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Kroon, Lars
Publications (10 of 12) Show all publications
Kroon, L. (2015). Cancellation of Acoustic Waves in Scattering Media. In: 9TH INTERNATIONAL CONGRESS ON ADVANCED ELECTROMAGNETIC MATERIALS IN MICROWAVES AND OPTICS (METAMATERIALS 2015): . Paper presented at 9th International Congress on Advanced Electromagnetic Materials in Microwaves and Optics (METAMATERIALS) (pp. 157-159). IEEE
Open this publication in new window or tab >>Cancellation of Acoustic Waves in Scattering Media
2015 (English)In: 9TH INTERNATIONAL CONGRESS ON ADVANCED ELECTROMAGNETIC MATERIALS IN MICROWAVES AND OPTICS (METAMATERIALS 2015), IEEE , 2015, p. 157-159Conference paper, Published paper (Refereed)
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.

Place, publisher, year, edition, pages
IEEE, 2015
National Category
Fluid Mechanics and Acoustics
Identifiers
urn:nbn:se:liu:diva-130457 (URN)10.1109/MetaMaterials.2015.7342557 (DOI)000379127300053 ()978-1-4799-7836-6 (ISBN)
Conference
9th International Congress on Advanced Electromagnetic Materials in Microwaves and Optics (METAMATERIALS)
Available from: 2016-08-19 Created: 2016-08-05 Last updated: 2016-08-19
Johansson, M., Kirr, K., Kovalev, A. S. & Kroon, L. (2011). Gap and out-gap solitons in modulated systems of finite length: exact solutions in the slowly varying envelope limit. PHYSICA SCRIPTA, 83(6)
Open this publication in new window or tab >>Gap and out-gap solitons in modulated systems of finite length: exact solutions in the slowly varying envelope limit
2011 (English)In: PHYSICA SCRIPTA, ISSN 0031-8949, Vol. 83, no 6Article in journal (Refereed) Published
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.

Place, publisher, year, edition, pages
Royal Swedish Academy of Sciences, 2011
National Category
Engineering and Technology
Identifiers
urn:nbn:se:liu:diva-69166 (URN)10.1088/0031-8949/83/06/065005 (DOI)000291153700005 ()
Available from: 2011-06-17 Created: 2011-06-17 Last updated: 2014-01-13
Kroon, L., Johansson, M., Kovalev, A. S. & Yu Malyuta, E. (2010). The appearance of gap solitons in a nonlinear Schrodinger lattice. PHYSICA D-NONLINEAR PHENOMENA, 239(5), 269-278
Open this publication in new window or tab >>The appearance of gap solitons in a nonlinear Schrodinger lattice
2010 (English)In: PHYSICA D-NONLINEAR PHENOMENA, ISSN 0167-2789, Vol. 239, no 5, p. 269-278Article in journal (Refereed) Published
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.

Keywords
Discrete gap solitons, Bifurcations, Linear stability, Thermalization
National Category
Engineering and Technology
Identifiers
urn:nbn:se:liu:diva-53814 (URN)10.1016/j.physd.2009.11.007 (DOI)000273924200004 ()
Available from: 2010-02-05 Created: 2010-02-05 Last updated: 2014-01-13
Usatenko, O. V., Melnik, S. S., Kroon, L., Johansson, M., Riklund, R. & Apostolov, A. A. (2008). Spectral analysis and synthesis of 1D dichotomous long-range correlated systems: From diffraction gratings to quantum wire. Physica A: Statistical Mechanics and its Applications, 387(19-20), 4733-4739
Open this publication in new window or tab >>Spectral analysis and synthesis of 1D dichotomous long-range correlated systems: From diffraction gratings to quantum wire
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2008 (English)In: Physica A: Statistical Mechanics and its Applications, ISSN 0378-4371, E-ISSN 1873-2119, Vol. 387, no 19-20, p. 4733-4739Article in journal (Refereed) 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.

