Sebastián Cuéllar | Searcharxiv

arXiv2021

Averaging Generalized Scalar Field Cosmologies II: Locally Rotationally Symmetric Bianchi I and flat Friedmann-Lemaître-Robertson-Walker models

Scalar field cosmologies with a generalized harmonic potential and a matter fluid with a barotropic Equation of State (EoS) with barotropic index $γ$ for the Locally Rotationally Symmetric (LRS) Bianchi I and flat Friedmann-Lemaître-Robertson-Walker (FLRW) metrics are investigated. Methods from the theory of averaging of nonlinear dynamical systems are used to prove that time-dependent systems and their corresponding time-averaged versions have the same late-time dynamics. Therefore, the simplest time-averaged system determines the future asymptotic behavior. Depending on the values of $γ$, the late-time attractors of physical interests are flat quintessence dominated FLRW universe and Einstein-de Sitter solution. With this approach, the oscillations entering the system through the Klein-Gordon (KG) equation can be controlled and smoothed out as the Hubble parameter $H$ - acting as time-dependent perturbation parameter - tends monotonically to zero. Numerical simulations are presented as evidence of such behavior.

gr-qc↗

arXiv2020

Constants of Motion of the Harmonic Oscillator

We prove that Weyl quantization preserves constant of motion of the Harmonic Oscillator. We also prove that if $f$ is a classical constant of motion and $\mathfrak{Op}(f)$ is the corresponding operator, then $\mathfrak{Op}(f)$ maps the Schwartz class into itself and it defines an essentially selfadjoint operator on $L^2(\mathbb R^n)$. As a consequence, we provide detailed spectral information of $\mathfrak{Op}(f)$. A complete characterization of the classical constants of motion of the Harmonic Oscillator is given and we also show that they form an algebra with the Moyal product. We give some interesting examples and we analyze Weinstein average method within our framework.

math-ph↗