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<p>Using the principles of the so-called <i>ETH</i>-Approach to Quantum Mechanics we describe fluorescence and the phenomenon of “quantum jumps” in idealized models of atoms coupled to the quantized electromagnetic field. In a limiting regime where the orbital motion of the atoms is neglected and the velocity of light tends to <InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="220_2025_5352_Article_IEq1.gif" Format="GIF" Height="10" Rendition="HTML" Resolution="72" Type="Linedraw" Width="21" /> </InlineMediaObject> <EquationSource Format="TEX">\(\infty \)</EquationSource> <EquationSource Format="MATHML"><math> <mi>∞</mi> </math></EquationSource> </InlineEquation> we derive explicit non-linear stochastic differential equations describing the effective time evolution of states of individual atoms. These equations give rise to a measure on state trajectories exhibiting quantum jumps representing a quantum-mechanical analogue of the Wiener measure on Brownian paths in the theory of diffusion.</p>

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A Theory of Quantum Jumps

  • 期刊论文

  • 发表日期：

    2025年7月2日

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  • Jürg Fröhlich,
  • Zhou Gang,
  • Alessandro Pizzo

摘要

Using the principles of the so-called ETH-Approach to Quantum Mechanics we describe fluorescence and the phenomenon of “quantum jumps” in idealized models of atoms coupled to the quantized electromagnetic field. In a limiting regime where the orbital motion of the atoms is neglected and the velocity of light tends to \(\infty \) ∞ we derive explicit non-linear stochastic differential equations describing the effective time evolution of states of individual atoms. These equations give rise to a measure on state trajectories exhibiting quantum jumps representing a quantum-mechanical analogue of the Wiener measure on Brownian paths in the theory of diffusion.