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| Format: | Preprint |
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2026
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| Online-Zugang: | https://arxiv.org/abs/2604.10663 |
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| _version_ | 1866910210719744000 |
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| author | Quevedo, David Santiago Abril-Bermúdez, Felipe Segundo Smith, Cristiane Morais |
| author_facet | Quevedo, David Santiago Abril-Bermúdez, Felipe Segundo Smith, Cristiane Morais |
| contents | Many complex systems are described by Langevin-type equations in which the noise exhibits long-range correlations and couples to the system in a state-dependent, multiplicative manner, leading to heterogeneous non-Markovian diffusion. Here, we investigate the problem of diffusion driven by fractional Gaussian noise with a general multiplicative coefficient from a path-integral perspective. Using a stationary-phase approximation, we derive a Gaussian propagator expressed in terms of the Lamperti transform of the process. In the additive limit, our results recover the path-integral representation of fractional Brownian motion based on its Riemann-Liouville formulation and establish its equivalence with the Langevin construction. We further analyze the effect of subordinating the process to a killing rate within the Feynman-Kac framework, and develop a general procedure to derive kinetic equations in terms of effective local Hamiltonians. We show that the interplay between multiplicative diffusion and confinement induces an effective drift term, leading to probability accumulation in regions of low noise amplitude. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_10663 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Confined kinetics and heterogeneous diffusion driven by fractional Gaussian noise: A path integral approach Quevedo, David Santiago Abril-Bermúdez, Felipe Segundo Smith, Cristiane Morais Statistical Mechanics Mathematical Physics Many complex systems are described by Langevin-type equations in which the noise exhibits long-range correlations and couples to the system in a state-dependent, multiplicative manner, leading to heterogeneous non-Markovian diffusion. Here, we investigate the problem of diffusion driven by fractional Gaussian noise with a general multiplicative coefficient from a path-integral perspective. Using a stationary-phase approximation, we derive a Gaussian propagator expressed in terms of the Lamperti transform of the process. In the additive limit, our results recover the path-integral representation of fractional Brownian motion based on its Riemann-Liouville formulation and establish its equivalence with the Langevin construction. We further analyze the effect of subordinating the process to a killing rate within the Feynman-Kac framework, and develop a general procedure to derive kinetic equations in terms of effective local Hamiltonians. We show that the interplay between multiplicative diffusion and confinement induces an effective drift term, leading to probability accumulation in regions of low noise amplitude. |
| title | Confined kinetics and heterogeneous diffusion driven by fractional Gaussian noise: A path integral approach |
| topic | Statistical Mechanics Mathematical Physics |
| url | https://arxiv.org/abs/2604.10663 |