Related papers: The semiclassical limit of a quantum Zeno dynamics

The semiclassical limit of a quantum Zeno dynamics

URL: http://arxiv.org/abs/2302.02673v3
Date: Sun, 15 Oct 2023 21:06:51 GMT
Title: The semiclassical limit of a quantum Zeno dynamics
Authors: Fabio Deelan Cunden, Paolo Facchi, Marilena Ligab\`o
Abstract summary: In a suitable topology, the limit is the discontinuous symbol $pchi_D(x,p)$ where $chi_D$ is the characteristic function of the region $D$ in phase space. A refined analysis shows that the symbol is close to the function $pchi_D(N)(x,p)$, where $chi_D(N)$ is a smooth version of $chi_D$ related to the integrated Airy function.
Score: 0.0
License: http://creativecommons.org/licenses/by/4.0/
Abstract: Motivated by a quantum Zeno dynamics in a cavity quantum electrodynamics setting, we study the asymptotics of a family of symbols corresponding to a truncated momentum operator, in the semiclassical limit of vanishing Planck constant $\hbar\to0$ and large quantum number $N\to\infty$, with $\hbar N$ kept fixed. In a suitable topology, the limit is the discontinuous symbol $p\chi_D(x,p)$ where $\chi_D$ is the characteristic function of the classically permitted region $D$ in phase space. A refined analysis shows that the symbol is asymptotically close to the function $p\chi_D^{(N)}(x,p)$, where $\chi_D^{(N)}$ is a smooth version of $\chi_D$ related to the integrated Airy function. We also discuss the limit from a dynamical point of view.

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