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  • 1.
    Johansson, Magnus
    et al.
    Linköpings universitet, Institutionen för fysik, kemi och biologi, Teoretisk Fysik. Linköpings universitet, Tekniska högskolan.
    Kirr, K
    Linköpings universitet, Tekniska högskolan. Linköpings universitet, Institutionen för fysik, kemi och biologi, Teoretisk Fysik.
    Kovalev, A S
    National Academy of Science Ukraine.
    Kroon, Lars
    Linköpings universitet, Institutionen för fysik, kemi och biologi, Teoretisk Fysik. Linköpings universitet, Tekniska högskolan.
    Gap and out-gap solitons in modulated systems of finite length: exact solutions in the slowly varying envelope limit2011Inngår i: PHYSICA SCRIPTA, ISSN 0031-8949, Vol. 83, nr 6Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    We discuss nonlinear excitations in finite-size one-dimensional modulated systems. Considering a binary modulated discrete nonlinear Schrodinger chain of large but finite length with periodic boundary conditions, we obtain exact elliptic-function solutions corresponding to stationary excitations in the slowly varying envelope limit. From these solutions, we analyze how the transformation between (localized) gap and (delocalized) out-gap solitons manifests itself in a system of finite length. The analogue of a localized gap soliton appears through a bifurcation at a critical point, so that gap soliton analogues exist only for chains longer than a critical value, which scales inversely proportional to the modulation depth. The total norm of these gap-out-gap states is found to be a monotonic function of the frequency, always inside a nonlinear gap with edges defined by the main nonlinear modes which approach the linear spectrum gap boundaries in the small-amplitude limit. The transformation from a gap to an out-gap state is associated with a particular frequency, close to the lower boundary of the linear gap; at this point the elliptic functions become trigonometric, corresponding to a finite-size analogue of an algebraic soliton. We compare the scenario with earlier results obtained numerically for purely discrete chains with few degrees of freedom.

  • 2.
    Kroon, Lars
    Linköpings universitet, Institutionen för fysik, kemi och biologi. Linköpings universitet, Tekniska fakulteten.
    Cancellation of Acoustic Waves in Scattering Media2015Inngår i: 9TH INTERNATIONAL CONGRESS ON ADVANCED ELECTROMAGNETIC MATERIALS IN MICROWAVES AND OPTICS (METAMATERIALS 2015), IEEE , 2015, s. 157-159Konferansepaper (Fagfellevurdert)
    Abstract [en]

    We find scattering cancellation in diffusive transport of acoustics waves propagating through strongly scattering media and for ballistic sound in the long wavelength limit.

  • 3.
    Kroon, Lars
    Linköpings universitet, Institutionen för fysik och mätteknik. Linköpings universitet, Tekniska högskolan.
    Delocalization in nonperiodic systems2004Licentiatavhandling, med artikler (Annet vitenskapelig)
    Abstract [en]

    The localization properties of non-interacting linear excitations in one-dimensional aperiodically ordered structures are investigated from a theoretical point of view. The models used have various relevance for real systems, like quasicrystals, photonic crystals, and deterministic aperiodic superlattices. The main objective is to gain a conceptual understanding of the localization phenomenon in different lattice models, especially with respect to their correlation measures.

    The localization properties of electronic wavefunctions in various nearest neighbor tight -binding models are studied in the framework of the dynamical systems induced by the trace maps of their corresponding transfer matrices. With a unit hopping and an on-site potential modulated by the Rudin-Shapiro sequence, which in analogy with a random potential has an absolutely continuous correlation measure, the electronic spectrum is proved to be purely singular continuous and of zero Lebesgue measure. The absence of localization is also confirmed by numerical simulations of the dynamics of electronic wavepackets showing weakly anomalous diffusion and an algebraic decay of the temporal autocorrelation function. These results are also found to be invariant under the introduction of correlated hopping integrals.

    The nature of localization of elastic vibrations in harmonic lattices is also studied. The generalized eigenvalue problem arising from classical interactions in diatomic chains can be mapped to mixed tight-binding models, which enables the use of the spectral theory of discrete Schrödinger operators. Like for the Rudin-Shapiro model, it is found that the vibrational spectra of harmonic chains with masses distributed according to the Thue-Morse sequence and the period-doubling sequence are purely singular continuous. These results are obtained by transforming the lattices to on-site models by the use of certain renormalization procedures.

