Bohmian quantum potential and chaos

A.C. Tzemos and G. Contopoulos

Chaos, Solitons & Fractals, 2022, vol. 160, issue C

Abstract: We study the quantum potential Q in a system of 2 degrees of freedom with emphasis on the regions where chaos is generated. Q goes to −∞ at the nodal points, where the wave function vanishes. But close to every nodal point, there is an unstable stagnant point in the frame of reference of the moving node, the X-point, which scatters the incoming trajectories and produces chaos. We first study the quantum potential of a wavefunction with a single nodal point, where we also give an analytical approximation of Q close to the node. Then we consider a wavefunction with infinitely many nodal points along a straight line and finally a system with a finite number of scattered nodal points in the configuration space. In all cases we find that the X-points are very close to the local maxima of Q. These maxima of Q form spikes at those times when the nodal points acquire large velocities, as they go to infinity in the inertial frame of reference (x,y).

Keywords: Bohmian Chaos; Quantum potential; Quantum harmonic oscillator; 2010 MSC (search for similar items in EconPapers)
Date: 2022
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Persistent link: https://EconPapers.repec.org/RePEc:eee:chsofr:v:160:y:2022:i:c:s0960077922003617

DOI: 10.1016/j.chaos.2022.112151

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