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Chaotic Zeeman effect: a fractional diffusion-like approch.

Octavian Postavaru1, Mariana M Stanescu2

  • 1Center for Research and Training in Innovative Techniques of Applied Mathematics in Engineering, University Politehnica of Bucharest, Splaiul Independentei 313, Bucharest, 060042, Romania. opostavaru@linuxmail.org.

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Summary
This summary is machine-generated.

Fractional calculus offers a new perspective on the chaotic Zeeman effect in quantum systems. This approach introduces a physical angle, linking fractional calculus to chaos and random matrix theory.

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Area of Science:

  • Quantum mechanics
  • Fractional calculus
  • Chaos theory

Background:

  • The chaotic Zeeman effect describes the complex behavior of quantum systems in magnetic fields.
  • Existing models do not fully capture the nuances of this chaotic behavior.

Purpose of the Study:

  • To explore the connection between fractional calculus and the chaotic Zeeman effect.
  • To provide a physical interpretation for the chaotic behavior using fractional calculus.

Main Methods:

  • Formalizing the chaotic Zeeman effect using fractional calculus.
  • Introducing the angle between internal and external magnetic fields into the equations.
  • Connecting fractional formalism with random matrix theory via Lorentzian distributions.

Main Results:

  • Fractional calculus formally describes the chaotic Zeeman effect.
  • The deviation of the fractional coefficient from ordinary values quantifies the chaotic effect.
  • A physical interpretation of chaos is established through the magnetic field angle.

Conclusions:

  • Fractional calculus provides a robust framework for understanding the chaotic Zeeman effect.
  • The introduced angle offers a physical interpretation, bridging theory and observation.
  • This work validates the link between fractional calculus, chaos, and random matrix theory.