    Remembering that the correlation measure of the T hue-Morse sequence is purely singular continuous, while that of the period-doubling sequence is pure point, these results strongly suggest that the criticality of localization in deterministic aperiodic lattices is generic and quite independent of the character of the correlation measure associated to the modeling sequence.

  • 4.
    Kroon, Lars
    Linköpings universitet, Institutionen för fysik, kemi och biologi, Teoretisk Fysik. Linköpings universitet, Tekniska högskolan.
    Spectra and Dynamics of Excitattions in Long-Range Correlated Strucutures2007Doktoravhandling, med artikler (Annet vitenskapelig)
    Abstract [sv]

    Vad karaktäriserar en kristall? Svaret på denna till synes enkla fråga blir kanske att det är en anordning av atomer uppradade i periodiska mönster. Så ordnade strukturer kan studeras genom att det uppträder så kallade Braggtoppar i röntgendiffraktionsmönstret. Om frågan gäller elektrontäthetsfördelningen, kanske svaret blir att denna är periodisk och grundar sig på elektronvågor som genomtränger hela kristallen. I och med att nya typer av ordnade system, så kallade kvasikristaller, upptäcks och framställs på artificiell väg blir svaren på dessa frågor mer intrikata.

    En kristall behöver inte bestå av enheter upprepade periodiskt i rummet, och den klassiska metoden att karaktärisera strukturer via röntgendiffraktionsmönstret kanske inte alls är den allena saliggörande. I denna avhandling visas att ett ordnat gitter vars röntgendiffraktionsmönster saknar inre struktur, dvs är av samma diffusa typ som vad ett oordnat material uppvisar, fortfarande kan ha elektronerna utsträckta över hela strukturen. Detta implicerar att det inte finns något enkelt samband mellan diffraktionsmönstret från gittret och dess fysikaliska egenskaper såsom t ex lokalisering av vågfunktionerna. Man talar om lokalisering när en vågfunktion är begränsad inom en del av materialet och inte utsträckt över hela dess längd, vilket är av betydelse när man vill avgöra huruvida ett material är en isolator, halvledare eller ledare. Det vittnar samtidigt om behovet av att söka efter andra karakteristika när man försöker beskriva skillnaden mellan ett ordnat och ett oordnat material, där den senare kategorin kan uppvisa lokalisering. Resultaten utgör en klassificering av det svåröverskådliga området aperiodiska gitter i en dimension. Det leder till hypotesen att ideala kvasikristaller, genererade med bestämda regler, har kontinuerligt energispektrum av fraktal natur.

    I reella material spelar korrelation en viktig roll. Vid icke-linjär återkoppling till gittret kan man erhålla intrinsiskt lokaliserade vågor, som i många avseenden beter sig som partiklar, solitoner, vilka har visat sig ha viktiga tillämpningar inom bl a optisk telekommunikation. Sådana vågors roll for lagring och transport av energi har undersökts i teoretiska modeller for optiska vågledare och kristaller där ljuset har en förmåga att manipulera sig självt.

    Delarbeid
    1. Localization-delocalization in aperiodic systems
    Åpne denne publikasjonen i ny fane eller vindu >>Localization-delocalization in aperiodic systems
    2002 (engelsk)Inngår i: Physical Review B, Condensed matter and materials physics, ISSN 1098-0121, Vol. 66, nr 9, s. 094204-Artikkel i tidsskrift (Fagfellevurdert) Published
    Abstract [en]

    The question of localization in a one-dimensional tight-binding model with aperiodicity given by substitutions is discussed. Since the localization properties of the well-known Rudin-Shapiro chain is still far from well understood, partly due to the absence of rigorous analytical results, we introduce a sequence that has several features in common with the Rudin-Shapiro sequence. We derive a trace map for this system and prove analytically that the electron spectrum is singular continuous. Despite the extended (non-normalizable) nature of the corresponding wave functions, the states show strong localization for finite approximations of the chain. Similar localization properties are found for the Rudin-Shapiro chain, where earlier results have indicated a pure point spectrum. We compare the properties for two other physical systems, ordered according to the two discussed sequences; stationary electron transmission is studied through finite chains using a dynamical map, optical properties of dielectric multilayer structures are investigated.

