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THU: Thursday Contributed Sessions

THU 10: Foundational / Mathematical Aspects – Methods and Approximations

THU 10.5: Talk

Thursday, September 11, 2025, 15:15–15:30, ZHG103

Tunneling Modeled via First-Passage Times — •Philipp Tesch, Kai-Hendrik Henk, and Wolfgang Paul — MLU Halle-Wittenberg

Since quantum mechanics lacks a self-adjoint time operator, time is not an observable in the standard formalism. As a result, time measurements such as tunneling durations are not directly accessible within the conventional framework. In 1966, Edward Nelson introduced a stochastic mechanics approach to describe quantum systems [1]. In this framework, quantum systems are treated as open systems undergoing conservative, time-reversible diffusion processes. This is modeled by Brownian motion guided by velocity fields. This framework is applied for quantum tunneling in symmetric double-well potentials. Instead of tunneling, particles overcome the finite potential barrier due to energy fluctuations. Ground states are obtained numerically via the stationary Schrödinger equation, from which probability densities and osmotic velocities are calculated. Solving the stochastic differential equations to simulate sample paths of particles allows us to compute first-passage times across the potential barrier under two different threshold criteria. An inverse relation between mean first-passage times τ and the energy splitting Δ E in double-well potentials emerges. Furthermore, this framework allows for a detailed study of the probability distribution of tunneling times (modelled as first passage times), which can be addressed by attosecond spectroscopy [2].

[1] E. Nelson, Phys. Rev. 150 (1966) [2] A. S. Landsmann et al., Optica 1 (2014)

Keywords: Stochastic Mechanics; SDE; Tunneling; Brownian motion