2024/09/24 by Masazumi Honda, Honda, Masazumi, Ryusuke Jinno +3 · 1 citation
Biochemistry, Genetics and Molecular Biology · Computer Science · #Cosmology and Nongalactic Astrophysics (astro-ph.CO) #Data Visualization and Analytics #Diffusion and Search Dynamics #Exactly Solvable and Integrable Systems (nlin.SI) #FOS: Physical sciences #General Relativity and Quantum Cosmology (gr-qc) #High Energy Physics - Theory (hep-th) #Mathematical Physics (math-ph) #Music Technology and Sound Studies
paper · pdf · doi:10.48550/arxiv.2409.16272
openalex publication_date 2024/09/24 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.