    HSV kategori
    Identifikatorer
    urn:nbn:se:liu:diva-14650 (URN)10.1103/PhysRevB.66.094204 (DOI)
    Tilgjengelig fra: 2007-09-20 Laget: 2007-09-20
    2. Renormalization of aperiodic model lattices: spectral properties
    Åpne denne publikasjonen i ny fane eller vindu >>Renormalization of aperiodic model lattices: spectral properties
    2003 (engelsk)Inngår i: Journal of Physics A: Mathematical and General, ISSN 1751-8113, Vol. 36, s. 4519-4532Artikkel i tidsskrift (Fagfellevurdert) Published
    Abstract [en]

    Many of the published results for one-dimensional deterministic aperiodic systems treat rather simplified electron models with either a constant site energy or a constant hopping integral. Here we present some rigorous results for more realistic mixed tight-binding systems with both the site energies and the hopping integrals having an aperiodic spatial variation. It is shown that the mixed Thue–Morse, period-doubling and Rudin–Shapiro lattices can be transformed to on-site models on renormalized lattices maintaining the individual order between the site energies. The character of the energy spectra for these mixed models is therefore the same as for the corresponding on-site models. Furthermore, since the study of electrons on a lattice governed by the Schrödinger tight-binding equation maps onto the study of elastic vibrations on a harmonic chain, we have proved that the vibrational spectra of aperiodic harmonic chains with distributions of masses determined by the Thue–Morse sequence and the period-doubling sequence are purely singular continuous.

    HSV kategori
    Identifikatorer
    urn:nbn:se:liu:diva-14651 (URN)10.1088/0305-4470/36/16/303 (DOI)
    Tilgjengelig fra: 2007-09-20 Laget: 2007-09-20
    3. Absence of localization in a model with correlation measure as a random lattice
    Åpne denne publikasjonen i ny fane eller vindu >>Absence of localization in a model with correlation measure as a random lattice
    2004 (engelsk)Inngår i: Physical Review B. Condensed Matter and Materials Physics, ISSN 1098-0121, E-ISSN 1550-235X, Vol. 69, nr 9, s. 094204-Artikkel i tidsskrift (Fagfellevurdert) Published
    Abstract [en]

    A coherent picture of localization in one-dimensional aperiodically ordered systems is still missing. We show the presence of purely singular continuous spectrum for a discrete system whose modulation sequence has a correlation measure which is absolutely continuous, such as for a random sequence. The system showing these properties is modeled by the Rudin-Shapiro sequence, whose correlation measure even has a uniform density. The absence of localization is also supported by a numerical investigation of the dynamics of electronic wave packets showing weakly anomalous diffusion and an extremely slow algebraic decay of the temporal autocorrelation function.

    sted, utgiver, år, opplag, sider
    American Physical Society, 2004
    HSV kategori
    Identifikatorer
    urn:nbn:se:liu:diva-14652 (URN)10.1103/PhysRevB.69.094204 (DOI)
    Tilgjengelig fra: 2007-09-20 Laget: 2007-09-20 Sist oppdatert: 2018-05-24
    4. Spectral analysis and synthesis of 1D dichotomous long-range correlated systems: From diffraction gratings to quantum wire
    Åpne denne publikasjonen i ny fane eller vindu >>Spectral analysis and synthesis of 1D dichotomous long-range correlated systems: From diffraction gratings to quantum wire
    Vise andre…
    2008 (engelsk)Inngår i: Physica A: Statistical Mechanics and its Applications, ISSN 0378-4371, E-ISSN 1873-2119, Vol. 387, nr 19-20, s. 4733-4739Artikkel i tidsskrift (Fagfellevurdert) Published
    Abstract [en]

    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.