Keywords
Markov chain, Diffraction grating, Correlation function, Lyapunov exponent, Mobility edge
National Category
Natural Sciences
Identifiers
urn:nbn:se:liu:diva-14653 (URN)10.1016/j.physa.2008.03.038 (DOI)
Available from: 2007-09-20 Created: 2007-09-20 Last updated: 2017-12-13
Kroon, L., Bogdan, M. M., Kovalev, A. S. & Malyuta, E. Y. (2007). Bifurcation picture and stability of the gap and out-gap discrete solitons. Low temperature physics (Woodbury, N.Y., Print), 33(5), 481-483
Open this publication in new window or tab >>Bifurcation picture and stability of the gap and out-gap discrete solitons
2007 (English)In: Low temperature physics (Woodbury, N.Y., Print), ISSN 1063-777X, E-ISSN 1090-6517, Vol. 33, no 5, p. 481-483Article in journal (Refereed) 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.

National Category
Natural Sciences
Identifiers
urn:nbn:se:liu:diva-14654 (URN)10.1063/1.2737564 (DOI)
Available from: 2007-09-20 Created: 2007-09-20 Last updated: 2017-12-13
Kroon, L. (2007). Spectra and Dynamics of Excitattions in Long-Range Correlated Strucutures. (Doctoral dissertation). : Institutionen för fysik, kemi och biologi
Open this publication in new window or tab >>Spectra and Dynamics of Excitattions in Long-Range Correlated Strucutures
2007 (English)Doctoral thesis, comprehensive summary (Other academic)
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.

Abstract [en]

Spectral and dynamical properties of electrons, phonons, electromagnetic waves, and nonlinear coherent excitations in one-dimensional modulated structures with long-range correlations are investigated from a theoretical point of view.

First a proof of singular continuous electron spectrum for the tight-binding Schrödinger equation with an on-site potential, which, in analogy with a random potential, has an absolutely continuous correlation measure, is given. The critical behavior of such a localization phenomenon manifests in anomalous diffusion for the time-evolution of electronic wave packets. Spectral characterization of elastic vibrations in aperiodically ordered diatomic chains in the harmonic approximation is achieved through a dynamical system induced by the trace maps of renormalized transfer matrices. These results suggest that the zero Lebesgue measure Cantor-set spectrum (without eigenvalues) of the Fibonacci model for a quasicrystal is generic for deterministic aperiodic superlattices, for which the modulations take values via substitution rules on finite sets, independent of the correlation measure.

Secondly, a method to synthesize and analyze discrete systems with prescribed long-range correlated disorder based on the conditional probability function of an additive Markov chain is effectively implemented. Complex gratings (artificial solids) that simultaneously display given characteristics of quasiperiodic crystals and amorphous solids on the Fraunhofer diffraction are designated. A mobility edge within second order perturbation theory of the tight-binding Schrödinger equation with a correlated disorder in the dichotomic potential realizes the success of the method in designing window filters with specific spectral components.

The phenomenon of self-localization in lattice dynamical systems is a subject of interest in various physical disciplines. Lattice solitons are studied using the discrete nonlinear Schrödinger equation with on-site potential, modeling coherent structures in, for example, photonic crystals. The instability-induced dynamics of the localized gap soliton is found to thermalize according to the Gibbsian equilibrium distribution, while the spontaneous formation of persisting intrinsic localized modes from the extended out-gap soliton reveals a phase transition of the solution.

