Unstable Points, Ergodicity and Born's Rule in 2d Bohmian Systems.

We study the role of unstable points in the Bohmian flow of a 2d system composed of two non-interacting harmonic oscillators. In particular, we study the unstable points in the inertial frame of reference as well as in the frame of reference of the moving nodal points, in cases with 1, 2 and multiple nodal points. Then, we find the contributions of the ordered and chaotic trajectories in the Born distribution, and when the latter is accessible by an initial particle distribution which does not satisfy Born's rule.

Ergodicity and Born's rule in an entangled three-qubit Bohmian system.

We study in detail the interplay between chaos and entanglement in the Bohmian trajectories of three entangled qubits, made of coherent states of the quantum harmonic oscillator. We find that all the three-dimensional (3D) chaotic trajectories are ergodic; namely, they have a common long time distribution of points regardless of the initial conditions, and for any nonzero entanglement, their number is much larger than in the corresponding two-qubit system. Furthermore, the range of entanglements for which practically all the trajectories are chaotic and ergodic is much larger than in the two-qubit case.

Ergodicity and Born's rule in an entangled two-qubit Bohmian system.

We study the Bohmian trajectories of a generic entangled two-qubit system, composed of coherent states of two harmonic oscillators with noncommensurable frequencies and focus on the relation between ergodicity and the dynamical approach to Born's rule for arbitrary distributions of initial conditions. We find that most Bohmian trajectories are ergodic and establish the same invariant ergodic limiting distributions of their points for any nonzero amount of entanglement. In the case of strong entanglement the distribution satisfying Born's rule is dominated by chaotic-ergodic trajectories.

Characteristic times in the standard map.

We study and compare three characteristic times of the standard map: the Lyapunov time t_{L}, the Poincaré recurrence time t_{r}, and the stickiness (or escape) time t_{st}. The Lyapunov time is the inverse of the Lyapunov characteristic number (L) and in general is quite small. We find empirical relations for the L as a function of the nonlinearity parameter K and of the chaotic area A.

Origin of chaos near three-dimensional quantum vortices: A general Bohmian theory.

We provide a general theory for the structure of the quantum flow near three-dimensional (3D) nodal lines, i.e., one-dimensional loci where the 3D wave function becomes equal to zero.

Global and local diffusion in the standard map.

We study the global and the local transport and diffusion in the case of the standard map, by calculating the diffusion exponent μ. In the global case, we find that the mean diffusion exponent for the whole phase space is either μ=1, denoting normal diffusion, or μ=2 denoting anomalous diffusion (and ballistic motion). The mean diffusion of the whole phase space is normal when no accelerator mode exists and it is anomalous (ballistic) when accelerator mode islands exist even if their area is tiny in the phase space.

How to observe a non-Kerr spacetime using gravitational waves.

We present a generic criterion which can be used in gravitational-wave data analysis to distinguish an extreme-mass-ratio inspiral into a Kerr background spacetime from one into a non-Kerr spacetime. We exploit the fact that when an integrable system, such as the system that describes geodesic orbits in a Kerr spacetime, is perturbed, the tori in phase space which initially corresponded to resonances disintegrate so as to form Birkhoff chains on a surface of section. The KAM curves of the islands in such a chain share the same ratio of frequencies, even though the frequencies themselves vary from one KAM curve to another inside an island.