A link between static and dynamical perturbation theory

TL;DR

This paper explores how emergent time, derived from static environments, connects static and dynamic perturbation theories in quantum mechanics, offering a new perspective on understanding time-dependent phenomena from static states.

Contribution

It establishes a theoretical link between static and dynamic perturbation theories using the concept of emergent time, supported by calculations of first-order contributions.

Findings

Demonstrates the role of emergent time in linking static and dynamic perturbation theory

Calculates first-order contributions in quantum perturbation theory

Discusses implications for systems with degenerate spectra

Abstract

Dynamics, the physical change in time and a pillar of natural sciences, can be regarded as an emergent phenomenon when the system of interest is part of a larger, static one. This "relational approach to time", in which the system's environment provides a temporal reference, does not only provide insight into foundational issues of physics, but holds the potential for a deeper theoretical understanding as it intimately links statics and dynamics. Reinforcing the significance of this connection, we demonstrate, based on recent progress [Phys. Rev. Lett. 131, 140202 (2023)], the role of emergent time as a vital link between time-independent and time-dependent perturbation theory in quantum mechanics. We calculate first order contributions, which are often the most significant, and discuss the issue of degenerate spectra. Based on our results, we envision future applications for the calculation of dynamical phenomena based on a single pure energy eigenstate.