History and Philosophy of Physics

A Lumped-Circuit Model of the Two-Level Atom: Eigenstate Resonators, an Environment-Gated Radiative Channel, and the Origin of Spontaneous Emission

Authors: Derrick Hiang Yaol Lim
Comments: 13 pages, 6 figures and 2 tables.

We present a classical, lumped-element circuit model of a two-level atom built around a specific conceptual claim: the two atomic energy eigenstates, represented as LC resonators with parameters fixed from the level energy and orbital magnetic moment, are exactly decoupled under the field-free Hamiltonian, which we realize as a literal open circuit between them. Coupling arises only from two distinct, independently gated perturbations: (i) an external oscillating field, modeled as a voltage source applied across the (otherwise open) inter-level branch, which produces reversible Rabi (continuous-wave drive) or Rosen—Zener (pulsed drive) dynamics; and (ii) theavailability of a radiative channel in the environment — schematically, a receptive absorber elsewhere in the universe — modeled as a resistive path to a shared radiative bath that opens and closes in time, which produces irreversible photon emission via a shared-bath coupled-mode-theory (Haus) formalism. In the absence of both perturbations the model predicts, exactly, that an isolated excited atom does not radiate. We show the emission channel comes in two dual circuit realizations, inductive (magnetic-dipole, M1) and capacitive (electric-dipole, E1) coupling to the environment, and validate both against the hydrogen 21 cm hyperfine line and the Lyman-α (2p → 1s) transition, reproducing the measured decay rates to within 1% and 0.2% respectively. We discuss the relationship of the "no absorber, no emission" baseline to Wheeler—Feynman absorber theory, to Cramer and Mead’s two-atom transactional formalism, and to the standard vacuum-fluctuation picture.
Category: History and Philosophy of Physics