Book of abstracts: Quodons in Mica 2013 - Nonlinear Localized Travelling Excitations in Crystals

Book of abstracts. Quodons in Mica 2013 Nonlinear localized travelling excitations in crystals. Altea, Alicante, Spain, September 18-21, 2013. Meeting in honour of Prof. Francis Michael Russell. E-mail: [email protected], url: http://www.quodons.webs.upv.es Honorary chairman Francis Michael Russell Chairmen Juan FR Archilla and V´ıctor S´anchez-Morcillo Scientific committee Yuriy Kosevich, Yury Gaididei, Vladimir Dubinko, V´ıctor S´anchez-Morcillo and Juan FR Archilla Organizing committee Luis Miguel Garc´ıa-Raffi, No´e Jim´enez, V´ıctor S´anchez-Morcillo, Juan FR Archilla and Jes´us Cuevas. Universitat Polit`ecnica de Val`encia: Instituto Universitario de Matem´atica Pura y Aplicada Instituto para la Gesti´on Integrada de las Zonas Costeras Universidad de Sevilla Group of Nonlinear Physics ISBN: 978-84-09-05975-1 Quodons in Mica 2013 Meeting in honour of Prof. Mike Russell. Index 1. Introduction. 3. JFR Archilla, SMM Coelho, FD Auret, V Dubinko and V Hizhnyakov. Experimental observation of moving discrete breathers in germanium. 5. L Brzihik. Bisolectrons in harmonic and anharmonic lattices. 6. AP Chetverikov. Solitons and charge transport in triangular and quadratic Morse lattices. 7. LA Cisneros-Ake. Travelling coherent structures in the electron transport in 2D anharmonic crystal lattices. 8. SMM Coelho, FD Auret, JM Nel and JFR Archilla. The origin of defects induced in ultra-pure germanium by Electron Beam Deposition. 10. S Comorosan and M Apostol. Theory vs. Reality - Localized excitations induced by optical manipulation of proteins, as a different approach to link experiments with theory. 12. L Cruzeiro. The amide I band of crystalline acetanilide: old data under new light. 13. SV Dmitriev and AA Kistanov. Moving discrete breathers in crystals with NaCl structure. 15. V Dubinko, JFR Archilla, SMM Coelho and V Hizhnyakov. Modeling of the annealing of radiation-induced defects in germanium by moving discrete breathers. 16. JC Eilbeck. Numerical simulations of nonlinear modes in mica: past, present and future. 17. A Ferrando, C Mili´an, DE Ceballos-Herrera and Dmitry V. Skryabin. Soliplasmon resonances at metal-dielectric interfaces. 19. YuB Gaididei. Energy localization in nonlinear systems with flexible geometry. 20. D Hennig. Existence and non-existence of breather solutions in damped and driven nonlinear lattices. 21. P Jason and M Johansson. Existence, dynamics and mobility of Quantum Compactons in an extended Bose-Hubbard model. 22. N. Jim´enez, JFR Archilla, Y. Kosevich, V. S´anchez-Morcillo and LM Garc´ıa-Raffi. A crowdion in mica. Between K40 recoil and transmission sputtering. 24. M Johansson. Strongly localized moving discrete solitons (breathers): new ways to beat the Peierls- Nabarro barrier. 26. YA Kosevich and AV Savin. Energy transport in molecular chains with combined anharmonic potentials of pair interatomic interaction. 28. B Malomed, C Mej´ıa-Cort´es and RA Vicencio. Mobile discrete solitons in the one-dimensional lattice with the cubic-quintic nonlinearity. 29. FM Russell. Recording process in iron-rich muscovite crystals. 30. L Salasnich. Bright solitons of attractive Bose-Einstein condensates confined in quasi-1D optical lattice. 31. V S´anchez-Morcillo, LM Garc´ıa-Raffi, V. Romero-Garc´ıa, R. Pic´o, A. Cebrecos, and Kestutis Staliunas. Wave localization in chirped sonic crystals. 32. P Selyschev, V Sugakov and T Didenko. Peculiarities of the change of temperature and heat transfer under irradiation. 33. K Staliunas. Taming of Modulation Instability: Manipulation, and Complete Suppression of Instability by Spatio-Temporal Periodic Modulation. 34. G Tsironis. Gain-Driven Breathers in PT −Symmetric Metamaterials. 