טכניון מכון טכנולוגי לישראל
הטכניון מכון טכנולוגי לישראל - בית הספר ללימודי מוסמכים  
Ph.D Thesis
Ph.D StudentGilary Ido
SubjectDynamics of Wavepackets in Non-Hermitian Quantum Mechanics
DepartmentDepartment of Chemistry
Supervisor Professor Emeritus Nimrod Moiseyev
Full Thesis textFull thesis text - English Version


Abstract

Non-Hermitian quantum mechanics has proven to be a powerful tool in the study of many resonance phenomena. The main achievement of the non-Hermitian formulation of quantum mechanics in the past decades has been in the ability to uncover the resonant energies from the continuum of scattering states as well as to predict the decay rate of these resonance states. Within the non-Hermitian description of quantum mechanics the resonance states become square integrable eigenstates of the non-Hermitian Hamiltonian. Until now, the time dependent study of resonance phenomena has been limited to cases where the evolution of the system in time is governed by one meta-stable resonance state. This is a common occurrence in many physical systems where the lifetime of one resonance state is much longer than the lifetimes of all other resonances. The main drawback of the existing non-Hermitian formalism of quantum mechanics is in its inability to encompass dynamics involving more than one resonance states.

The introduction of non-Hermitian Hamiltonians leads to decay of the wavefunction at times which approach ∞ but also to divergence at the infinite history of the wavefunction at times approaching -∞. This impairs the evaluation of time dependent observables within the existing non-Hermitian formalism.

This work focuses on the study of systems where the dynamics are governed by more than one resonance. Such analysis requires a time-dependent non-Hermitian formulation which will be able to include more than one eigenstate of the non-Hermitian Hamiltonian. In this research we formulate non-Hermitian quantum mechanics in a manner which enables the calculation of physical properties of any given wavepacket regardless of the number of resonances it populates. We show that the Non-Hermitian evolution in time portrays the Hermitian dynamics in the restricted part in space inside the interaction region.

The introduction of this modified non-Hermitian formalism to the study of matter-radiation interaction might explain or suggest new experimental phenomena. By studying laser driven dynamics involving more than one resonance state we are able to predict the observation of even harmonic peaks in the spectrum of higher harmonics generated by the interaction of helium atoms with high intensity laser fields.

The non-Hermitian formulation presented here stands on a solid mathematical ground which enables to draw parallel lines to the basic foundations of conventional quantum mechanics and to reflect on the physical similarities as well as the differences between the two.