Quantum adiabatic theorem for chemical reactions and systems with time-dependent orthogonalization

TL;DR

This paper extends the quantum adiabatic theorem to systems with time-dependent orthogonalization, providing insights into chemical reaction activation energies and the dynamics of systems with energy level crossings.

Contribution

It introduces a generalized quantum adiabatic theorem applicable to systems with time-dependent orthogonalization, linking internal and external time scales in quantum dynamics.

Findings

Proves a generalized quantum adiabatic theorem with and without orthogonalization.

Establishes the relationship between internal and external time scales in quantum systems.

Demonstrates applications to chemical reactions and systems with energy level crossings.

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 relationship between the internal (due to time-dependent eigenfunctions) and external (due to time-dependent Hamiltonian) time scales. We prove that this relationship needs to be taken as an independent quantum adiabatic approximation criterion. 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.