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Bohmian quantum potential and chaos

Author

Listed:
  • Tzemos, A.C.
  • Contopoulos, G.

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).

Suggested Citation

  • Tzemos, A.C. & Contopoulos, G., 2022. "Bohmian quantum potential and chaos," Chaos, Solitons & Fractals, Elsevier, vol. 160(C).
    • Handle: RePEc:eee:chsofr:v:160:y:2022:i:c:s0960077922003617
    DOI: 10.1016/j.chaos.2022.112151
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