Riccati Equations as a Scale-Relativistic Gateway to Quantum Mechanics

Al-Rashid, Saeed Naif Turki; Habeeb, M A Z; LeBohec, Tugdual

doi:10.1007/s10701-020-00324-w

Found Phys

2020

DOI: 10.1007/s10701-020-00324-w

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Riccati Equations as a Scale-Relativistic Gateway to Quantum Mechanics

Saeed Naif Turki Al-Rashid

M A Z Habeeb

Tugdual LeBohec

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2024

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The virial theorem for nondifferentiable dynamical paths in resolution-scale relativity and possible implications

LeBohec

2024

Int. J. Mod. Phys. A

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The virial theorem is established in the framework of resolution-scale relativity for stochastic dynamics characterized by a diffusion constant [Formula: see text]. It only relies on a simple time average just like the classical virial theorem, while the quantum mechanical virial theorem involves the expectation values of the observables. Nevertheless, by the emergence of a quantum-like potential term, the resolution-scale relativity virial theorem also encompasses quantum mechanical dynamics under the identification [Formula: see text]. This provides an illustration of the resolution-scale relativistic approach to the foundation of standard quantum mechanics. Furthermore, it is pointed out that if the resolution-scale relativity principle is implemented in macroscopic systems that are complex and/or chaotic, then the application of the classical virial theorem in the analysis of the dynamics of astrophysical systems neglects the contribution from a resolution-scale relativistic quantum-like potential. It is shown that this quantum-like potential could account for some fraction of the dark matter hypothesis.

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The virial theorem for nondifferentiable dynamical paths in resolution-scale relativity and possible implications

LeBohec

2024

Int. J. Mod. Phys. A

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Riccati Equations as a Scale-Relativistic Gateway to Quantum Mechanics

Cited by 1 publication

References 15 publications

The virial theorem for nondifferentiable dynamical paths in resolution-scale relativity and possible implications

The virial theorem for nondifferentiable dynamical paths in resolution-scale relativity and possible implications

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