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Q: Fachverband Quantenoptik und Photonik

Q 28: Poster – Quantum Optics

Q 28.22: Poster

Dienstag, 3. März 2026, 17:00–19:00, Philo 2. OG

Quantum dynamical transitions when the corresponding classical phase space has a separatrix: extension of the QKNH theorem beyond double wells — •Peter Stabel and James Anglin — RPTU Kaiserslautern-Landau, 67663 Kaiserslautern

In classical Hamiltonian systems with a slowly time-dependent parameter, adiabatic approximations break down near a separatrix, where a constant-energy contour splits into separate contours, forcing the system to choose which contour to follow. The Kruskal-Neishtadt-Henrard (KNH) theorem relates the probabilities of such post-adiabatic dynamical transitions to the growth rates of the phase space areas enclosed by the different adiabatic contours. Quantum mechanically, in contrast, adiabaticity can persist at energies where it breaks down classically, through dynamical tunneling. Since the adiabatic and classical limits do not commute, the quantum-classical correspondence for dynamical transitions, where a separatrix is crossed in the classical system, is non-trivial. We recently demonstrated that a quantum version of the KNH theorem (QKNH) holds. We derived the QKNH theorem for a time-dependent double-well system, where the nearly degenerate levels below the potential barrier split due to tunneling through the barrier. We demonstrate that these findings are not restricted to double-well systems. We investigate the dynamical transitions of a general quantum pendulum where the crossings of adiabatic energy levels are avoided due to above-barrier reflection.

Keywords: Adiabatic physics; Dynamical transitions; Quantum-classical correspondence; Semiclassical physics; time-dependent systems