Conservation laws arising in the study of forward-forward Mean-Field Games

We consider forward-forward Mean Field Game (MFG) models that arise in numerical approximations of stationary MFGs. First, we establish a link between these models and a class of hyperbolic conservation laws as well as certain nonlinear wave equations. Second, we investigate existence and long-time behavior of solutions for such models

On spin-1 massive particles coupled to a Chern-Simons field

We study spin one particles interacting through a Chern-Simons field. In the Born approximation, we calculate the two body scattering amplitude considering three possible ways to introduce the interaction: (a) a Proca like model minimally coupled to a Chern-Simons field, (b) the model obtained from (a) by replacing the Proca's mass by a Chern-Simons term and (c) a complex Maxwell-Chern-Simons model minimally coupled to a Chern-Simons field. In the low energy regime the results show similarities with the Aharonov-Bohm scattering for spin 1/2 particles. We discuss the one loop renormalization program for the Proca's model. In spite of the bad ultraviolet behavior of the matter field propagator, we show that, up to one loop the model is power counting renormalizable thanks to the Ward identities satisfied by the interaction vertices.Comment: 14 pages, 5 figures, revte

A Lorentz-violating low-energy model for the bilayer Graphene

In this work, we propose a model with Lorentz symmetry violation which describes the electronic low energy limit of the AA-bilayer graphene (BLG) system. The AA-type bilayer is known to preserve the linear dispersion relation of the graphene layer in the low energy limit. The theoretical model shows that in the BLG system, a time-like vector can be associated with the layer separation and contributes to the energy eigenstates. Based on these properties, we can describe in a $(2+1)$-dimensional space-time the fermionic quasi-particles that emerge in the low-energy limit with the introduction of a Lorentz-violating parameter, in analogy with the $(3 + 1)$-dimensional Standard Model Extension (SME). Moreover, we study the consequences of the coupling of these fermionic quasi-particles with the electromagnetic field, and we show via effective action that the low-energy photon acquires a massive spectrum. Finally, using the hydrodynamic approach in the collisionless limit, one finds that the LSV generates a new kind of anomalous thermal current to the vortexes of the system via coupling of the LSV vector.Comment: 13 pages, 4 figures, published version in EPJ Plu

Crumpling a Thin Sheet

Crumpled sheets have a surprisingly large resistance to further compression. We have studied the crumpling of thin sheets of Mylar under different loading conditions. When placed under a fixed compressive force, the size of a crumpled material decreases logarithmically in time for periods up to three weeks. We also find hysteretic behavior when measuring the compression as a function of applied force. By using a pre-treating protocol, we control this hysteresis and find reproducible scaling behavior for the size of the crumpled material as a function of the applied force.Comment: revtex 4 pages, 6 eps figures submitted to Phys Rev. let

Tilted Dirac cone effects in superconducting phase transitions in planar four-fermion models

The chiral and superconducting gaps are studied in the context of a planar fermion model with four-fermion interactions. The effect of the tilt of the Dirac cone on both gaps is shown and discussed. The changes caused by the presence of a non-null chemical potential are also analyzed. Our results point to two different behaviors exhibited by planar fermionic systems. For values of the effective tilt parameter $|{\bf \tilde{t}}| < \tilde{t}^*$, where $\tilde{t}^* \approx 0.55$, the superconducting phase persists for negative values of the superconducting coupling constant. For positive values of the superconducting coupling constant, the induction of a superconducting gap by a chemical potential exists and which is similar as seen in graphene-like systems. For $|{\bf \tilde{t}}| > \tilde{t}^*$ and for a positive superconducting coupling constant, the superconducting phase can be present, but it is restricted to a smaller area in the phase portrait. Finally, our analysis shows that, in the case of positive values for the superconducting coupling constant, the induction of a superconducting gap in the presence of a chemical potential is ruled out and the increase of the chemical potential works in favor of the manifestation of a metallic phase.Comment: 11 pages, 8 figure

Effective models of quantum gravity induced by Planck scale modifications in the covariant quantum algebra

In this paper we introduce a modified covariant quantum algebra based in the so-called Quesne-Tkachuk algebra. By means of a deformation procedure we arrive at a class of higher derivative models of gravity. The study of the particle spectra of these models reveals an equivalence with the physical content of the well-known renormalizable and super-renormalizable higher derivative gravities. The particle spectrum exhibits the presence of spurious complex ghosts and, in light of this problem, we suggest an interesting interpretation in the context of minimal length theories. Also, a discussion regarding the non-relativistic potential energy is proposed.Comment: Small corrections were made; improved figures; results unchanged; published versio