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R. Vilela Mendes

Publications and source records attributed to R. Vilela Mendes.

At least 19 recordsLinked to original sources
arXiv2026

A Kähler and quaternion-Kähler spacetime structure

When real Lorentzian spacetime is embedded into a manifold parametrized by higher division algebras (complex or quaternion with Hermitean metric) and the representation constraints of their symmetry groups are made compatible, a set of quantum numbers is generated that is evocative of those of the standard model of particle physics. This is taken here as a hint that in spacetime there is a pseudo-Kähler or pseudo-quaternion-Kähler structure, real spacetime being a submanifold that inherits the symmetry contraints of the larger ambient manifold.

physics.gen-ph↗
arXiv2025

Spinors and the quaternionic Poincaré group

When four dimensional spacetime R is considered as locally embedded on a larger manifold M, labelled by higher division algebra coordinates, a natural question to ask is how much of the symmetry properties of the larger space are inherited by R. Here this question is studied when M is a quaternion manifold. Of particular relevance is the absence of spinors in the linear representations of the symmetry group of the larger manifold and the emergence of new quantum numbers when, by Whitney sums, spinors are implemented on the vector bundles associated to the coset manifolds of the symmetry groups of M. A possible relation to the structures of the standard model is briefly discussed.

hep-th↗
arXiv2025

Sustainability, behavior patterns and crises

Sustainability has been defined as meeting the needs of the present without compromising the ability of future generations to meet their own needs. But what are the needs of the present? And are they met? From the poor performance of the 2030 Sustainable Development Goals (SDG), defined by the UN in 2015, not even the collective needs of the present seem to be met. How to expect not to compromise the needs of the future? Is the achievement of global world goals incompatible with the characteristic processes of human evolution, as some authors have recently suggested? Simple mathematical models cannot capture the whole breadth of human experience and destiny. But, on the other hand, one should not neglect whatever insights they may provide. And what these models teach us is how the behavior pattern "Parochial cooperation - Conflict - Growth" was reached and how this pattern, in addition to leading to several types of crises, is also on the way of the global governance needed to achieve the SDG's

q-bio.PE↗
arXiv2025

On three-body effects and nuclear fusion

Confined to small regions, quantum systems exhibit electronic and structural properties different from their free space behavior. In Coulomb 3-body problems, configurations of close proximity of identically charged particles are classically unstable. They however exist as excited quantum states in confined systems. Quantum control of such states might be useful to induce nuclear fusion. The difficult nature of the quantum control of these {\it % quantum collision states} is discussed here, as well as a possible solution using a two-step nonunitary evolution process.

quant-ph↗
arXiv2025

Complex hidden symmetries in real spacetime and their algebraic structures

Considering real spacetime as a Lorentzian fiber in a complex manifold, there is a mismatch of the elementary linear representations of their symmetry groups, the real and complex Poincaré groups. No spinors are allowed as linear irreducible representations for the complex case, but when a spin$^{h}$ structure is implemented on the associated principal bundles, one is naturally led to an algebraic structure similar to the one of the standard model. This last (dynamical) structure might therefore be inherited from the kinematical symmetries of a larger space.

hep-th↗
arXiv2024

A hidden symmetry of complex spacetime and the emergence of the standard model algebraic structure

When spacetime is considered as a subspace of a wider complex spacetime manifold, there is a mismatch of the elementary linear representations of their symmetry groups, the real and complex Poincaré groups. In particular, no spinors are allowed for the complex case. When a spin$^{h}$ structure is implemented on principal bundles in complex spacetime, one is naturally led to an algebraic structure analogous to the one of the standard model.

hep-th↗
arXiv2024

Brownian and fractional polymers with self-repulsion

Brownian and fractional processes are useful computational tools for the modelling of physical phenomena. Here, modelling linear homopolymers in solution as Brownian or fractional processes, we develop a formalism to take into account both the interactions of the polymer with the solvent as well as the effect of arbitrary polymer-polymer potentials and Gibbs factors. As an example the average squared length is computed for a non-trivial Gaussian Gibbs factor, which is also compared with the Edwards' and a step factor.

