Monitoring continuous spectrum observables: the strong measurement limit

TL;DR

This paper analyzes how continuous spectrum observables in quantum systems evolve under strong measurement, revealing a spectrum diffusion process and a detailed crossover between classical and diffusive regimes.

Contribution

It provides a detailed analysis of the strong measurement limit for continuous spectrum observables, including the effects of competition with Lindbladian and Hamiltonian dynamics.

Findings

Strong measurement induces spectrum diffusion.

Crossover between classical and diffusive regimes is characterized.

Scaling limits elucidate measurement and dynamics competition.

Abstract

We revisit aspects of monitoring observables with continuous spectrum in a quantum system subject to dissipative (Lindbladian) or conservative (Hamiltonian) evolutions. After recalling some of the salient features of the case of pure monitoring, we deal with the case when monitoring is in competition with a Lindbladian evolution. We show that the strong measurement limit leads to a diffusion on the spectrum of the observable. For the case with competition between observation and Hamiltonian dynamics, we exhibit a scaling limit in which the crossover between the classical regime and a diffusive regime can be analyzed in details.