bogomolny's method of the quantum surface of section is evaluated by applying it to the quantization of the motion of a particle in a smooth 2-D potential. This method defines a transfer operator T in terms of classical trajectories of one Poincaré crossing; knowledge of T provides information about the eigenstates of the quantum system. By using a more robust quantization criterion than the one proposed by Bogomolny, we are able to locate more than five hundred quantum states in both the regular and the chaotic regimes--in most cases unambiguously--and see no reason that the spectra could not be continued indefinitely. The errors of the predictions are comparable in the two regimes, and roughly constant for increasing excitation, but grow as a fraction of the (shrinking) mean level spacing. We also show computed surface of section wavefunctions, and present other theoretical and practical results related to the technique.

chao-dyn↗