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Bruno G da Costa1, Ignacio S Gomez2, Ernesto P Borges2

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This study identifies overlooked issues in a recent comment, limiting its conclusions about the Langevin equation for inhomogeneous media with position-dependent mass. These findings impact the validity of specific equations used in physics research.

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Area of Science:

  • Statistical Physics
  • Theoretical Physics
  • Mathematical Physics

Background:

  • The Langevin equation is a fundamental tool for modeling systems with fluctuating forces.
  • Investigating the behavior of the Langevin equation in media with position-dependent mass is crucial for understanding complex physical phenomena.
  • A recent comment discussed the validity of the Langevin equation for such systems, proposing specific conclusions.

Purpose of the Study:

  • To critically analyze the "Comment on 'Deformed Fokker-Planck equation: Inhomogeneous medium with a position-dependent mass'" by da Costa et al.
  • To identify crucial overlooked observations within the aforementioned comment.
  • To assess the impact of these overlooked observations on the comment's conclusions regarding the Langevin equation for position-dependent mass.

Main Methods:

  • Detailed examination of the theoretical arguments presented in the comment.
  • Identification of logical gaps and unaddressed physical considerations.
  • Comparison of the comment's claims with established principles of statistical mechanics and Fokker-Planck equations.

Main Results:

  • Three significant observations within the comment were found to be overlooked.
  • These overlooked observations directly challenge the restrictive conclusions drawn by the comment.
  • The legitimacy of the Langevin equation (Eq. 46) for a position-dependent mass, as concluded in the comment, is restricted.

Conclusions:

  • The comment's assessment of the Langevin equation's validity for position-dependent mass is incomplete due to the identified oversights.
  • Further theoretical work is needed to fully establish the applicability and limitations of the Langevin equation in inhomogeneous media with position-dependent mass.
  • The findings necessitate a re-evaluation of the conclusions presented in da Costa et al.'s comment.