Chaos and ergodicity in an entangled two-qubit Bohmian system
- URL: http://arxiv.org/abs/2003.03989v1
- Date: Mon, 9 Mar 2020 09:26:27 GMT
- Title: Chaos and ergodicity in an entangled two-qubit Bohmian system
- Authors: Athanasios C. Tzemos, George Contopoulos
- Abstract summary: We study in detail the onset of chaos and the probability measures formed by individual Bohmian trajectories in entangled states of two-qubit systems.
In weakly entangled states chaos is manifested through the sudden jumps of the Bohmian trajectories between successive Lissajous-like figures.
In strongly entangled states, the chaotic form of the Bohmian trajectories is manifested after a short time.
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- License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
- Abstract: We study in detail the onset of chaos and the probability measures formed by
individual Bohmian trajectories in entangled states of two-qubit systems for
various degrees of entanglement. The qubit systems consist of coherent states
of 1-d harmonic oscillators with irrational frequencies. In weakly entangled
states chaos is manifested through the sudden jumps of the Bohmian trajectories
between successive Lissajous-like figures. These jumps are succesfully
interpreted by the `nodal point-X-point complex' mechanism. In strongly
entangled states, the chaotic form of the Bohmian trajectories is manifested
after a short time. We then study the mixing properties of ensembles of Bohmian
trajectories with initial conditions satisfying Born's rule. The trajectory
points are initially distributed in two sets $S_1$ and $S_2$ with disjoint
supports but they exhibit, over the course of time, abrupt mixing whenever they
encounter the nodal points of the wavefunction. Then a substantial fraction of
trajectory points is exchanged between $S_1$ and $S_2$, without violating
Born's rule. Finally, we provide strong numerical indications that, in this
system, the main effect of the entanglement is the establishment of ergodicity
in the individual Bohmian trajectories as $t\to\infty$: different initial
conditions result to the same limiting distribution of trajectory points.
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