Localization properties of a one-dimensional tight-binding model with non-random long-range inter-site interactions

We perform both analytical and numerical studies of the one-dimensional tight-binding Hamiltonian with stochastic uncorrelated on-site energies and non-fluctuating long-range hopping integrals . It was argued recently [A. Rodriguez at al., J. Phys. A: Math. Gen. 33, L161 (2000)] that this model reveals a localization-delocalization transition with respect to the disorder magnitude provided . The transition occurs at one of the band edges (the upper one for and the lower one for). The states at the other band edge are always localized, which hints on the existence of a single mobility edge. We analyze the mobility edge and show that, although the number of delocalized states tends to infinity, they form a set of null measure in the thermodynamic limit, i.e. the mobility edge tends to the band edge. The critical magnitude of disorder for the band edge states is computed versus the interaction exponent by making use of the conjecture on the universality of the normalized participation number distribution at transition.Comment: 7 pages, 6 postscript figures, uses revtex

Editorial: Woody plants and forest ecosystems in a complex world—Ecological interactions and physiological functioning above and below ground

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Statistics of low-energy levels of a one-dimensional weakly localized Frenkel exciton: A numerical study

Numerical study of the one-dimensional Frenkel Hamiltonian with on-site randomness is carried out. We focus on the statistics of the energy levels near the lower exciton band edge, i. e. those determining optical response. We found that the distribution of the energy spacing between the states that are well localized at the same segment is characterized by non-zero mean, i.e. these states undergo repulsion. This repulsion results in a local discrete energy structure of a localized Frenkel exciton. On the contrary, the energy spacing distribution for weakly overlapping local ground states (the states with no nodes within their localization segments) that are localized at different segments has zero mean and shows almost no repulsion. The typical width of the latter distribution is of the same order as the typical spacing in the local discrete energy structure, so that this local structure is hidden; it does not reveal itself neither in the density of states nor in the linear absorption spectra. However, this structure affects the two-exciton transitions involving the states of the same segment and can be observed by the pump-probe spectroscopy. We analyze also the disorder degree scaling of the first and second momenta of the distributions.Comment: 10 pages, 6 figure

Bloch-like oscillations in a one-dimensional lattice with long-range correlated disorder

We study the dynamics of an electron subjected to a uniform electric field within a tight-binding model with long-range-correlated diagonal disorder. The random distribution of site energies is assumed to have a power spectrum $S(k) \sim 1/k^{\alpha}$ with $\alpha > 0$. Moura and Lyra [Phys. Rev. Lett. {\bf 81}, 3735 (1998)] predicted that this model supports a phase of delocalized states at the band center, separated from localized states by two mobility edges, provided $\alpha > 2$. We find clear signatures of Bloch-like oscillations of an initial Gaussian wave packet between the two mobility edges and determine the bandwidth of extended states, in perfect agreement with the zero-field prediction.Comment: 4 pages, 5 figure

Bloch oscillations in an aperiodic one-dimensional potential

We study the dynamics of an electron subjected to a static uniform electric field within a one-dimensional tight-binding model with a slowly varying aperiodic potential. The unbiased model is known to support phases of localized and extended one-electron states separated by two mobility edges. We show that the electric field promotes sustained Bloch oscillations of an initial Gaussian wave packet whose amplitude reflects the band width of extended states. The frequency of these oscillations exhibit unique features, such as a sensitivity to the initial wave packet position and a multimode structure for weak fields, originating from the characteristics of the underlying aperiodic potential.Comment: 6 pages, 7 figure

Low secondary electron yield engineered surface for electron cloud mitigation

Secondary electron yield (SEY or δ) limits the performance of a number of devices. Particularly, in high-energy charged particle accelerators, the beam-induced electron multipacting is one of the main sources of electron cloud (e-cloud) build up on the beam path; in radio frequency wave guides, the electron multipacting limits their lifetime and causes power loss; and in detectors, the secondary electrons define the signal background and reduce the sensitivity. The best solution would be a material with a low SEY coating and for many applications δ < 1 would be sufficient. We report on an alternative surface preparation to the ones that are currently advocated. Three commonly used materials in accelerator vacuum chambers (stainless steel, copper, and aluminium) were laser processed to create a highly regular surface topography. It is shown that this treatment reduces the SEY of the copper, aluminium, and stainless steel from δmax of 1.90, 2.55, and 2.25 to 1.12, 1.45, and 1.12, respectively. The δmax further reduced to 0.76-0.78 for all three treated metals after bombardment with 500 eV electrons to a dose between 3.5 × 10-3 and 2.0 × 10-2 C·mm-2