Geometric Phases in Quantum Systems NUS（几何量子系统新加坡国立大学阶段）.pdfVIP

Geometric Phases in Quantum Systems 1 2 Lam M. and Singh K. Department of Physics, Faculty of Science, National University of Singapore 10 Kent Ridge Road, Singapore 117546 ABSTRACT The geometric phase appears as a special condition of adiabatic time-evolution of a Hamiltonian. Unlike regular phase factors, it cannot be removed with a different choice of gauge. This project aims to understand the origin of such a phase and its applicability to the fundamental Born-Oppenheimer approximation of molecular physics, a cornerstone of molecular physics conceived before the geometric phase, paying particular attention to its gauge structure and the behaviour of potential energy surfaces. As a final objective, this reports looks at the physical implications in the simplest Jahn Teller system. INTRODUCTION The (1984) introduction by Sir Michael Berry of an ‘extra’ phase factor, the Berry or adiabatic geometric phase, appearing in time-dependent Hamiltonians under adiabatic conditions and, significantly, ‘immune’ to being discarded by gauge transformations opened up a new area of exploration in fundamental physics. Prior to this, it had always been assumed that this ‘immunity’ did not exist, the argument for which was put forth by Vladimir Fock much earlier in 1928. The appearance of such terms in fundamental equations implied the possibility of it describing physical phenomena which the Berry-less quantum mechanical regime could not, and this, indeed, was the case as described by the preceding work of Yakir Aharanov and David Bohm in 1959 A fundamental equation of molecular ph