Nature of the extended states in one-dimensional random trimers

Okbani, Zahira; Ouasti, R.; Zekri, N.

doi:10.1016/s0378-4371(96)00322-6

Cited by 11 publications

(5 citation statements)

References 27 publications

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“…We consider a non-interacting electron moving in a periodic system of δ-peak potentials having complex strength λ = λ 0 + iη where both λ 0 and η are constant numbers. By using the Poincaré map, the Schrödinger equation of this system can be transformed to the following discrete second-order equation [10,11]:…”

Section: The Modelmentioning

confidence: 99%

“…Obviously, in successive bands the sign of η must be changed alternately to get the same sign of γ . We note also that since we choose in our model, for the initial conditions of the discrete equation ( 1), an electron moving from the right-hand side to the left-hand side of the sample (see reference [11]) the amplification should occur for negative values of γ . Therefore the imaginary part of the potential should be positive in the first allowed band of the corresponding passive system.…”

Section: The Modelmentioning

confidence: 99%

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Amplification and disorder effects in a Kronig-Penney chain of active potentials

Zekri

Bahlouli

Sen

1998

J. Phys.: Condens. Matter

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We report in this paper the analytical and numerical results on the effect of amplification on the transmission and reflection coefficient of a periodic one-dimensional Kronig-Penney lattice. A qualitative agreement is found with the tight-binding model where the transmission and reflection increase for small lengths before strongly oscillating with a maximum at a certain length. For larger lengths the transmission decays exponentially with the same rate as in the growing region while the reflection saturates at a high value. However, the maximum transmission (and reflection) moves to larger lengths and diverges in the limit of vanishing amplification instead of going to unity. In very large samples, it is anticipated that the presence of disorder and the associated length scale will limit this uninhibited growth in amplification. Also, there are other interesting competitive effects between disorder and localization giving rise to some nonmonotonic behavior in the peak of transmission.

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Section: The Modelmentioning

confidence: 99%

Section: The Modelmentioning

confidence: 99%

Amplification and disorder effects in a Kronig-Penney chain of active potentials

Zekri

Bahlouli

Sen

1998

J. Phys.: Condens. Matter

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“…In the case of random dimers with linear potentials (a = 0) this transition was found to be symmetrical, i.e., the same behavior of c is observed at both sides of the resonance [8]. In Fig.…”

Section: Resultsmentioning

confidence: 54%

“…However, recently some examples of 1D disordered systems exhibited either a finite [5] or an infinite number of extended states [6]. One of such examples, random dimer chains (a binary system with one component appearing in pairs) were extensively studied within the framework of Anderson and Kronig-Penney models [7,8] in order to simulate conducting polymers chains. It was mainly found extended states in such systems due to resonant tunneling in dimer components.…”

Section: Introductionmentioning

confidence: 99%

Effect of electron interactions on the electronic properties of random dimer systems

Okbani

Zekri

2006

Journal of Non-Crystalline Solids

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“…[9]. Since then, the RDM has been generalized to include the random trimer model [8], the random dimer-trimer model [10],and the random binary n-mer model [11]. For the particular case of the symmetric trimer, there are two possible resonances and Giri et al analyzed the possibility of merging these two resonances, which has as a consequence an increase of the width of the extended states.…”

Section: Introductionmentioning

confidence: 99%

Transport of localized and extended excitations in chains embedded with randomly distributed linear and nonlinearn-mers

López-González

Molina

2016

Phys. Rev. E

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We examine the transport of extended and localized excitations in one-dimensional linear chains populated by linear and nonlinear symmetric identical n-mers (with n=3, 4, 5, and 6), randomly distributed. First, we examine the transmission of plane waves across a single linear n-mer, paying attention to its resonances, and looking for parameters that allow resonances to merge. Within this parameter regime we examine the transmission of plane waves through a disordered and nonlinear segment composed by n-mers randomly placed inside a linear chain. It is observed that nonlinearity tends to inhibit the transmission, which decays as a power law at long segment lengths. This behavior still holds when the n-mer parameters do not obey the resonance condition. On the other hand, the mean square displacement exponent of an initially localized excitation does not depend on nonlinearity at long propagation distances z, and shows a superdiffusive behavior ∼z(1.8) for all n-mers, when parameters obey the resonance merging condition; otherwise the exponent reverts back to the random dimer model value ∼z(1.5).

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Nature of the extended states in one-dimensional random trimers

Cited by 11 publications

References 27 publications

Amplification and disorder effects in a Kronig-Penney chain of active potentials

Amplification and disorder effects in a Kronig-Penney chain of active potentials

Effect of electron interactions on the electronic properties of random dimer systems

Transport of localized and extended excitations in chains embedded with randomly distributed linear and nonlinearn-mers

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