Motion of vortices implies chaos in Bohmian mechanics

Bohmian mechanics is a causal interpretation of quantum mechanics in which particles describe trajectories guided by the wave function. The dynamics in the vicinity of nodes of the wave function, usually called vortices, is regular if they are at rest. However, vortices generically move during time evolution of the system. We show that this movement is the origin of chaotic behavior of quantum trajectories. As an example, our general result is illustrated numerically in the two-dimensional isotropic harmonic oscillator.Comment: 7 pages 5 figure

Robust transitivity and domination for endomorphisms displaying critical points

We show that robustly transitive endomorphisms of a closed manifolds must have a non-trivial dominated splitting or be a local diffeomorphism. This allows to get some topological obstructions for the existence of robustly transitive endomorphisms. To obtain the result we must understand the structure of the kernel of the differential and the recurrence to the critical set of the endomorphism after perturbation.Comment: We rewrote Lemmas 2.7 and 4.7 in order to be clearer. we also would like to thanks the referee for their suggestion and comment

Vortex interaction, chaos and quantum probabilities

The motion of a single vortex is able to originate chaos in the quantum trajectories defined in Bohm's interpretation of quantum mechanics. In this Letter, we show that this is also the case in the general situation, in which many interacting vortices exist. This result gives support to recent attempts in which Born's probability rule is derived in terms of an irreversible time evolution to equilibrium, rather than being postulated.Comment: 4 pages, 4 figure

Vortices and chaos in the quantum fluid

The motion of a single vortex originates chaos in the quantum fluid defined in Bohm\u27s interpretation of quantum mechanics. Here we analize this situation in a very simple case: one single vortex in a rectangular billiard

Bifurcations of periodic and chaotic attractors in pinball billiards with focusing boundaries

We study the dynamics of billiard models with a modified collision rule: the outgoing angle from a collision is a uniform contraction, by a factor lambda, of the incident angle. These pinball billiards interpolate between a one-dimensional map when lambda=0 and the classical Hamiltonian case of elastic collisions when lambda=1. For all lambda<1, the dynamics is dissipative, and thus gives rise to attractors, which may be periodic or chaotic. Motivated by recent rigorous results of Markarian, Pujals and Sambarino, we numerically investigate and characterise the bifurcations of the resulting attractors as the contraction parameter is varied. Some billiards exhibit only periodic attractors, some only chaotic attractors, and others have coexistence of the two types.Comment: 30 pages, 17 figures. v2: Minor changes after referee comments. Version with some higher-quality figures available at http://sistemas.fciencias.unam.mx/~dsanders/publications.htm

The ESCRT-III machinery participates in the production of extracellular vesicles and protein export during Plasmodium falciparum infection

Malaria is a disease caused by Plasmodium parasites that is still a leading cause of death in many low-income countries, and for which currently available therapeutic strategies are not succeeding in its control, let alone eradication. An interesting feature observed after Plasmodium invasion is the increase of extracellular vesicles (EVs) generated by parasitized red blood cells (pRBCs), which lack a vesicular trafficking that would explain EV production. Here, by combining different approaches, we demonstrated the participation of the endosomal sorting complex required for transport (ESCRT) machinery from Plasmodium falciparum in the production of EVs in pRBCs. Moreover, we were able to detect ESCRT-III proteins adjacent to the membrane of the host and in EVs purified from a pRBC culture, which shows the export of these proteins and their participation in EV production. Finally, the disruption of an ESCRT-III associated gene, Pfvps60, led to a significant reduction in the amount of EVs. Altogether, these results confirm ESCRT-III participation in EV production and provide novel information on the P. falciparum protein export mechanisms, which can be used for the development of new therapeutic strategies against malaria, based on the disruption of EV formation and trafficking