טכניון מכון טכנולוגי לישראל
הטכניון מכון טכנולוגי לישראל - בית הספר ללימודי מוסמכים  
Ph.D Thesis
Ph.D StudentShachar Klaiman
SubjectResonances in Mesoscopic Systems
DepartmentDepartment of Chemistry
Supervisor Professor Emeritus Moiseyev Nimrod
Full Thesis textFull thesis text - English Version


Abstract

Scattering experiments are one of the basic methods by which one can probe a physical system of interest. The analysis of the scattering cross section provides an invaluable tool by which atomic, molecular, mesoscopic, and macroscopic systems can be studied. The actual doorway into the system is provided by resonances, i.e., sharp variations in the cross section, which are linked to the meta-stable states of the composite system comprised of the projectile and the target. Through these resonance one can probe the structure of the target, its stability, composition, and the interaction between the projectile and the target. The Extraction of the above information from the cross section is done by fitting a resonance profile to the measured resonance. Through the fit parameters of the profile, the scattering mechanism along with the target's structure unfold.


A major emphasis of this research thesis is the improvement of available resonance profiles such that more information can be extracted from the aforementioned process. In this aspect, we have been successful in providing new insight into the Fano asymmetry parameter and in deriving a novel resonance profile for the case of isolated single channel resonances. In the case of the Fano profile, we present a new expression for the asymmetry parameter as a product of two contributions: the background channel and the bound-continuum interaction. With this factorization the resulting asymmetry of the resonance profile could be traced back to the target's structure. It also provided a method by which the resulting asymmetry could be controlled. Our second achievement was in the derivation of a new resonance profile to replace the Breit-Wigner profile in the case of an isolated single channel resonance. Here we show that the resonance profile falls on the absolute value of the resonance state's energy as opposed to the previous belief that it falls on the real part of the resonance energy. The new profile also corrects for the asymmetry of the resonance profile and for the first time gives physical meaning to resonance states whose positions fall below the energy threshold.


We also treat the spectral properties of non-Hermitian operators and provide new methods to analyze and construct such operators which have a real spectrum. We trace back this special property to the point-group symmetry of the operator and suggest an experiment exemplifying the use of these properties.