arXiv subjects

Matheus E. Pereira

Publications and source records attributed to Matheus E. Pereira.

3 recordsLinked to original sources

arXiv2026

Perturbative aspects of analogue FLRW spacetime Jellium models

We study electro-acoustic perturbative modes in homogeneous, isotropic and expanding -- dubbed as Friedmann-Lemaitre-Robertson-Walker (FLRW) -- Jellium models, thereby mimicking density perturbations in analogous Newtonian cosmological expansions. We present both novel analytic solutions for linear perturbations in specific analogue cosmological expansions and full numerical evaluations that characterize the temporal evolution of the electro-acoustic modes capturing their full dynamical behavior across the linear and the nonlinear regimes. For both the case of pressure supported evolution or modes sourced by nonadiabatic contributions, we also characterize the temporal evolution of such perturbations by introducing their scale dependent particle number fluctuation power spectrum which can act as a tool to connect theory and experiments. The dependence of the latter on the physical parameters of the model is demonstrated in detail.

gr-qc↗

arXiv2025

Schrödinger equation is $\mathcal{R}$-separable in toroidal coordinates

We present, for the first time, exact solutions for the Schrödinger equation in Moon and Spencer's toroidal coordinates, and in the electromagnetic toroidal--poloidal coordinate systems. Curiously, both systems present a fractional angular momentum, because of the torus's hole. We achieve these novel solutions using the irregular $\mathcal{R}$-separation of variables, an unexplored approach in Physics, which results in a wavefunction with fractional angular momentum eigenvalues. Numerous solutions for the Schrödinger equation in a variety of external potentials are shown, including an external magnetic field. A plane-wave expansion and a Green function are also presented, setting the stage for future progress in this area.

quant-ph↗

arXiv2024

Analogue black string in a quantum harmonic oscillator

For a scalar particle without self-interaction or backreaction from the space-time background, the dynamics are governed by the Klein-Gordon equation. In this work, we write the exact solution of this equation in the background of a chargeless, static black string in terms of the biconfluent Heun function. In this curious system, we are able to explore what happens if we have negative values for the masses. The eigenvalue problem provides complex energy values for the particle, which may indicate the presence of quasinormal modes. We show a simple quantum system that can imitate the particle in the black string background, whose solutions are also applications of the biconfluent Heun function.

hep-th↗