Place, publisher, year, edition, pages
Institutionen för fysik, kemi och biologi, 2007. p. 52
Series
Linköping Studies in Science and Technology. Dissertations, ISSN 0345-7524 ; 1109
Keywords
quasicrystals, deterministic aperiodic superlattices, Markov chains, electronic structure and diffusion, elastic vibrations, Fraunhofer diffraction, discrete solitons, phase transitions
National Category
Condensed Matter Physics
Identifiers
urn:nbn:se:liu:diva-9727 (URN)978-91-85831-57-9 (ISBN)
Public defence
2007-09-14, Planck, Fysikhuset, Campus Valla, Linköpings universitet, Linköping, 14:15 (English)
Opponent
Supervisors
Available from: 2007-09-20 Created: 2007-09-20 Last updated: 2014-01-13
Usatenko, O., Melnik, S., Kroon, L., Johansson, M. & Riklund, R. (2007). Spectral Analysis and Syntesis of Long-Rang Correlated Systems: Antennas, Diffraction Gratings and Solids. In: Physics and Engineering of Microwaves, Millimeter and Submillimeter Waves and Workshop on Terahertz Technologies, 2007: Volume 1. Paper presented at The Sixth International Kharkov Symposium on Physics and Engineering of Microwaves, Millimeter and Submillimeter Waves and Workshop on Terahertz Technologies (MSMW 2007), Kharkov, Ukraine, June 25-30, 2007 (pp. 246-248). IEEE
Open this publication in new window or tab >>Spectral Analysis and Syntesis of Long-Rang Correlated Systems: Antennas, Diffraction Gratings and Solids
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2007 (English)In: Physics and Engineering of Microwaves, Millimeter and Submillimeter Waves and Workshop on Terahertz Technologies, 2007: Volume 1, IEEE , 2007, p. 246-248Conference paper, Published paper (Refereed)
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.

Place, publisher, year, edition, pages
IEEE, 2007
National Category
Other Physics Topics
Identifiers
urn:nbn:se:liu:diva-91573 (URN)10.1109/MSMW.2007.4294623 (DOI)1-4244-1237-4 (ISBN)
Conference
The Sixth International Kharkov Symposium on Physics and Engineering of Microwaves, Millimeter and Submillimeter Waves and Workshop on Terahertz Technologies (MSMW 2007), Kharkov, Ukraine, June 25-30, 2007
Available from: 2013-04-26 Created: 2013-04-26 Last updated: 2014-01-13
Usatenko, O., Melnyk, S., Yampolski, V., Johansson, M., Kroon, L. & Riklund, R. (2007). Three types of spectra in one-dimensional systems with random correlated binary potential. Telecommunications and Radio Engineering, 66(4), 353-362
Open this publication in new window or tab >>Three types of spectra in one-dimensional systems with random correlated binary potential
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2007 (English)In: Telecommunications and Radio Engineering, ISSN 0040-2508, Vol. 66, no 4, p. 353-362Article in journal (Refereed) Published
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.

National Category
Natural Sciences
Identifiers
urn:nbn:se:liu:diva-41737 (URN)10.1615/TelecomRadEng.v66.i4 (DOI)58944 (Local ID)58944 (Archive number)58944 (OAI)
Available from: 2009-10-10 Created: 2009-10-10 Last updated: 2014-01-13
Kroon, L. & Riklund, R. (2004). Absence of localization in a model with correlation measure as a random lattice. Physical Review B. Condensed Matter and Materials Physics, 69(9), 094204
Open this publication in new window or tab >>Absence of localization in a model with correlation measure as a random lattice
2004 (English)In: Physical Review B. Condensed Matter and Materials Physics, ISSN 1098-0121, E-ISSN 1550-235X, Vol. 69, no 9, p. 094204-Article in journal (Refereed) 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.

Place, publisher, year, edition, pages
American Physical Society, 2004
National Category
Natural Sciences
Identifiers
urn:nbn:se:liu:diva-14652 (URN)10.1103/PhysRevB.69.094204 (DOI)
Available from: 2007-09-20 Created: 2007-09-20 Last updated: 2018-05-24
Kroon, L. (2004). Delocalization in nonperiodic systems. (Licentiate dissertation). Linköping: Linköpings universitet
Open this publication in new window or tab >>Delocalization in nonperiodic systems
2004 (English)Licentiate thesis, comprehensive summary (Other academic)
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.

Place, publisher, year, edition, pages
Linköping: Linköpings universitet, 2004. p. 66
Series
Linköping Studies in Science and Technology. Thesis, ISSN 0280-7971 ; 1074
National Category
Physical Sciences
Identifiers
urn:nbn:se:liu:diva-153016 (URN)LiU-TEK-LIC-2004:03 (Local ID)9173739049 (ISBN)LiU-TEK-LIC-2004:03 (Archive number)LiU-TEK-LIC-2004:03 (OAI)
Available from: 2019-01-29 Created: 2019-01-25 Last updated: 2019-05-08Bibliographically approved
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