A Bohmian approach to quantum fractals

Abstract

A quantum fractal is a wavefunction with a real and an imaginary part continuous everywhere, but differentiable nowhere. This lack of differentiability has been used as an argument to deny the general validity of Bohmian mechanics (and other trajectory--based approaches) in providing a complete interpretation of quantum mechanics. Here, this assertion is overcome by means of a formal extension of Bohmian mechanics based on a limiting approach. Within this novel formulation, the particle dynamics is always satisfactorily described by a well defined equation of motion. In particular, in the case of guidance under quantum fractals, the corresponding trajectories will also be fractal.

19 pages, 3 figures (revised version)

References in corpus (3)

• Quantum Equilibrium and the Origin of Absolute Uncertainty
• Incompleteness of trajectory-based interpretations of quantum mechanics
• Fractal Noise in Quantum Ballistic and Diffusive Lattice Systems

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• Boundary bound diffraction: A combined spectral and Bohmian analysis
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• Laser agitates probability flow in atoms to form alternating current and its peak-dip phenomenon
• Quantum Interference, Hidden Symmetries: Theory and Experimental Facts