    Emneord
    Markov chain, Diffraction grating, Correlation function, Lyapunov exponent, Mobility edge
    HSV kategori
    Identifikatorer
    urn:nbn:se:liu:diva-14653 (URN)10.1016/j.physa.2008.03.038 (DOI)
    Tilgjengelig fra: 2007-09-20 Laget: 2007-09-20 Sist oppdatert: 2017-12-13
    5. Bifurcation picture and stability of the gap and out-gap discrete solitons
    Åpne denne publikasjonen i ny fane eller vindu >>Bifurcation picture and stability of the gap and out-gap discrete solitons
    2007 (engelsk)Inngår i: Low temperature physics (Woodbury, N.Y., Print), ISSN 1063-777X, E-ISSN 1090-6517, Vol. 33, nr 5, s. 481-483Artikkel i tidsskrift (Fagfellevurdert) Published
    Abstract [en]

    The dynamics of a quaternary fragment of a discrete system of coupled nonlinear oscillators with modulated frequency parameters is investigated, and the stability of its gap and out-gap soliton-like excitations is studied.

    HSV kategori
    Identifikatorer
    urn:nbn:se:liu:diva-14654 (URN)10.1063/1.2737564 (DOI)
    Tilgjengelig fra: 2007-09-20 Laget: 2007-09-20 Sist oppdatert: 2017-12-13
    6. The appearance of gap solitons in a nonlinear Schrödinger lattice
    Åpne denne publikasjonen i ny fane eller vindu >>The appearance of gap solitons in a nonlinear Schrödinger lattice
    Manuskript (Annet vitenskapelig)
    Identifikatorer
    urn:nbn:se:liu:diva-14655 (URN)
    Tilgjengelig fra: 2007-09-20 Laget: 2007-09-20 Sist oppdatert: 2010-01-13
  • 5.
    Kroon, Lars
    et al.
    Linköpings universitet, Institutionen för fysik, kemi och biologi, Teoretisk Fysik. Linköpings universitet, Tekniska högskolan.
    Bogdan, M. M.
    B. Verkin Institute for Low Temperature Physics and Engineering of the National Academy of Sciences of Ukraine, Kharkov, Ukraine.
    Kovalev, A S
    B. Verkin Institute for Low Temperature Physics and Engineering of the National Academy of Sciences of Ukraine, Kharkov, Ukraine.
    Malyuta, E Yu
    Electrophysical Scientific and Technical Center, Kharkov, Ukraine.
    Bifurcation picture and stability of the gap and out-gap discrete solitons2007Inngår i: Low temperature physics (Woodbury, N.Y., Print), ISSN 1063-777X, E-ISSN 1090-6517, Vol. 33, nr 5, s. 481-483Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    The dynamics of a quaternary fragment of a discrete system of coupled nonlinear oscillators with modulated frequency parameters is investigated, and the stability of its gap and out-gap soliton-like excitations is studied.

  • 6.
    Kroon, Lars
    et al.
    Linköpings universitet, Institutionen för fysik, kemi och biologi, Teoretisk Fysik. Linköpings universitet, Tekniska högskolan.
    Johansson, Magnus
    Linköpings universitet, Institutionen för fysik, kemi och biologi, Teoretisk Fysik. Linköpings universitet, Tekniska högskolan.
    Kovalev, A S
    National Acadamy of Science Ukraine.
    Yu Malyuta, E
    National Acadamy of Science Ukraine.
    The appearance of gap solitons in a nonlinear Schrodinger lattice2010Inngår i: PHYSICA D-NONLINEAR PHENOMENA, ISSN 0167-2789, Vol. 239, nr 5, s. 269-278Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    We study the appearance of discrete gap solitons in a nonlinear Schrodinger model with a periodic on-site potential that possesses a gap evacuated of plane-wave solutions in the linear limit. For finite lattices supporting an anti-phase (q = pi/2) gap edge phonon as an anharmonic standing wave in the nonlinear regime, gap solitons are numerically found to emerge via pitchfork bifurcations from the gap edge. Analytically, modulational instabilities between pairs of bifurcation points on this "nonlinear gap boundary" are found in terms of critical gap widths, turning to zero in the infinite-size limit, which are associated with the birth of the localized soliton as well as discrete multisolitons in the gap. Such tunable instabilities can be of relevance in exciting soliton states in modulated arrays of nonlinear optical waveguides or Bose-Einstein condensates in periodic potentials. For lattices whose gal) edge phonon only asymptotically approaches the anti-phase solution, the nonlinear gap boundary splits in a bifurcation scenario leading to the birth of the discrete gap soliton as a continuable orbit to the gap edge in the linear limit. The instability-induced dynamics of the localized soliton in the gap regime is found to thermalize according to the Gibbsian equilibrium distribution, while the spontaneous formation of persisting intrinsically localized modes (discrete breathers) from the extended out-gap soliton reveals a phase transition of the solution.

