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

Athanasios C Tzemos; George Contopoulos

doi:10.3390/e25071089

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

Entropy (Basel). 2023 Jul 20;25(7):1089. doi: 10.3390/e25071089.

Authors

Athanasios C Tzemos¹, George Contopoulos¹

Affiliation

¹ Research Center for Astronomy and Applied Mathematics of the Academy of Athens, Soranou Efessiou 4, GR-11527 Athens, Greece.

Abstract

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.

Keywords: Bohmian Quantum Mechanics; Born’s rule; chaos.

Grants and funding

This research received no external funding.