Falsifiable Criterion for Dissipative Quantum Tunneling under the Ratia Energy-Dissipation Threshold Postulate

Luis Ratia

Published Aug 9, 2026• 0 citations

Abstract

The Ratia postulate proposes that wave function collapse is triggered when energydissipated from a quantum system into its environment satisfies a Heisenberg–Landauer-typeaction threshold, ∆Edis · τcollapse ≥ ℏ/2. This note derives a falsifiable structural criterion forwhen this threshold would be crossed during a dissipative quantum tunneling event, usingthe well-established framework of Grabert, Weiss, and Hanggi (Phys. Rev. Lett. 52, 2193,1984) for tunneling out of a metastable state coupled to an Ohmic thermal bath. Usingonly quantities already defined in that framework — the friction coefficient η, the barrierwidth q0, and the "bounce length" τB — we show that the postulate’s threshold condition,evaluated over the characteristic duration of the tunneling bounce trajectory, reduces to acompact dimensionless criterion, R = 4α (M ω0q20 /ℏ) ≷ 1, independent of τB itself. Thiscriterion is dimensionally verified and shown to coincide, up to a numerical prefactor, withthe dissipative tunneling literature’s own characteristic action scale. We discuss its physicalinterpretation, its qualitative behavior across parameter regimes, and its current limitations— principally the absence of a numerically evaluated real physical system, which we identifyas the necessary next step.

DOI: 10.5281/zenodo.21856073

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