Exactly solvable stochastic spectator
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arXiv
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| Hauptverfasser: | , , |
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866909324421365760 |
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| author | Honda, Masazumi Jinno, Ryusuke Tokeshi, Koki |
| author_facet | Honda, Masazumi Jinno, Ryusuke Tokeshi, Koki |
| contents | The stochastic formalism of inflation allows us to describe the scalar-field dynamics in a non-perturbative way. The correspondence between the diffusion and Schrödinger equations makes it possible to exhaustively construct analytical solutions in stochastic inflation. Those exact statistical quantities such as distribution and correlation functions have one-to-one correspondence to the exactly solvable solutions in non-relativistic quantum mechanics in terms of classical orthogonal polynomials. A class of such solutions is presented by means of isospectral Hamiltonians with an underlying symmetry called shape invariance. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2409_16272 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Exactly solvable stochastic spectator Honda, Masazumi Jinno, Ryusuke Tokeshi, Koki Cosmology and Nongalactic Astrophysics General Relativity and Quantum Cosmology High Energy Physics - Theory Mathematical Physics Exactly Solvable and Integrable Systems The stochastic formalism of inflation allows us to describe the scalar-field dynamics in a non-perturbative way. The correspondence between the diffusion and Schrödinger equations makes it possible to exhaustively construct analytical solutions in stochastic inflation. Those exact statistical quantities such as distribution and correlation functions have one-to-one correspondence to the exactly solvable solutions in non-relativistic quantum mechanics in terms of classical orthogonal polynomials. A class of such solutions is presented by means of isospectral Hamiltonians with an underlying symmetry called shape invariance. |
| title | Exactly solvable stochastic spectator |
| topic | Cosmology and Nongalactic Astrophysics General Relativity and Quantum Cosmology High Energy Physics - Theory Mathematical Physics Exactly Solvable and Integrable Systems |
| url | https://arxiv.org/abs/2409.16272 |