36. JAD Wattis and IA Butt. Moving breather modes in two-dimensional lattices. ISBN: 978-84-09-05975-1, Altea, Spain, 18/09/2013. c CC-BY-ND 4.0 by Quodons in Mica 2013 and the authors of each abstract. Quodons in Mica 2013 Meeting in honour of Prof. Mike Russell. Experimental observation of moving discrete breathers in Germanium Juan FR Archilla1, Sergio M. M. Coelho2, F. Danie Auret2, Vladimir Dubinko3and Vladimir Hizhnyakov4 1Group of Nonlinear Physics, University of Sevilla, Spain, Email: archil[email protected] 2Department of Physics, University of Pretoria, Pretoria, South Africa 3Kharkov Physical-Technical Institute, Kharkov, Ukraine 4Institute of Physics, University of Tartu, Estonia Keywords: ILM, breather, electric traps, germanium, DLTS Abstract Los energy ICP Plasma produce Atoms that arrive at a semiconductor surface with very low energy (2-8 eV) but are able to anneal defects deep inside the semiconductor [1], as shown in the figure. The number of defects before and after plasma irradiation is obtained through the well proven technique of Deep Level Transient Spectroscopy (DLTS) [2]. Several different defects were removed or modified in Sb-doped germanium, some of the them are known, such as the E center, which has the highest concentration. After eliminating other possibilities (electric field, light, heat) we now conclude that moving discrete breathers (DBs)[3], as a mechanism of long-distance energy transport, are the most likely cause. Stationary and moving breathers have been found recently by molecular dynamics in different materials with energies from 0.1 eV to a few eV [4,5]. The mechanism of annealing is an activated process, and discrete breathers have already been shown to accelerate this type of processes [6]. This would be a striking evidence of the importance of DBs in crystals and opens the way to further experiments to probe DB properties both in semiconductors and in the metals used for contacts. Most of the measurements have been done in germanium, but also it have been shown that similar effects take place in silicon. Acknowledgements: The authors’ research was funded by the following institutions: JFRA by project FIS2008-04848 from MICINN. SMM and FDA by the South African National Research Foundation. VH by the European Union through the European Regional Development Fund (Centre of Excellence Mesosystems: Theory and Applications. References [1] J. F. R. Archilla, S. M. M. Coelho, F. D. Auret, V. I. Dubinko, and V. Hizhnyakov, Experimental observation of moving discrete breathers in Germanium. To be published. [2] F. D. Auret, S. Coelho, G. Myburg, P. J. Janse van Rensburg and W. E. Meyer, Defect introduction in Ge during inductively coupled plasma etching and Schottky barrier diode fabrication processes Thin. Solid. Films. 518:2485, 2010. [3] S. Flach and A. Gorbach, Discrete Breathers: Advances in Theory and Applications Phys. Rep. 467:1-116, 2008. [4] M. Hass, V. Hizhnyakov, A. Shelkan, M. Klopov, and A. J. Sievers, Prediction of high-frequency intrinsic localised modes in Ni and Nb, Phys. Rev. B 84:144303, 2011. [5] V. Hizhnyakov, M Haas, A Shelkan and M Klopov, 2013, Theory and MD simulations of intrinsic localized modes and defect formation in solids Phys. Script. To appear. [6] V. I. Dubinko, P. A. Selyshchev, and J. F. R. Archilla, Reaction rate theory with account of the crystal anharmonicity, Phys. Rev. E 83:041124, 2011. 3 Figure 1: Three DLTS spectra performed in Sb-doped Ge after being damaged by 5 MeV αparticles followed by 24 hours or room temperature annealing. The labels at the right Y-axis indicate the defect concentration at the respective peaks and are meaningless otherwise. Black (thin line): before ICP; red (dashed): after 30’ ICP through an Au contact; blue (thick line): after 30’ ICP directly on Ge. See text for explanation. The highest peak at 185 K corresponds to the E center defect. 4 Quodons in Mica 2013 Meeting in honour of Prof. Mike Russell. Bisolectrons in harmonic and anharmonic lattices Larissa Brzihik1,2,3 1Bogolyubov Institute for Theoretical Physics, Metrolohichna Str., 14b, Kyiv 03680, Ukraine 2Instituto Pluridisciplinar, Universidad Complutense, Paseo Juan XXIII, 1, Madrid 28040, Spain 3Wessex Institute of Technology, Ashurst, Southampton SO40 7AA, UK E-mail: [email protected] Keywords: bisolitons, bisolectrons, anharmonic lattice, electron-lattice interaction Abstract It is shown that electron-lattice interaction leads to binding of two extra electrons (holes) with antiparallel spins in a molecular lattice into a bound bisoliton state at the intermediate values of electron-lattice coupling, when the adiabatic