Analysis of the Fokker-Planck Equation in Schwarzschild Spacetime: A Supersymmetric Connection
Fuente:
arXiv
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Preprint |
| Published: |
2025
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866908394357522432 |
|---|---|
| author | Sharma, Ojaswini Shukla, Aradhya |
| author_facet | Sharma, Ojaswini Shukla, Aradhya |
| contents | We have re-analyzed the dynamics of the thermal potential within Schwarzschild spacetime by employing the Fokker-Planck equation. We demonstrate that the Fokker-Planck equation reduces to a simplified form equivalent to a scaled quantum mechanical problem with a harmonic oscillator potential. In this framework, we highlight an interesting correspondence between supersymmetric quantum mechanics (SUSY QM) and the Fokker-Planck dynamics associated with the Schwarzschild metric. Utilizing the isospectral deformation, an intrinsic feature of SUSY QM, we derive a family of one-parameter isospectral potentials. Notably, this new class of potentials exhibits the same energy spectrum as the original harmonic oscillator potential, but with distinct wavefunctions. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2506_04643 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Analysis of the Fokker-Planck Equation in Schwarzschild Spacetime: A Supersymmetric Connection Sharma, Ojaswini Shukla, Aradhya High Energy Physics - Theory Quantum Physics We have re-analyzed the dynamics of the thermal potential within Schwarzschild spacetime by employing the Fokker-Planck equation. We demonstrate that the Fokker-Planck equation reduces to a simplified form equivalent to a scaled quantum mechanical problem with a harmonic oscillator potential. In this framework, we highlight an interesting correspondence between supersymmetric quantum mechanics (SUSY QM) and the Fokker-Planck dynamics associated with the Schwarzschild metric. Utilizing the isospectral deformation, an intrinsic feature of SUSY QM, we derive a family of one-parameter isospectral potentials. Notably, this new class of potentials exhibits the same energy spectrum as the original harmonic oscillator potential, but with distinct wavefunctions. |
| title | Analysis of the Fokker-Planck Equation in Schwarzschild Spacetime: A Supersymmetric Connection |
| topic | High Energy Physics - Theory Quantum Physics |
| url | https://arxiv.org/abs/2506.04643 |