1. |
- Usatenko, O.V., et al.
(author)
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Three types of spectra in one-dimensional systems with random correlated binary potential
- 2007
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In: Telecommunications and Radio Engineering. - 0040-2508. ; 66:4, s. 353-362
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Journal article (peer-reviewed)abstract
- The stationary one-dimensional tight-binding Schredinger equation with a weak diagonal long-range correlated disorder in the potential is studied. An algorithm for constructing the discrete binary on-site potential exhibiting a hybrid spectrum with three different spectral components (absolutely continues, singular continues and point) ordered in any predefined manner in the region of energy and/or wave number is presented. A new approach to generating a binary sequence with the long-range memory based on a concept of additive Markov chains is used.
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2. |
- Usatenko, O.V., et al.
(author)
-
Spectral Analysis and Syntesis of Long-Rang Correlated Systems: Antennas, Diffraction Gratings and Solids
- 2007
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In: Physics and Engineering of Microwaves, Millimeter and Submillimeter Waves and Workshop on Terahertz Technologies, 2007. - : IEEE. - 1424412374 ; , s. 246-248
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Conference paper (peer-reviewed)abstract
- A new method for constructing a long-range correlated sequence of two-valued random elements with a given correlator is discussed. A Fourier transform of a correlation function having an arbitrary complexity is designed. The real-space correlator, the memory function, and the conditional probability function of the additive Markov chain are calculated sequentially. The diffraction grating and the antenna are considered as a series of 2M+1 scatterers.
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3. |
- Usatenko, O. V., et al.
(author)
-
Spectral analysis and synthesis of 1D dichotomous long-range correlated systems : From diffraction gratings to quantum wire
- 2008
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In: Physica A. - : Elsevier BV. - 0378-4371 .- 1873-2119. ; 387:19-20, s. 4733-4739
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Journal article (peer-reviewed)abstract
- Spectral properties of 1D systems with long-range correlated disorder and their response to an applied field are examined. An algorithm based on the additive multi-step Markov chains is used to analyze and synthesize layered systems consisting of two randomly alternated elements. Using an equation connecting the correlation and memory functions enables one to reveal the microscopic structure, which can be expressed in terms of the Markov chain conditional probability function. Specifically, a method of designing complex gratings with prescribed characteristics that simultaneously display periodic, quasi-periodic and random properties is emphasized. The tight-binding Schrödinger equation with a weak correlated disorder in the dichotomic potential exhibiting sharp transition in conductivity is studied.
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