arXiv subjects

Raphael De Sousa

Publications and source records attributed to Raphael De Sousa.

2 recordsLinked to original sources

arXiv2026

From Analytic Structure to Quantum Complexity: Walsh-Pauli Representations of Continuum Operators

How does continuum operator structure appear in a finite qubit register? We address this question for analytic functions of diagonal operators represented in a binary basis, focusing on the Jordan--Lee--Preskill (JLP) momentum operator, by developing an operator-level generating-function framework for their Walsh-Pauli spectra. The construction determines the spectrum analytically and reveals exact support and parity selection rules, together with a nontrivial intra-shell hierarchy induced by the binary encoding. This provides a systematic characterization of Walsh compressibility and its relation to Pauli locality. As a controlled application, we consider generalized uncertainty-principle (GUP) kinematics as a tunable nonlinear odd deformation of momentum, showing how higher-order momentum terms redistribute spectral weight into progressively higher Pauli-weight sectors

quant-ph↗

arXiv2024

The energy-frequency diagram of the (1+1)-dimensional $Φ^4$ oscillon

Two different methods are used to study the existence and stability of the (1+1)-dimensional $Φ^4$ oscillon. The variational technique approximates it by a periodic function with a set of adiabatically changing parameters. An alternative approach treats oscillons as standing waves in a finite-size box; these are sought as solutions of a boundary-value problem on a two-dimensional domain. The numerical analysis reveals that the standing wave's energy-frequency diagram is fragmented into disjoint segments with $ω_{n+1} < ω< ω_{n}$, where $ω_n= ω_0/ (n+1)$, $n=0,1,2, ...$, and $ω_0$ is the endpoint of the continuous spectrum (mass threshold of the model). The variational approximation involving the first, zeroth and second harmonic components provides an accurate description of the oscillon with the frequency in $(ω_1, ω_0)$, but breaks down as $ω$ falls out of that interval.

hep-th↗