Spectrum of the fokker-planck operator representing diffusion in a random velocity field
We study spectral properties of the Fokker-Planck operator that represents particles moving via a combination of diffusion and advection in a time-independent random velocity field, presenting in detail work outlined elsewhere [J. T. Chalker and Z. J. Wang, Phys. Rev. Lett. 79, 1797 (1997)]. We calc...
| Main Authors: | , |
|---|---|
| Format: | Journal article |
| Language: | English |
| Published: |
2000
|
| _version_ | 1826287436943065088 |
|---|---|
| author | Chalker, J Wang, Z |
| author_facet | Chalker, J Wang, Z |
| author_sort | Chalker, J |
| collection | OXFORD |
| description | We study spectral properties of the Fokker-Planck operator that represents particles moving via a combination of diffusion and advection in a time-independent random velocity field, presenting in detail work outlined elsewhere [J. T. Chalker and Z. J. Wang, Phys. Rev. Lett. 79, 1797 (1997)]. We calculate analytically the ensemble-averaged one-particle Green function and the eigenvalue density for this Fokker-Planck operator, using a diagrammatic expansion developed for resolvents of non-Hermitian random operators, together with a mean-field approximation (the self-consistent Born approximation) which is well controlled in the weak-disorder regime for dimension d>2. The eigenvalue density in the complex plane is nonzero within a wedge that encloses the negative real axis. Particle motion is diffusive at long times, but for short times we find a novel time dependence of the mean-square displacement, <r(2)> approximately t(2/d) in dimension d>2, associated with the imaginary parts of eigenvalues.</r(2)> |
| first_indexed | 2024-03-07T01:58:39Z |
| format | Journal article |
| id | oxford-uuid:9c9986cd-c9f3-411c-af79-70e9b6cbefde |
| institution | University of Oxford |
| language | English |
| last_indexed | 2024-03-07T01:58:39Z |
| publishDate | 2000 |
| record_format | dspace |
| spelling | oxford-uuid:9c9986cd-c9f3-411c-af79-70e9b6cbefde2022-03-27T00:37:08ZSpectrum of the fokker-planck operator representing diffusion in a random velocity fieldJournal articlehttp://purl.org/coar/resource_type/c_dcae04bcuuid:9c9986cd-c9f3-411c-af79-70e9b6cbefdeEnglishSymplectic Elements at Oxford2000Chalker, JWang, ZWe study spectral properties of the Fokker-Planck operator that represents particles moving via a combination of diffusion and advection in a time-independent random velocity field, presenting in detail work outlined elsewhere [J. T. Chalker and Z. J. Wang, Phys. Rev. Lett. 79, 1797 (1997)]. We calculate analytically the ensemble-averaged one-particle Green function and the eigenvalue density for this Fokker-Planck operator, using a diagrammatic expansion developed for resolvents of non-Hermitian random operators, together with a mean-field approximation (the self-consistent Born approximation) which is well controlled in the weak-disorder regime for dimension d>2. The eigenvalue density in the complex plane is nonzero within a wedge that encloses the negative real axis. Particle motion is diffusive at long times, but for short times we find a novel time dependence of the mean-square displacement, <r(2)> approximately t(2/d) in dimension d>2, associated with the imaginary parts of eigenvalues.</r(2)> |
| spellingShingle | Chalker, J Wang, Z Spectrum of the fokker-planck operator representing diffusion in a random velocity field |
| title | Spectrum of the fokker-planck operator representing diffusion in a random velocity field |
| title_full | Spectrum of the fokker-planck operator representing diffusion in a random velocity field |
| title_fullStr | Spectrum of the fokker-planck operator representing diffusion in a random velocity field |
| title_full_unstemmed | Spectrum of the fokker-planck operator representing diffusion in a random velocity field |
| title_short | Spectrum of the fokker-planck operator representing diffusion in a random velocity field |
| title_sort | spectrum of the fokker planck operator representing diffusion in a random velocity field |
| work_keys_str_mv | AT chalkerj spectrumofthefokkerplanckoperatorrepresentingdiffusioninarandomvelocityfield AT wangz spectrumofthefokkerplanckoperatorrepresentingdiffusioninarandomvelocityfield |