The semiclassical limit of a quantum Zeno dynamics

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 $\hslash \to 0$ and large quantum number $N\to \infty$, with $\hslash N$ 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.

28 pages, 5 figures

References in corpus (3)

• Quantum Zeno dynamics: mathematical and physical aspects
• Point processes in arbitrary dimension from fermionic gases, random matrix theory, and number theory
• Note on a Product Formula Related to Quantum Zeno Dynamics

Cited by in corpus (1)

• Truncated quantum observables and their semiclassical limit