Evolution of quantum non-equilibrium for coupled harmonic oscillators

Abstract

In the context of de Broglie–Bohm pilot-wave theory, violations of the Born rule are allowed and can be considered as describing non-equilibrium distributions. We study the effects of interactions on quantum relaxation towards equilibrium for a system of one-dimensional coupled harmonic oscillators. We show by numerical simulations that interactions can delay or even prevent complete relaxation for some initial states. We also discuss how this effect might be relevant for cosmological scenarios and how non-equilibrium could be detected in some models.

Chaos and ergodicity in a partially integrable 3d Bohmian system: a comparison with 2d systems

“…The existence of ergodicity led us to interesting results [15] on the establishment of Born's Rule (BR), which states that the probability density of finding a particle in a certain region of space is given by P(x, t) = |Ψ(x, t)| 2 (for the origin of BR in BQM see [18][19][20][21][22][23][24][25][26][27]). If BR is initially satisfied (P 0 = |Ψ 0 | 2 ) then it remains valid at all times.…”

Critical points and trajectories of the Bohmian quantum flow

“…Since BQM is a trajectory based quantum theory, the role of order and chaos is crucial for all of its aspects. However, an important part of the theory where the nature of the Bohmian trajectories plays a major role is the origin of Born's rule (BR) (see for example [31,32,33,34,35,36,37]), according to which the probability density of finding a particle in a certain region of space is 𝑃 = |Ψ| 2 . In contrast to standard QM, Born's rule is not taken as an axiom in BQM and one can, in principle, start with a distribution of Bohmian particles with 𝑃 0 ̸ = |Ψ| 2 .…”

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

“…On the other hand, if P 0 = |Ψ 0 | 2 , then as t → ∞, the distribution P tends, in general, to satisfy Born's rule. The origin of BR in BQM has been studied by many authors in the past [39][40][41][42][43][44][45].…”