approximation is valid [1,2]. If the potential energy of the inter-site interactions in the lattice is harmonic, such bisolitons are stable at velocities less than the velocity of the sound. It is proved that the account of the lattice anharmonicity results in the formation of the bound bisolectron state [3-4] which is stable in the whole range of its velocities up to the velocity of the sound. Such a bisolectron propagates along the chain practically without energy dissipation and is an ideal charge carrier in quasi-one-dimensional molecular systems with moderately strong electron-lattice coupling. We show also that supersonic bisolectrons can exist in an anharmonic lattice. According to the analytical study, the envelope function of a bisolectron can have one or two maxima depending on the strength of the Coulomb repulsion between the electrons. This result is shown to explain the results of the numerical modeling of two electrons in an anharmonic lattice with Morse-type interactions between unit sites [5] within a wide range of the Coulomb interaction strength. It also agrees with other numerical data [6]. Acknowledgements:The author acknowledges the financial support from COFAA-IPN, IPN-CGPI- 20130803 and UPM. References [1] . S. Brizhik, A. S. Davydov. The electrosoliton pairing in soft molecular chains. J. Low Temp. Phys.,10, (1984) 748–753. [2] . S. Brizhik. Bisolitons in one-dimensional molecular systems. J. Low Temp. Phys.,12, (1986) 437–438. [3] . G. Velarde, L. Brizhik, A. P. Chetverikov, L. Cruzeiro, V. Ebeling, G. Roepke. On Electron Pairing In One- Dimensional Anharmonic Lattices. Int. J. Q. Chem.,112 (2012) 551–565. [4] . Brizhik, A. P. Chetverikov, V. Ebeling, G. Roepke, M. G. Velarde. Electron pairing and Coulomb repulsion in one-dimensional anharmonic lattices. Phys. Rev. B 85 (2012) 245105 (9 pp). [5] . Hennig, M. G. Velarde, W. Ebeling, A. P. Chetverikov. Compounds of paired electrons and lattice solitons moving with supersonic velocity. Phys. Rev. E 78 (2008), 066606 (9 pp). [6] . S. Dias, M. L. Lyra, and F. A. B. F. de Moura. Self-trapping of interacting electrons in crystalline nonlinear chains Eur. Phys. J. B,85 (2012) 7–15. 5 Quodons in Mica 2013 Meeting in honour of Prof. Mike Russell. Solitons and charge transport in triangular and quadratic Morse lattices Alexander P. Chetverikov1,2 1Dept. of Physics, Saratov State University, Astrakhanskaya 83, Saratov-410012, Russia E-mail: [email protected] 2Instituto Pluridisciplinar, Universidad Complutense, Paseo Juan XXIII, 1, Madrid-28040, Spain Keywords: 2d-Morse lattices, quasi-1d and horse-shoe solitons, charge transport, solectrons, tight-binding model Abstract Localized moving soliton-like excitations are considered to be potentially effective carriers for electric charges in one- and two-dimensional nonlinear lattices to model some real physical, chemical, biological substances. We study here via numerical simulations the excitation and propagation along crystallographic axes of both quasi-1d and horse-shoe supersonic solitons in triangular lattices and in quadratic lattices of particles interacting via potential Morse forces. Also soliton-like excitations are studied in quadratic lattices with additional on-site potential (cuprate-like lattices). Analysis of dispersion characteristics and solutions of the Kadomtsev-Petviashvili equation appear useful to describe properties of solitons in 2d- lattices. Then trapping of an added excess electron due to its potential quasi-electrostatic interaction with lattice particles thus forming a quasi particle soliton-electron (”solectron”) is studied in the frame of tight-binding model (TBM). It is shown that trapping of electron may be realized even if the electron is located first far enough from the soliton and its wave function is not localized (“vacuum cleaner effect”). Acknowledgements: This research was supported by the Spanish Ministerio de Ciencia e Innovacion, under Grant MAT2011-26221 and by the Ministry of Education and Science of the Russian Federation within FTP Scientific and pedagogical personnel of the innovative Russia, 2009-2013, grant 14.B37.21.0751. References [1] A.P. Chetverikov, W. Ebeling, M.G. Velarde. Properties of nano-scale soliton-like excitations in twodimensional lattice layers.Physica D, 240 (2011) 1954–1959. [2] A.P. Chetverikov, W. Ebeling, M.G. Velarde. Localized nonlinear, soliton-like waves in two-dimensional anharmonic lattices. Wave Motion, 48 (2011) 753–760. [3] A.P. Chetverikov, W. Ebeling, M.G. Velarde. Controlling fast electron transfer at the nano-scale by solitonic excitations along crystallographic axes. Eur. Phys. J. B,85, 291 (2012)1–8. 