  • 7.
    Kroon, Lars
    et al.
    Linköpings universitet, Institutionen för fysik, kemi och biologi, Teoretisk Fysik. Linköpings universitet, Tekniska högskolan.
    Lennholm, Erik
    Linköpings universitet, Institutionen för fysik, kemi och biologi.
    Riklund, Rolf
    Linköpings universitet, Institutionen för fysik, kemi och biologi, Teoretisk Fysik. Linköpings universitet, Tekniska högskolan.
    Localization-delocalization in aperiodic systems2002Inngår i: Physical Review B, Condensed matter and materials physics, ISSN 1098-0121, Vol. 66, nr 9, s. 094204-Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    The question of localization in a one-dimensional tight-binding model with aperiodicity given by substitutions is discussed. Since the localization properties of the well-known Rudin-Shapiro chain is still far from well understood, partly due to the absence of rigorous analytical results, we introduce a sequence that has several features in common with the Rudin-Shapiro sequence. We derive a trace map for this system and prove analytically that the electron spectrum is singular continuous. Despite the extended (non-normalizable) nature of the corresponding wave functions, the states show strong localization for finite approximations of the chain. Similar localization properties are found for the Rudin-Shapiro chain, where earlier results have indicated a pure point spectrum. We compare the properties for two other physical systems, ordered according to the two discussed sequences; stationary electron transmission is studied through finite chains using a dynamical map, optical properties of dielectric multilayer structures are investigated.

  • 8.
    Kroon, Lars
    et al.
    Linköpings universitet, Institutionen för fysik, kemi och biologi, Teoretisk Fysik. Linköpings universitet, Tekniska högskolan.
    Riklund, Rolf
    Linköpings universitet, Institutionen för fysik, kemi och biologi, Teoretisk Fysik. Linköpings universitet, Tekniska högskolan.
    Absence of localization in a model with correlation measure as a random lattice2004Inngår i: Physical Review B. Condensed Matter and Materials Physics, ISSN 1098-0121, E-ISSN 1550-235X, Vol. 69, nr 9, s. 094204-Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    A coherent picture of localization in one-dimensional aperiodically ordered systems is still missing. We show the presence of purely singular continuous spectrum for a discrete system whose modulation sequence has a correlation measure which is absolutely continuous, such as for a random sequence. The system showing these properties is modeled by the Rudin-Shapiro sequence, whose correlation measure even has a uniform density. The absence of localization is also supported by a numerical investigation of the dynamics of electronic wave packets showing weakly anomalous diffusion and an extremely slow algebraic decay of the temporal autocorrelation function.

  • 9.
    Kroon, Lars
    et al.
    Linköpings universitet, Institutionen för fysik, kemi och biologi, Teoretisk Fysik. Linköpings universitet, Tekniska högskolan.
    Riklund, Rolf
    Linköpings universitet, Institutionen för fysik, kemi och biologi, Teoretisk Fysik. Linköpings universitet, Tekniska högskolan.
    Renormalization of aperiodic model lattices: spectral properties2003Inngår i: Journal of Physics A: Mathematical and General, ISSN 1751-8113, Vol. 36, s. 4519-4532Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    Many of the published results for one-dimensional deterministic aperiodic systems treat rather simplified electron models with either a constant site energy or a constant hopping integral. Here we present some rigorous results for more realistic mixed tight-binding systems with both the site energies and the hopping integrals having an aperiodic spatial variation. It is shown that the mixed Thue–Morse, period-doubling and Rudin–Shapiro lattices can be transformed to on-site models on renormalized lattices maintaining the individual order between the site energies. The character of the energy spectra for these mixed models is therefore the same as for the corresponding on-site models. Furthermore, since the study of electrons on a lattice governed by the Schrödinger tight-binding equation maps onto the study of elastic vibrations on a harmonic chain, we have proved that the vibrational spectra of aperiodic harmonic chains with distributions of masses determined by the Thue–Morse sequence and the period-doubling sequence are purely singular continuous.

