Finite-size corrections to Fermi's Golden rule II: Quasi-stationary composite states

TL;DR

This paper derives finite-size corrections to Fermi's Golden Rule for many-body quantum states, revealing new transition components and macroscopic quantum effects, especially in dilute QED systems, with potential experimental verification.

Contribution

It introduces a rigorous approach using normalized functions for the S-matrix, uncovering correction terms and macroscopic phenomena overlooked by traditional Fermi's Golden Rule.

Findings

Visible energy smaller than initial energy due to corrections.

Significant corrections in dilute quantum electrodynamics systems.

Potential for laboratory verification of these quantum states.

Abstract

Many-body states described by a Schr\"{o}dinger equation include states of overlapping waves of non-vanishing interaction energies. These peculiar states formed in many-body transitions remain in asymptotic regions, and lead a new component to the transition probability. The probability is computed rigorously following the von Neumann's fundamental principle of quantum mechanics with an S-matrix that is defined with normalized functions, instead of plane waves. That includes the intriguing correction term to the Fermi's golden rule, in which a visible energy is smaller than the initial energy, and reveals macroscopic quantum phenomena for light particles. Processes in Quantum Electrodynamics are analyzed and the sizable corrections are found in the dilute systems. The results suggest that these states play important roles in natural phenomena, and the verification in laboratory would be possible with recent advanced technology.