arXiv subjects
Publications and source records attributed to Manuel Martínez-Quesada.
Quantum billiards have been simulated so far in many ways, but in this work a new aproximation is considerated. This study is based on the quantum billiard already obtained by others authors via a tensor product of two 1-D quantum walks . Chaotic and non chaotic billiards are tested.
Quantum Rings have been simulated so far in many ways, but in this work a new aproximation is deemed. We use particles without angular momentum and several spectra, for different geometric settings, are gotten. These spectra depends on K, not on L. The application of a magnetic field is also analysed, and an Aharonov-Bohm kind of effect is observed. Some new math technique is introduced as well. We think that with this new approach the spectrum matrix can be treated in a distinct way, and in such a manner is how we get to handle the Moire pattern spectrum. Furthermore, we show that two electrons quantum walking by some kind of double concentric Quantum Rings and those very same electrons quantum walking by a Moire circunference could indeed have, if not for some parameters, the same spectrum. So they might somehow display similar behaviour and similar properties
We present and study a two-particle quantum walk on the line in which the two particles interact via a long-range Coulombian-like interaction. We obtain the spectrum of the system as well as study the type of molecules that form, attending to the bosonic or fermionic nature of the walkers. The usual loss of distinction between attractive and repulsive forces does not entirely apply in our model because of the long-range of the interaction.
We study pattern formation in a complex Swift Hohenberg equation with phase-sensitive (parametric) gain. Such an equation serves as a universal order parameter equation describing the onset of spontaneous oscillations in extended systems submitted to a kind of forcing dubbed rocking when the instability is towards long wavelengths. Applications include two-level lasers and photorefractive oscillators. Under rocking, the original continuous phase symmetry of the system is replaced by a discrete one, so that phase bistability emerges. This leads to the spontaneous formation of phase-locked spatial structures like phase domains and dark-ring (phase-) cavity solitons. Stability of the homogeneous solutions is studied and numerical simulations are made covering all the dynamical regimes of the model, which turn out to be very rich. Formal derivations of the rocked complex Swift-Hohenberg equation, using multiple scale techniques, are given for the two-level laser and the photorefractive oscillator.