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Carvalho, Túlio Oliveira de; Oliveira, César R. de

doi:10.1023/a:1015153523475

Journal of Statistical Physics

2002

DOI: 10.1023/a:1015153523475

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Túlio Oliveira de Carvalho

César R. de Oliveira

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Cited by 4 publications

(1 citation statement)

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“…The mixing together of two periodic media or an interface problem involving two different periodic media on the two sides of the interface [11] may be thought of as an almost periodic microstructure. Finally, dimers and polymers have also been modeled with almost periodic potentials [15]. Although almost periodic media is completely deterministic, it serves as a bridge to stochastic descriptions of nature.…”

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confidence: 99%

Bloch wave approach to almost periodic homogenization and approximations of effective coefficients

Sista¹,

Tewary²

2022

DCDS-B

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Bloch wave homogenization is a spectral method for obtaining effective coefficients for periodically heterogeneous media. This method hinges on the direct integral decomposition of periodic operators, which is not available in a suitable form for almost periodic operators. In particular, the notion of Bloch eigenvalues and eigenvectors does not exist for almost periodic operators. However, we are able to recover the almost periodic homogenization result by employing a sequence of periodic approximations to almost periodic operators. We also establish a rate of convergence for approximations of homogenized tensors for a class of almost periodic media. The results are supported by a numerical study.

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mentioning

confidence: 99%

Bloch wave approach to almost periodic homogenization and approximations of effective coefficients

Sista¹,

Tewary²

2022

DCDS-B

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Hybrid Quasicrystals, Transport and Localization in Products of Minimal Sets

Carvalho

Oliveira

2007

J Stat Phys

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We consider convex combinations of finite-valued almost periodic sequences (mainly substitution sequences) and put them as potentials of one-dimensional tight-binding models. We prove that these sequences are almost periodic. We call such combinations hybrid quasicrystals and these studies are related to the minimality, under the shift on both coordinates, of the product space of the respective (minimal) hulls. We observe a rich variety of behaviors on the quantum dynamical transport ranging from localization to transport. * CRdO thanks the partial support by CNPq.

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Critical energies in random palindrome models

Carvalho

Oliveira

2003

Journal of Mathematical Physics

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We investigate the occurrence of critical energies—where the Lyapunov exponent vanishes—in random Schrödinger operators when the potentials have some local order, which we call random palindrome models. We give necessary and sufficient conditions for the presence of such critical energies: the commutativity of finite word elliptic transfer matrices. Finally, we perform some numerical calculations of the Lyapunov exponents showing their behavior near the critical energies and the respective time evolution of an initially localized wave packet, obtaining the exponent ruling the algebraic growth of the second momentum. We also consider special random palindrome models with one-letter bounded gap property; the transport effects of such long range order are showed numerically.

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Cited by 4 publications

References 21 publications

Bloch wave approach to almost periodic homogenization and approximations of effective coefficients

Bloch wave approach to almost periodic homogenization and approximations of effective coefficients

Hybrid Quasicrystals, Transport and Localization in Products of Minimal Sets

Critical energies in random palindrome models

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