Bohmian Trajectories in a Bistable Potential Well

TL;DR

This paper investigates the dynamics of a quantum particle in a bistable potential using Bohmian mechanics, demonstrating the possibility of chaotic trajectories in one-dimensional systems.

Contribution

It challenges the belief that Bohmian trajectories in 1D systems cannot be chaotic, showing that chaos can occur with suitable initial conditions.

Findings

Bohmian trajectories can be periodic, quasiperiodic, or chaotic.

Transitions between motion regimes are continuous.

Appropriate initial conditions induce complex dynamics.

Abstract

We analyze the dynamics of a quantum particle in a one-dimensional bistable potential within the framework of Bohm's quantum mechanics. We give arguments that evidence the fallacy of certain claims found in the literature dealing with the impossibility of chaotic behavior of Bohmian trajectories in one-dimensional systems. We find that an appropriate choice for the initial position and wave packet causes the particle to undergo periodic, quasiperiodic, or chaotic motion. The transitions between these regimes occur in a continuos fashion.