Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Chaos in Bohmian Quantum Mechanics: A short review   This is a short review in the theory of chaos in Bohmian Quantum Mechanics
based on our series of works in this field. Our first result is the development
of a generic theoretical mechanism responsible for the generation of chaos in
an arbitrary Bohmian system (in 2 and 3 dimensions). This mechanism allows us
to explore the effect of chaos on Bohmian trajectories and study in detail
(both analytically and numerically) the different kinds of Bohmian trajectories
where, in general, chaos and order coexist. Finally we explore the effect of
quantum entanglement on the evolution of the Bohmian trajectories and study
chaos and ergodicity in qubit systems which are of great theoretical and
practical interest. We find that the chaotic trajectories are also ergodic,
i.e. they give the same final distribution of their points after a long time
regardless of their initial conditions. In the case of strong entanglement most
trajectories are chaotic and ergodic and an arbitrary initial distribution of
particles will tends to Born's rule over the course of time. On the other hand,
in the case of weak entanglement the distribution of Born's rule is dominated
by ordered trajectories and consequently an arbitrary initial configuration of
particles will not tend, in general, to Born's rule, unless it is initially
satisfied. Our results shed light on a fundamental problem in Bohmian
Mechanics, namely whether there is a dynamical approximation of Born's rule by
an arbitrary initial distribution of Bohmian particles.

23
The categories of this paper are: solv-int
8
The categories of this paper are: hep-ex
16
The categories of this paper are: stat
2
The categories of this paper are: math
1
The categories of this paper are: cs
31
The categories of this paper are: ao-sci
36
The categories of this paper are: cmp-lg
28
The categories of this paper are: alg-geom
10
The categories of this paper are: q-bio
37
The categories of this paper are: supr-con
35
The categories of this paper are: mtrl-th
14
The categories of this paper are: math-ph
20
The categories of this paper are: acc-phys
6
The categories of this paper are: astro-ph
24
The categories of this paper are: dg-ga
26
The categories of this paper are: bayes-an