6 Quodons in Mica 2013 Meeting in honour of Prof. Mike Russell. Travelling coherent structures in the electron transport in 2D anharmonic crystal lattices Luis A. Cisneros-Ake1,2 1Department of Mathematics, Escuela Superior de F´ısica y Matem´aticas, Instituto Polit´ecnico Nacional, M´exico. 2Instituto Pluridisciplinar, Universidad Complutense de Madrid, Spain. E-mail: cisner[email protected] Keywords: Anharmonic lattice, lump solution. Abstract We study the feasibility of soliton-mediated electron transport in two dimensional (2D) anharmonic square crystal lattices. To this end we consider cubic and Morse anharmonic interactions in 2D lattices in the absence of the electron and numerically show the possibility of propagation of lump coherent structures similar to those in the Kadomtsev-Petviashvili (KP) equation. We finally insert the electron into the lattice to consider the electron-soliton bound state and numerically show the possibility of solectron formation. Acknowledgements: The author thanks the financial support from COFAA-IPN, IPN-CGPI-20130803 and UCM. 7 -0,4 -0,2 0,0 0,2 0,4 -0,4 -0,2 0,0 0,2 0,4 -0,4 -0,2 0,0 0,2 0,4 -0,4 -0,2 0,0 0,2 0,4 -0,4 -0,2 0,0 0,2 0,4 -0,4 -0,2 0,0 0,2 0,4 -0,4 -0,2 0,0 0,2 0,4 40 80 120 160 200 240 280 -0,4 -0,2 0,0 0,2 0,4 u x =u y ,Å (a) (b) u x =u y ,Å (c) u x =u y ,Å (d) u x =u y ,Å (e) u x =u y ,Å (f) u x =u y ,Å (g) ux=uy,Å (h) u x =u y ,Å t/ Figure 1: Displacements ux=uyof light atoms located along (110) direction as the functions of time. Energy exchange between light atoms of the crystal resulting in motion of the DB along (110) crystallographic direction can be seen. [3] J. F. R. Archilla, J. Cuevas, M. D. Alba, M. Naranjo and J. M. Trillo. Discrete breathers for understanding reconstructive mineral processes at low temperatures. J. Phys. Chem. B,110, 47 (2006) 24112–24120. [4] M.E. Manley, A.J. Sievers, J.W. Lynn, S.A. Kiselev, N.I. Agladze, Y. Chen, A. Llobet and A. Alatas. Intrinsic localized modes observed in the high-temperature vibrational spectrum of NaI. Phys. Rev. B 79 (2009) 134304- 134308. [5] S. A. Kiselev, A. J. Sievers. Generation of intrinsic vibrational gap modes in three-dimensional ionic crystals. Phys. Rev. B 55 (1997) 5755-5758. [6] M. E. Manley, D. L. Abernathy, N. I. Agladze and A. J. Sievers. ymmetry-breaking dynamical pattern and localization observed in the high-temperature vibrational spectrum of NaI. Scientific Reports 1(2011) 4. [7] D. Chen, S. Aubry and G.P. Tsironis. Breather mobility in discrete φ4nonlinear lattices. Phys. Rev. Lett. 77 (1996) 4776-4779. [8] L. Z. Khadeeva, S. V. Dmitriev. Discrete breathers in crystals with NaCl structure. Phys. Rev. B 81 (2010) 214306-214313. 14 Quodons in Mica 2013 Meeting in honour of Prof. Mike Russell. Modeling of the annealing of radiation-induced defects in Germanium by moving discrete breathers Vladimir Dubinko1, Juan FR Archilla2, Sergio M. M. Coelho3and Vladimir Hizhnyakov4 1Kharkov Physical-Technical Institute, Kharkov, Ukraine, Email: [email protected] 2Group of Nonlinear Physics, University of Sevilla, Spain 3Department of Physics, University of Pretoria, Pretoria, South Africa 4Institute of Physics, University of Tartu, Estonia Keywords: ILM, breather, electric traps, germanium, DLTS Abstract There is an increasing interest in the mechanism and properties of non-linear lattice vibrations in crystals, which may have large lifetimes and propagation distances, and are called intrinsic localized modes (ILM) or discrete breathers (DB) [1]. In recent theoretical works by some of the present authors, existence of sessile [2] as well as mobile DBs [3] have been demonstrated in metals by means of molecular dynamics using well defined MD potentials. An important peculiarity of this phenomenon is its