  • 10.
    Usatenko, O. V.
    et al.
    A. Ya. Usikov Institute for Radiophysics and Electronics, Ukrainian Academy of Science, Kharkov, Ukraine.
    Melnik, S. S.
    A. Ya. Usikov Institute for Radiophysics and Electronics, Ukrainian Academy of Science, Kharkov, Ukraine.
    Kroon, Lars
    Linköpings universitet, Institutionen för fysik, kemi och biologi, Teoretisk Fysik. Linköpings universitet, Tekniska högskolan.
    Johansson, Magnus
    Linköpings universitet, Institutionen för fysik, kemi och biologi, Teoretisk Fysik. Linköpings universitet, Tekniska högskolan.
    Riklund, Rolf
    Linköpings universitet, Institutionen för fysik, kemi och biologi, Teoretisk Fysik. Linköpings universitet, Tekniska högskolan.
    Apostolov, A. A.
    A. Ya. Usikov Institute for Radiophysics and Electronics, Ukrainian Academy of Science, Kharkov, Ukraine.
    Spectral analysis and synthesis of 1D dichotomous long-range correlated systems: From diffraction gratings to quantum wire2008Inngår i: Physica A: Statistical Mechanics and its Applications, ISSN 0378-4371, E-ISSN 1873-2119, Vol. 387, nr 19-20, s. 4733-4739Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    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.

  • 11.
    Usatenko, O.V.
    et al.
    A. Ya. Usikov Inst. for Radiophys. & Electron., Ukrainian Acad. of Sci., Kharkov.
    Melnik, S.S.
    A. Ya. Usikov Inst. for Radiophys. & Electron., Ukrainian Acad. of Sci., Kharkov.
    Kroon, Lars
    Linköpings universitet, Institutionen för fysik, kemi och biologi, Teoretisk Fysik. Linköpings universitet, Tekniska högskolan.
    Johansson, Magnus
    Linköpings universitet, Institutionen för fysik, kemi och biologi, Teoretisk Fysik. Linköpings universitet, Tekniska högskolan.
    Riklund, Rolf
    Linköpings universitet, Institutionen för fysik, kemi och biologi, Teoretisk Fysik. Linköpings universitet, Tekniska högskolan.
    Spectral Analysis and Syntesis of Long-Rang Correlated Systems: Antennas, Diffraction Gratings and Solids2007Inngår i: Physics and Engineering of Microwaves, Millimeter and Submillimeter Waves and Workshop on Terahertz Technologies, 2007: Volume 1, IEEE , 2007, s. 246-248Konferansepaper (Fagfellevurdert)
    Abstract [en]

    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.

  • 12.
    Usatenko, O.V.
    et al.
    National Academy of Sciences of Ukraine.
    Melnyk, S.S.
    National Academy of Sciences of Ukraine.
    Yampolski, V.A.
    National Academy of Sciences of Ukraine.
    Johansson, Magnus
    Linköpings universitet, Institutionen för fysik, kemi och biologi. Linköpings universitet, Tekniska högskolan.
    Kroon, Lars
    Linköpings universitet, Institutionen för fysik, kemi och biologi. Linköpings universitet, Tekniska högskolan.
    Riklund, Rolf
    Linköpings universitet, Institutionen för fysik, kemi och biologi. Linköpings universitet, Tekniska högskolan.
    Three types of spectra in one-dimensional systems with random correlated binary potential2007Inngår i: Telecommunications and Radio Engineering, ISSN 0040-2508, Vol. 66, nr 4, s. 353-362Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    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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