QUANTUM ADIABATIC THEOREM FOR CHEMICAL REACTIONS AND SYSTEMS WITH TIME- DEPENDENT ORTHOGONALIZATION
Andrew Das Arulsamy · 2016
Abstract. A general quantum adiabatic theorem with and without the time-dependent orthogonalization is proven, which can be applied to understand the origin of activation energies in chemical reactions. Further proofs are also developed for the oscillating Schwinger Hamiltonian to establish the relation-ship between the internal (due to time-dependent eigenfunctions) and external (due to time-dependent Hamiltonian) timescales. We prove that this relation-ship needs to be taken as an independent condition for the quantum adiabatic approximation. We give four examples, including logical expositions based on the spin- 1 2 two-level system to address the gapped and gapless (due to energy level crossings) systems, as well as to understand how does this theorem allows one to study dynamical systems such as chemical reactions.