arXiv subjects

Emerson Sadurní

Publications and source records attributed to Emerson Sadurní.

6 recordsLinked to original sources

arXiv2020

Hidden duality and accidental degeneracy in cycloacene and Möbius cycloacene

The accidental degeneracy appearing in cycloacenes as triplets and quadruplets is explained with the concept of segmentation, introduced here with the aim of describing the effective disconnection of $π$ orbitals on these organic compounds. For periodic systems with time reversal symmetry, the emergent nodal domains are shown to divide the atomic chains into simpler carbon structures analog to benzene rings, diallyl chains, anthracene (triacene) chains and tetramethyl-naphtalene skeletal forms. The common electronic levels of these segments are identified as members of degenerate multiplets of the global system. The peculiar degeneracy of Möbius cycloacene is also explained by segmentation. In the last part, it is shown that the multiplicity of energies for cycloacene can be foreseen by studying the continuous limit of the tight-binding model; the degeneracy conditions are put in terms of Chebyshev polynomials. The results obtained in this work have important consequences on the physics of electronic transport in organic wires, together with their artificial realizations.

physics.chem-ph↗

arXiv2014

Discrete symmetry in graphene: the Dirac equation and beyond

In this pedagogical paper we review the discrete symmetries of the Dirac equation using elementary tools, but in a comparative order: the usual 3 + 1 dimensional case and the 2 + 1 dimensional case. Motivated by new applications of the 2d Dirac equation in condensed matter, we further analyze the discrete symmetries of a full tight-binding model in hexagonal lattices without conical approximations. We touch upon an effective CPT symmetry breaking that occurs when deformations and second-neighbor corrections are considered.

cond-mat.other↗

arXiv2013

Canonical Transformations in Crystals

The space representations of linear canonical transformations were studied by Moshinsky and Quesne in 1972. For a few decades, the bilinear hamiltonian remained as the only exactly solvable representative for such problems. In this work we show that the Mello-Moshinsky equations can be solved exactly for a class of problems with discrete symmetry, leading to exact propagators for Wannier-Stark ladders in one and two dimensional crystals. We give a detailed study for a particle in a triangular lattice under the influence of a time-dependent electric field. A more general set of Mello-Moshinsky equations for arbitrary lattices is presented.

quant-ph↗

arXiv2013

Propagators in two-dimensional lattices

This paper is devoted to the computation of discrete propagators in two-dimensional crystals and their application to a number of time dependent problems. The methods to compute such kernels are provided by a tight-binding representation of Dirac matrices and the generalizations of Bessel functions. Diffusive effects of point-like distributions on crystalline sheets are studied in a second quantization scheme. In the last part, a compendium of propagators is presented. The cases of square, triangular and hexagonal arrays are covered.

quant-ph↗

arXiv2012

Exact propagators on the lattice with applications to diffractive effects

The propagator of the discrete Schrödinger equation is computed and its properties are revealed through a Feynman path summation in discrete space. Initial data problems such as diffraction in discrete space and continuous time are studied analytically by the application of the new propagator. In the second part of this paper, the analogy between time propagation and 2D scattering by 1D obstacles is explored. New results are given in the context of diffraction by edges within a periodic medium. A connection with tight-binding arrays and photonic crystals is indicated.

quant-ph↗

arXiv2005

Transient Phenomena in Quantum Bound States Subjected to a Sudden Perturbation

Transient phenomena in quantum mechanics have been of interest to one of the authors (MM) since long ago and, in this paper, we focus on the problem of a potential V_- which for negative times gives rise to bound states and is suddenly changed at t=0 to a potential V_+ which includes V_- plus a perturbed term. An example will be the deuteron (where the proton and neutron are assumed to interact through an oscillator potential) submitted to a sudden electrostatic field. The analysis for t>0 can be carried out with the help of appropriate Feynmann propagators and we arrive at the result that the separation between the nucleons has an amplitude that depends on the intensity of the electrostatic field, but its period continues to be related with the inverse of the frequency of the oscillator proposed for the interaction. A general approximate procedure for arbitrary problems of this type is also presented at the end.

quant-ph↗