• Citer

Quantum Scattering, Transport, and Decoherence in Disordered Media: An Application to Gaseous Particle Detectors

par Gaspard, David
Président du jury Vaeck, Nathalie
Promoteur Sparenberg, Jean-Marc
Publication Non publié, 2022-06-28

Thèse de doctorat

• Accès en ligne
• Détails
• Contenu
• Statistiques

Résumé :

The main purpose of this thesis is to investigate the physics of particle detectors from first principles combining quantum mechanics and statistical physics. In particular, this work aims at studying the Mott problem, that is the issue of the appearance, within the framework of quantum mechanics, of linear tracks in Wilson cloud chambers due to the passage of ionizing particles. Although the Mott problem is closely related to the quantum measurement problem, this thesis focuses on the phenomenological questions regarding the propagation of a quantum particle in a detector rather than the question of the interpretation of quantum mechanics. To this end, models of a quantum particle evolving in a gaseous environment are developed. In the first considered model, called the random Lorentz gas, the constituents of the medium are assumed to be point-like and fixed at random positions. The Schrödinger equation can thus be solved systematically using the Foldy-Lax method. This model is first studied with the tools of scattering theory, namely the cross section and the complex resonance spectrum. An efficient numerical method is devised to compute the density of resonances in the complex plane of the wavenumber, without having to find them one by one. This method leads to hitherto unknown structures in the resonance spectrum. These structures are then explained by resorting to wave transport theory, which includes an effective Schrödinger equation at large wavelength, and an integral transport equation at small wavelength. The phase averaging effect is especially highlighted in the latter case. This effect is the cancellation of most of the off-diagonal elements of the density matrix after the average over the random configurations of the scatterers. The second considered model is more comprehensive, as it accounts for the quantum nature of the gaseous environment. The density matrix of the full system is governed by the quantum Liouville equation. Since the gas is in a thermal state, the partial trace of the density matrix over the environmental degrees of freedom is equivalent to the configurational average done in the Lorentz gas model. The second model is thus related to the first one. A linear quantum Boltzmann equation is derived from the Redfield equation to describe the time evolution of the Wigner distribution of the quantum particle. The Boltzmann equation is then approximated by a Fokker-Planck equation to study the decoherence of the reduced density matrix resulting from the collisions with the scatterers. The decoherence is dominated by the phase averaging, which comes from the uncertainty in the positions of the scatterers. Finally, the transverse coherence length of an alpha particle in air is estimated by fitting the transport parameters on the experimental stopping power. These results open important perspectives on the Mott problem.