arXiv subjects

Renato Vieira dos Santos

Publications and source records attributed to Renato Vieira dos Santos.

10 recordsLinked to original sources

arXiv2026

The Soul of Waves: Physical Interpretation of Dispersion Relations

This pedagogical paper presents a comprehensive framework for interpreting dispersion relations across fundamental physical systems. We adopt a novel approach that starts from the mathematical form $ω(\mathbf{k})$ and systematically extracts its physical content, rather than deriving it from first principles. Through an in-depth case study of the massive Klein-Gordon dispersion relation $ω^2 = ω_0^2 + c^2k^2$, we demonstrate how this single equation encodes phase velocity, group velocity, density of states, effective mass, and impedance. The analysis reveals the universal nature of this dispersion form, which manifests in quantum fields, plasmas, superconductors, and photonic crystals with different physical interpretations of its parameters. We complement this with detailed examination of classical systems including mass-spring chains and hydrodynamic waves, providing tangible analogies that bridge conceptual understanding between quantum and classical wave phenomena. The paper includes eleven carefully designed figures that visualize key concepts and a comprehensive catalog of dispersion relations in the Appendix. Aimed at advanced undergraduates and instructors, this work emphasizes conceptual understanding through physical interpretation, offering a unified pedagogical framework for teaching wave propagation across physics curricula while maintaining mathematical rigor and depth.

physics.class-ph↗

arXiv2026

Toward Charge-Dependent Tests of the Equivalence Principle: A Phenomenological Parameter and an Unexplored Frontier

We introduce and define the phenomenological parameter $κ$, defined by $Δa/g = κ\, Δ(q/m)$, to quantify potential linear coupling between electric charge and gravitational acceleration. A synthesis of existing precision equivalence principle experiments yields the first quantitative estimate of the effective sensitivity to this coupling: $|κ| < 2.1 \times 10^{-4}$ kg/C at 95\% confidence level. This constraint is approximately eleven orders of magnitude less stringent than corresponding bounds on composition-dependent violations, revealing that the electromagnetic axis remains a largely underexplored frontier in empirical gravity. We connect $κ$ to established frameworks -- the Standard-Model Extension and the $THεμ$ formalism -- showing that it occupies a region of parameter space untouched by existing high-precision tests. An effective field theory analysis shows that dimension-six operators that couple curvature directly to the electromagnetic field strength are suppressed by the minuscule terrestrial spacetime curvature ($G_N ρ_\oplus \sim 10^{-55}~\text{GeV}^2$) and are therefore phenomenologically irrelevant. Consequently, a future measurement of $κ$ at an accessible level would not probe minimal geometric couplings but would signal physics beyond minimal gravitational EFT, such as mediation by light scalar fields as in Einstein-Maxwell-Dilaton theory. We examine the Schiff-Barnhill effect, the primary systematic background for any such measurement, and show how it can be separated from a genuine signal. We outline the necessary experimental strategy, focused on maximizing charge-to-mass ratio differences, to transform this overlooked axis into a targeted probe for new physics.

hep-ph↗

arXiv2026

Fermi--Born--Infeld electrodynamics: a nonlinear theory with physical gauge

We construct a nonlinear extension of Fermi's electrodynamics by incorporating a Born--Infeld structure that depends directly on the four-potential $A_μ$ rather than on the field strength $F_{μν}$. The resulting theory, which we call Fermi--Born--Infeld (FBI) electrodynamics, eliminates the $U(1)$ gauge redundancy by elevating the Lorenz gauge to a dynamical condition. The Lagrangian is built from the determinant of a metric-like tensor $g_{μν} = η_{μν} + 2κ\, \partial_{(μ} A_{ν)}$, ensuring that the canonical energy--momentum tensor and the spin density remain unique and free of gauge ambiguities. We derive the field equations, which reduce to $\partial_ν(\sqrt{-g}\, g^{μν}) = 0$, and show that the Lorenz condition $\partial_μA^μ= 0$ emerges dynamically from retarded boundary conditions and the requirement of a positive-energy spectrum. The nonlinearities modify the propagation of longitudinal modes; we argue, via a Vainshtein-like mechanism, that the nonlinear self-interactions may stabilize the longitudinal mode, opening the possibility of a stable massive scalar photon under extreme field conditions. We also compute the spin density from the Noether current and discuss its properties. The FBI theory preserves the physical gauge of Fermi's original formulation while incorporating the regularization features of Born--Infeld electrodynamics, making it a candidate for describing electromagnetic phenomena in strong-field regimes.

physics.class-ph↗

arXiv2026

Beyond the Lorenz Gauge: Probing a Stueckelberg Scalar in the Electric Aharonov-Bohm Effect

The electric Aharonov-Bohm effect -- a time-dependent scalar potential imparting a measurable phase shift on electrons in a region free of electromagnetic fields -- has never been experimentally tested in its original formulation with shielded, time-dependent potentials. This unexplored regime offers a rare opportunity: the Lorenz condition $\partial_μA^μ= 0$, a choice that eliminates a scalar degree of freedom from the electromagnetic potential, may not be the last word. If the Stueckelberg scalar $B = \partial_μA^μ$ survives as a physical field and couples to matter, it would produce a phase shift with a distinctive $1-\cos(ωT)$ signature -- orthogonal to the standard $\sin(ωT)$ and separable by a frequency sweep even if both contributions coexist. We propose a measurement protocol based on single-electron interferometry with picosecond time resolution, within reach of current technology. The experiment asks a question that has lingered since 1959: is the Lorenz gauge a matter of convenience, or a matter of principle?