cond-mat.soft↗
arXiv2023

T violation and the dark sector

It is argued, as a working hypothesis, that "normal" and dark matter interactions can only be T and CP violating. One way to implement this idea is to consider that time reversal in dark matter is implemented, not by an antiunitary operator, but by a unitary operator. It is shown how this occurs naturally in the context of complex spacetime with an extended symmetry group.

hep-ph↗
arXiv2022

The fractional volatility model and rough volatility

The question of the volatility roughness is interpreted in the framework of a data-reconstructed fractional volatility model, where volatility is driven by fractional noise. Some examples are worked out and also, using Malliavin calculus for fractional processes, an option pricing equation and its solution are obtained.

q-fin.GN↗
arXiv2022

On a family of Levy processes without support in S'

The distributional support of the sample paths of Lévy processes is an important issue for the construction of sparse statistical models, theories of integration in infinite dimensions and the existence of generalized solutions of stochastic partial differential equations driven by Lévy white noise. Here one considers a family K_α(0<α<2) of Lévy processes which have no support in S'. For 1<α<2 they are supported in K', the space of distributions of exponential type and for 0<α=<1 on similar spaces of power exponential type.

math.PR↗
arXiv2022

Long-range connections, real-world networks and rates of diffusion

Long range connections play an essential role in dynamical processes on networks, on the processing of information in biological networks, on the structure of social and economical networks and in the propagation of opinions and epidemics. Here we review the evidence for long range connections in real world networks and discuss the nature of the nonlocal diffusion arising from different distance-dependent laws. Particular attention is devoted to exponential and power laws.

nlin.AO↗
arXiv2022

Nonabelian lattice theories: Consistent measures and strata

The role of consistent measures in the rigorous construction of nonabelian lattice theories is analized. General conditions that measures must fulfill to insure consistency, positivity and a mass gap are obtained. The impact of nongeneric strata on the nature of the Hamiltonian lattice potential is also discussed.

hep-lat↗
arXiv2021

A stable semi-implicit algorithm

When the singular values of the evolution operator are all smaller or all greater than one, stable integration algorithms are obtained either by explicit or implicit methods. When the singular spectrum mixes greater and smaller than one values, neither explicit nor implicit methods insure stabilty. The problem is solved by using a splitting of the evolution operator and a semi-implicit scheme. The method is illustrated in the study of a two-field model of the tokamak scrape-off layer.

physics.plasm-ph↗
arXiv2021

Modular quantum computing and quantum-like devices

The two essential ideas in this paper are, on the one hand, that a considerable amount of the power of quantum computation may be obtained by adding to a classical computer a few specialized quantum modules and, on the other hand, that such modules may be constructed out of classical systems obeying quantum-like equations where a space coordinate is the evolution parameter (thus playing the role of time in the quantum algorithms).

quant-ph↗
arXiv2020

Long-range connections and mixed diffusion in fractional networks

Networks with long-range connections obeying a distance-dependent power law of sufficiently small exponent display superdiffusion, Lévy flights and robustness properties very different from the scale-free networks. It has been proposed that these networks, found both in society and biology, be classified as a new structure, the fractional networks. Particular important examples are the social networks and the modular hierarchical brain networks where both short- and long-range connections are present. The anomalous superdiffusive and the mixed diffusion behavior of these networks is studied here as well as its relation to the nature and density of the long-range connections.

nlin.AO↗
arXiv2020

Characterizing correlations and synchronization in collective dynamics

Synchronization, that occurs both for non-chaotic and chaotic systems, is a striking phenomenon with many practical implications in natural phenomena. However, even before synchronization, strong correlations occur in the collective dynamics of complex systems. To characterize their nature is essential for the understanding of phenomena in physical and social sciences. The emergence of strong correlations before synchronization is illustrated in a few piecewise linear models. They are shown to be associated to the behavior of ergodic parameters which may be exactly computed in some models. The models are also used as a testing ground to find general methods to characterize and parametrize the correlated nature of collective dynamics.

nlin.AO↗