The appearance of particle tracks in detectors -- II: the semi-classical realm

TL;DR

This paper rigorously analyzes how particle tracks resembling classical orbits emerge from quantum particles in detectors within the semi-classical regime, especially for quadratic Hamiltonians, revealing symmetry breaking and classical trajectory reconstruction.

Contribution

It provides a detailed mathematical analysis of particle tracks in the semi-classical limit for quadratic Hamiltonians, highlighting symmetry breaking and trajectory reconstruction.

Findings

Symmetries of initial states are broken by particle tracks.

Classical trajectories can be reconstructed from quantum tracks.

The analysis applies to particles in magnetic fields and free motion.

Abstract

The appearance of tracks, close to classical orbits, left by charged quantum particles propagating inside a detector, such as a cavity periodically illuminated by light pulses, is studied for a family of idealized models. In the semi-classical regime, which is reached when one considers highly energetic particles, we present a detailed, mathematically rigorous analysis of this phenomenon. If the Hamiltonian of the particles is quadratic in position- and momentum operators, as in the examples of a freely moving particle or a particle in a homogeneous external magnetic field, we show how symmetries, such as spherical symmetry, of the initial state of a particle are broken by tracks consisting of infinitely many approximately measured particle positions and how, in the classical limit, the initial position and velocity of a classical particle trajectory can be reconstructed from the observed particle track.