Circular Kardar-Parisi-Zhang interfaces evolving out of the plane.
Phys Rev E
; 99(3-1): 032140, 2019 Mar.
Article
em En
| MEDLINE
| ID: mdl-30999413
Circular KPZ interfaces spreading radially in the plane have Gaussian unitary ensemble (GUE) Tracy-Widom (TW) height distribution (HD) and Airy_{2} spatial covariance, but what are their statistics if they evolve on the surface of a different background space, such as a bowl, a mountain, or any surface of revolution? To give an answer to this, we report here extensive numerical analyses of several one-dimensional KPZ models on substrates whose size enlarges as ãL(t)ã=L_{0}+ωt^{γ}, while their mean height ãhã increases as usual [ãhãâ¼t]. We show that the competition between the L enlargement and the correlation length (ξ≃ct^{1/z}) plays a key role in the asymptotic statistics of the interfaces. While systems with γ>1/z have HDs given by GUE and the interface width increasing as wâ¼t^{ß}, for γ<1/z the HDs are Gaussian, in a correlated regime where wâ¼t^{αγ}. For the special case γ=1/z, a continuous class of distributions exists, which interpolate between Gaussian (for small ω/c) and GUE (for ω/câ«1). Interestingly, the HD seems to agree with the Gaussian symplectic ensemble (GSE) TW distribution for ω/c≈10. Despite the GUE HDs for γ>1/z, the spatial covariances present a strong dependence on the parameters ω and γ, agreeing with Airy_{2} only for ωâ«1, for a given γ, or when γ=1, for a fixed ω. These results considerably generalize our knowledge on 1D KPZ systems, unveiling the importance of the background space on their statistics.
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Coleções:
01-internacional
Base de dados:
MEDLINE
Idioma:
En
Revista:
Phys Rev E
Ano de publicação:
2019
Tipo de documento:
Article
País de afiliação:
Brasil
País de publicação:
Estados Unidos