quant-ph↗

arXiv2026

Does Gravity Care About Electric Charge? A Minimalist Model and Experimental Test

Does gravity care about electric charge? Precision tests of the weak equivalence principle achieve remarkable sensitivity but deliberately minimize electric charge on test masses, leaving this fundamental question experimentally open. We present a minimalist framework coupling electromagnetism to linearized gravity through conservation of a complex charge-mass current, predicting charge-dependent violations $Δa/g = κ(q/m)$. Remarkably, this prediction occupies unexplored experimental territory precisely because precision gravity tests avoid charge variation. We identify this as a significant gap and propose a modified torsion balance experiment where $q/m$ is treated as a controlled variable. Such an experiment could test whether gravitational acceleration depends on electric charge, probing physics in genuinely new parameter space. This work exemplifies how theoretical minimalism can reveal overlooked opportunities in fundamental physics.

gr-qc↗

arXiv2026

Engineering polarization: How contradictory stimulation systematically undermines political moderation

Political moderation, a key attractor in democratic systems, proves highly fragile under realistic information conditions. We develop a stochastic model of opinion dynamics to analyze how noise and differential susceptibility reshape the political spectrum. Extending Marvel et al.'s deterministic framework, we incorporate stochastic media influence $ζ(t)$ and neuropolitically-grounded sensitivity differences ($σ_y > σ_x$). Analysis reveals the moderate population -- stable in deterministic models -- undergoes catastrophic collapse under stochastic forcing. This occurs through an effective deradicalization asymmetry ($u_{B}^{\text{eff}} = u + σ_y^2/2 > u_{A}^{\text{eff}}$) that drives conservatives to extinction, eliminating cross-cutting interactions that sustain moderates. The system exhibits a phase transition from multi-stable coexistence to liberal dominance, demonstrating how information flow architecture -- independent of content -- systematically dismantles the political center. Our findings reveal moderation as an emergent property highly vulnerable to stochastic perturbations in complex social systems.

physics.soc-ph↗

arXiv2017

Cosmology from a Lagrangian formulation for Rastall's theory

We give a Lagrangian formulation for the theory of Rastall of gravitation. After proposing a Lagrangian density that reproduces the equations of motion postulated by Rastall, we study the cosmological consequences and fit the parameters using recent data from Hubble function $H(z).$ According to two model selection criteria, one based on corrected Akaike Information Criterion (AICc) and another on Bayesian Information Criterion (BIC), known to penalize models with a greater number of parameters, particularly BIC, we obtain some competitive models relative do $ΛCDM.$ In one of these models the cosmological constant is interpreted as having origin in the creation of matter due to time dependent gravitational field, as opposed to the origin in the vacuum energy.

gr-qc↗

arXiv2016

Fractal Dimension and Universality in Avascular Tumor Growth

The comprehension of tumor growth is a intriguing subject for scientists. New researches has been constantly required to better understand the complexity of this phenomenon. In this paper, we pursue a physical description that account for some experimental facts involving avascular tumor growth. We have proposed an explanation of some phenomenological (macroscopic) aspects of tumor, as the spatial form and the way it growths, from a individual-level (microscopic) formulation. The model proposed here is based on a simple principle: competitive interaction between the cells dependent on their mutual distances. As a result, we reproduce many empirical evidences observed in real tumors, as exponential growth in their early stages followed by a power law growth. The model also reproduces the fractal space distribution of tumor cells and the universal behavior presented in animals and tumor growth, conform reported by West, Guiot {\it et. al.}\cite{West2001,Guiot2003}. The results suggest that the universal similarity between tumor and animal growth comes from the fact that both are described by the same growth equation - the Bertalanffy-Richards model - even they does not necessarily share the same biophysical properties.

physics.bio-ph↗

arXiv2013

The importance of being discrete in sex

The puzzle associated with the cost of sex, an old problem of evolutionary biology, is discussed here from the point of view of nonequilibrium statistical mechanics. The results suggest, in a simplified model, that the prevalence of sexual species in nature can be a natural and necessary consequence of the discrete character of the nonlinear interactions between couples and their pathogens/parasites. Mapped into a field theory, the stochastic processes performed by the species are described by continuous fields in space and time. The way that the model's parameters scale with subsequent iterations of the renormalization group gives us information about the stationary emergent properties of the complex interacting systems modeled. We see that the combination of one aspect of the Red Queen theory with the stochastic processes theory, including spatiotemporal interactions, provides interesting insights into this old Darwinian dilemma.

q-bio.PE↗

arXiv2013

Survival of the Scarcer in Space

The dynamics leading to extinction or coexistence of competing species is of great interest in ecology and related fields. Recently a model of intra- and interspecific competition between two species was proposed by Gabel et al. [Phys. Rev. E 87 (2013) 010101], in which the scarcer species (i.e., with smaller stationary population size) can be more resistant to extinction when it holds a competitive advantage; the latter study considered populations without spatial variation. Here we verify this phenomenon in populations distributed in space. We extend the model of Gabel et al. to a d-dimensional lattice, and study its population dynamics both analytically and numerically. Survival of the scarcer in space is verified for situations in which the more competitive species is closer to the threshold for extinction than is the less competitive species, when considered in isolation. The conditions for survival of the scarcer species, as obtained applying renormalization group analysis and Monte Carlo simulation, differ in detail from those found in the spatially homogeneous case. Simulations highlight the speed of invasion waves in determining the survival times of the competing species.

q-bio.PE↗