2023/03/31 by Leonardo Tinti, Tinti, Leonardo
Engineering · Physics and Astronomy · #Advanced Thermodynamics and Statistical Mechanics #FOS: Physical sciences #Fluid Dynamics and Turbulent Flows #High Energy Physics - Phenomenology (hep-ph) #Nuclear Theory (nucl-th) #Statistical Mechanics and Entropy
paper · pdf · doi:10.48550/arxiv.2304.00109
openalex publication_date 2023/03/31 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The collisionless Boltzmann equation, also called free-streaming, is a convenient approximation. It is rather simple to implement numerically, and and it is effective at reducing the irregularities of rough initial conditions. It can be obtained as a small ℏ limit from a free scalar quantum field. Namely, by neglecting the ℏ2 term in the dynamical evolution of the Wigner distribution, the quantum precursor of the distribution function. In this work it is presented the general form for the exact solutions of the Wigner distribution, for a scalar field undergoing a (1+1)-dimensional expansion. Namely, with the symmetry constraint of rotation and translation invariance in the transverse plane. It is very different from the (on-shell) free-streaming of classical particles. It is shown how to recognize the classical, ℏ→ 0, limit from the general form. The numerical analysis for a specific example shows very large quantum corrections to the classical free-streaming.