Self Consistent Expansion for the Molecular Beam Epitaxy Equation
| dc.creator | Katzav, Eytan | |
| dc.date | 2001-07-06 | |
| dc.date | 2001-11-30 | |
| dc.date.accessioned | 2026-07-07T09:33:32Z | |
| dc.date.available | 2026-07-07T09:33:32Z | |
| dc.description | Motivated by a controversy over the correct results derived from the dynamic renormalization group (DRG) analysis of the non linear molecular beam epitaxy (MBE) equation, a self-consistent expansion (SCE) for the non linear MBE theory is considered. The scaling exponents are obtained for spatially correlated noise of the general form $D({\vec r - \vec r',t - t'}) = 2D_0 | {\vec r - \vec r'} |^{2ρ- d} δ({t - t'})$. I find a lower critical dimension $d_c (ρ) = 4 + 2ρ$, above, which the linear MBE solution appears. Below the lower critical dimension a r-dependent strong-coupling solution is found. These results help to resolve the controversy over the correct exponents that describe non linear MBE, using a reliable method that proved itself in the past by predicting reasonable results for the Kardar-Parisi-Zhang (KPZ) system, where DRG failed to do so. | |
| dc.description | 16 pages | |
| dc.identifier | https://arxiv.org/abs/cond-mat/0107153 | |
| dc.identifier | http://arxiv.org/abs/cond-mat/0107153 | |
| dc.identifier | Phys. Rev. E 65, 032103 (2002) | |
| dc.identifier | doi:10.1103/PhysRevE.65.032103 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/159163 | |
| dc.subject | Materials Science | |
| dc.subject | Statistical Mechanics | |
| dc.title | Self Consistent Expansion for the Molecular Beam Epitaxy Equation | |
| dc.type | text |