arXiv subjects

A. G. Martins

Publications and source records attributed to A. G. Martins.

5 recordsLinked to original sources

arXiv2026

A Unified Description of Dirac-Cone Anisotropies in Two Dimensions

Anisotropies in two-dimensional materials are responsible for a variety of effects that significantly modify their physical properties. In this paper, we present a covariant modification of the Dirac equation that incorporates anisotropies into the effective low-energy description around the Dirac point. The model is constructed by analogy with a Lorentz-violating extension of the Standard Model of elementary particles and yields a (2+1)-dimensional framework describing physical effects such as shifted, tilted, and distorted Dirac cones through its free parameters. The proposed model thus provides a general and unified framework in which distinct anisotropy-induced modifications of the Dirac spectrum and their combinations can be systematically characterized. We further apply the model to strained graphene and show that its effective parameters can be quantitatively extracted from first-principles electronic band structures while retaining a direct geometrical interpretation. These results establish a connection between the microscopic electronic structure and a material-independent effective description of anisotropic two-dimensional Dirac systems.

cond-mat.mes-hall↗

arXiv2018

Energy nonconservation as a link between $f(R,T)$ gravity and noncommutative quantum theory

$f(R,T)$ gravity was proposed as an extension of the $f(R)$ theories, containing not just geometrical correction terms to the General Relativity equations, but also material correction terms, dependent on the trace of the energy-momentum tensor $T$. These material extra terms prevent the energy-momentum tensor of the theory to be conserved, even in a flat background. Energy nonconservation is a prediction of quantum theory with time-space noncommutativity. If time is considered as an operator and there are compact spatial coordinates which do not commute with time, then the time evolution gets quantized and energy conservation can be violated. In the present work we construct a model in a 5-dimensional flat spacetime consisting of 3 commutative spatial dimensions and 1 compact spatial dimension whose coordinate does not commute with time. We show that energy flows from the 3-dimensional commutative slice into the compact extra dimension (and vice-versa), so that conservation of energy is restored. In this model the energy flux is proportional to the energy density of the matter content, leading to a differential equation for $f(R,T)$, thus providing a physical criterion to restrict the functional form of $f(R,T)$. We solve this equation and analyze the behavior of its solution in a spherically symmetric context.

gr-qc↗

arXiv2011

Free-fall in a uniform gravitational field in non-commutative quantum mechanics

We study the free-fall of a quantum particle in the context of noncommutative quantum mechanics (NCQM). Assuming noncommutativity of the canonical type between the coordinates of a two-dimensional configuration space, we consider a neutral particle trapped in a gravitational well and exactly solve the energy eigenvalue problem. By resorting to experimental data from the GRANIT experiment, in which the first energy levels of freely falling quantum ultracold neutrons were determined, we impose an upper-bound on the noncommutativity parameter. We also investigate the time of flight of a quantum particle moving in a uniform gravitational field in NCQM. This is related to the weak equivalence principle. As we consider stationary, energy eigenstates, i.e., delocalized states, the time of flight must be measured by a quantum clock, suitably coupled to the particle. By considering the clock as a small perturbation, we solve the (stationary) scattering problem associated and show that the time of flight is equal to the classical result, when the measurement is made far from the turning point. This result is interpreted as an extension of the equivalence principle to the realm of NCQM.

hep-th↗

arXiv2007

Discrete Time Evolution and Energy Nonconservation in Noncommutative Physics

Time-space noncommutativity leads to quantisation of time and energy nonconservation when time is conjugate to a compact spatial direction like a circle. In this context energy is conserved only modulo some fixed unit. Such a possibility arises for example in theories with a compact extra dimension with which time does not commute. The above results suggest striking phenomenological consequences in extra dimensional theories and elsewhere. In this paper we develop scattering theory for discrete time translations. It enables the calculation of transition probabilities for energy nonconserving processes and has a central role both in formal theory and phenomenology. We can also consider space-space noncommutativity where one of the spatial directions is a circle. That leads to the quantisation of the remaining spatial direction and conservation of momentum in that direction only modulo some fixed unit, as a simple adaptation of the results in this paper shows.

hep-th↗

arXiv2005

Time-Space Noncommutativity: Quantised Evolutions

In previous work, we developed quantum physics on the Moyal plane with time-space noncommutativity, basing ourselves on the work of Doplicher et al.. Here we extend it to certain noncommutative versions of the cylinder, $\mathbb{R}^{3}$ and $\mathbb{R}\times S^{3}$. In all these models, only discrete time translations are possible, a result known before in the first two cases. One striking consequence of quantised time translations is that even though a time independent Hamiltonian is an observable, in scattering processes, it is conserved only modulo $\frac{2π}θ$, where $θ$ is the noncommutative parameter. (In contrast, on a one-dimensional periodic lattice of lattice spacing $a$ and length $L=Na$, only momentum mod $\frac{2π}{L}$ is observable (and can be conserved).) Suggestions for further study of this effect are made. Scattering theory is formulated and an approach to quantum field theory is outlined.

hep-th↗