Geometric phase and quantum transport in mesoscopic systems
Abstract of thesis entitled
GEOMETRIC PHASE AND QUANTUM TRANSPORT IN MESOSCOPIC SYSTEMS
for the Degree of Doctor of Philosophy
at The University of Hong Kong
in March 2001
The non-adiabatic non-cyclic geometric phase (Pancharatnam phase) plays a key role in some physical systems. An approach was developed to calculate this phase for a quantum spin-| particle subject to an arbitrary magnetic field. This approach can be used for all two-level systems and was applied to three specific kinds of magnetic fields. A kind of topological transition in a mesoscopic ring subject to an in-plane magnetic field was proposed, and the non-adiabatic effect on this phenomenon was addressed.
The generalization of Yang's theory from the U(l) gauge field to the non-Abelian U(l) x SU(2)spin gauge field is presented. Based on this generalization and taking into account the Pancharatnam phase as well as an effective
Aharonov-Bohm (AB) phase in non-adiabatic noncyclic transport, the ensemble average Fourier spectrum of the conductance in disordered mesoscopic rings connected to two leads was calculated. The observed splitting stems from the non-adiabatic non-cyclic Pancharatnam phase and the effective AB phase, both being dependent on spin-orbit (SO) coupling
The non-adiabatic correction on the quantum computation using coupled low-capacitance Josephson junctions was studied. It has been found that the non-adiabatic effect is important in performing geometric quantum computation.
The persistent current in a normal-metal mesoscopic ring was shown to be determined from the total geometric phase. The geometric phase and the persistent current in a ring subject to a cylindrically symmetric electromagnetic field were studied. The Pancharatnam phase has been found to recover the Aharonov-Anandan phase in the case of cyclic evolution, as well as the Berry's phase in the adiabatic evolution. Moreover, the persistent current induced by the SO-induced geometric phase was observed in the presence of a local magnetic field.
Finally, a recursive Green's function technique was developed to calculate the spin-dependent conductance of a quantum point contact (QPC), which is of current interest in fundamental physics. For a QPC in the presence of the Rashba SO interaction, some oscillations in the 'quantized' conductance induced by the SO interaction were observed in numerical calculations. These oscillations may stem from the multiple reflections associated with SO coupling.
School:The University of Hong Kong
School Location:China - Hong Kong SAR
Source Type:Master's Thesis
Keywords:geometric quantum phases mesoscopic phenomena physics transport theory
Date of Publication:01/01/2001