Spontaneous Transitions in Quantum Mechanics

TL;DR

This paper revisits spontaneous pair creation in static external fields, proves a weaker version of Nenciu's conjecture, and discusses approaches for proving the full conjecture using time-dependent Hamiltonian evolution.

Contribution

It establishes a proof for a weaker form of Nenciu's conjecture and explores methods to prove the full conjecture in quantum mechanics.

Findings

Proved a weak version of Nenciu's conjecture.

Reduced the general conjecture to studying eigenvector evolution.

Discussed potential approaches for full proof.

Abstract

The problem of spontaneous pair creation in static external fields is reconsidered. A weak version of the conjecture proposed by G Nenciu (1980) is seated and proved. The method reduces the proof of the general conjecture to the study of the evolution, associated with a time dependent Hamiltonian, of a vector which is eigenvector of this Hamiltonian at some given time. Possible ways of proving the general conjecture are discussed.