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Circular Kardar-Parisi-Zhang interfaces evolving out of the plane.
Carrasco, I S S; Oliveira, T J.
Afiliação
  • Carrasco ISS; Departamento de Física, Universidade Federal de Viçosa, 36570-900, Viçosa, Minas Gerais, Brazil.
  • Oliveira TJ; Instituto de Física, Universidade Federal Fluminense, 24210-340, Niterói, Rio de Janeiro, Brazil.
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 〈L(t)〉=L_{0}+ωt^{γ}, while their mean height 〈h〉 increases as usual [〈h〉∼t]. 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 w∼t^{ß}, for γ<1/z the HDs are Gaussian, in a correlated regime where w∼t^{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/c≫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 ω≫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.

Texto completo: 1 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

Texto completo: 1 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