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G093621N#56129226

Abstract:

In this work, we investigate a number of physical systems, where we will consistently focus on the paths that particles follow. Trajectories are a known concept in classical mechanics, in fact, the essence of this field can be summarized as figuring out the paths particles take, given the forces acting on them. In quantum mechanics, applying this concept proves to be much more challenging, but it can also lead to a deeper understanding. To begin with, we revisit canonical quantization of gravity, where we employ point particles for matter. These theories are typically plagued by the problem of time, a conceptual conflict over this concept between quantum field theory on one hand and general relativity on the other, resulting in equations that do not describe evolution through time. We postulate equations of motion for both the point particles and the spatial metric itself, based on the continuity equation associated to the Wheeler-DeWitt equation. These equations of motion yield the classical trajectories of both the particles and the metric, along with an additional non-local term derived from the modulus of the wave function, the quantum potential. In addition, this allows us to define a conserved energy-momentum tensor. Next, we turn our attention to another quantum theory, that of the Dirac electron. Here, we find a connection with a concept from non-equilibrium statistical mechanics, active matter. Specifically, we observe that the electron can be seen as a run-and-tumble particle, switching between chiralities. These trajectories are used to illustrate the two-slit experiment. Furthermore, they also serve to explore concepts such as the arrival times of particles at detectors. Finally, we shift our focus to a very different type of particle, the photon. We consider a photon gas that exchanges energy with the environment, where the dominant process is assumed to be inverse Compton scattering. We review the derivation of the Kompaneets equation, a nonlinear Fokker-Planck equation for the dynamics of this system, and generalize the process to a nonlinear Langevin dynamics. This is applied in simulations with the goal of enabling or facilitating extensions to non-equilibrium conditions, which are also briefly illustrated. One motivation considered for this is the processes of the early universe, shortly after the Big Bang, where we question whether this non-equilibrium environment could have left traces on the cosmic microwave background radiation. We also briefly study another application of non-equilibrium, resetting, where the photon is regularly abruptly lowered in frequency. Several possibilities for resetting are discussed and simulated.