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

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.