low energy ranging from fractions to a few eV, which makes further investigations of low-energy collision events especially appropriate for various applications. Deep Level Transient Spectroscopy or DLTS is an especially useful technique for direct experimental observation of such phenomena in semiconductors, since it allows one to detect microstructural changes deep inside the material produced by low-energy collision events at the surface, which are analyzed in the present paper. We assume that moving DB can be trapped by structural defects thus creating trapped DB (TDB), which are shown to result in the amplification of the reaction rates involving the defects. The amplification mechanism has been proposed originally to explain anomalous low-temperature reconstructive transformations in layered silicates [4]. It is based on modification of the classical Kramers escape rate from a potential well due to a periodic modulation of the well depth (or the reaction barrier height). Then, a macroscopic reaction rate (averaged over a macroscopic number of defects) can be shown to depend on the frequency of the DB collisions with a defect resulting in the TDB formation (which is proportional to the irradiation flux) and the average TDB life-time, τTDB, during which the reaction is accelerated. Besides, it depends almost exponentially on the average TDB energy, ETDB. A quantitative comparison of the model with experimental data on annealing of E-centers in Germanium by low-energy Ar plasma (∼4 eV) [5] shows an excellent agreement at the following TDB parameters: τTDB = 10−11 s , ETDB = 0.62 eV, which seem to be a reasonable estimate for the life-time and the mean energy of TDB produced by moving DB with energies ranging from 0.5 to 5 eV. Acknowledgements: VD and JFRA acknowledge the hospitality of the Institute of Physics in Tartu, Estonia. JFRA acknowledges financial support from the project FIS2008-04848. References [1] S. Flach and A. Gorbach, Phys. Rep. 467:1, 2008. [2] M. Hass, V. Hizhnyakov, A. Shelkan, M. Klopov, and A. J. Sievers, Phys. Rev. B 84:144303, 2011. [3] V. Hizhnyakov, 2013. Private communication. To be published. [4] V. I. Dubinko, P. A. Selyshchev, and J. F. R. Archilla, Phys. Rev. E 83:041124, 2011. [5] J. F. R. Archilla, S. M. M. Coelho, F. D. Auret, V. I. Dubinko, and V. Hizhnyakov, Experimental observation of moving discrete breathers in Germanium. To be published. 15 1 Quodons in Mica 2013 Meeting in honour of Prof. Mike Russell. Numerical simulations of nonlinear modes in mica: past, present and future J. Chris Eilbeck Department of Mathematics and Maxwell Institute, Heriot-Watt University, Edinburgh EH14 4AS, UK E-mail: J.C.Eilbe[email protected] Keywords: nonlinear lattice excitations, numerical simulations Abstract Mike’s work on mica goes back to the late 60’s, but I first met him at the 1995 Solitons conference at Heriot-Watt. At that time, soliton research seemed to be getting more and more abstract, so it was refreshing to find an applied problem in nonlinear waves. Fortunately I had some postdoc money from the LOCNET EU collaboration, and we were able to enlist a very gifted Spanish post-doc, Jos´e Mar´ın, to work on the hexagonal and cubic lattice problems. It is now 15 years since the original 1D and 2D calculations from this time were carried out [1-3], so I thought it might be worthwhile to review what was achieved at that time, and what were the limitations in understanding Mike’s observations of tracks in real mica crystals. I will also look at the simple 1D numerical simulations of Mike’s groundbreaking transmission/ejection experiments around 2005 [4,5]. Although a number of other researchers have come up with new numerical simulations and experimental work in this area, I feel much more remains to be done to pin down the link between theory and experiments. I will review a program of work in hand to improve these results with higher dimensional and more detailed simulations. References [1] J. L. Mar´ın, J. C. Eilbeck, and F. M. Russell. Localized moving breathers in a 2-D hexagonal lattice. Phys. Letts. A, 248:225–229, 1998. [2] J. L. Mar´ın, F. M. Russell, and J. C. Eilbeck. Breathers in cuprate-like lattices. Phys. Letts. A, 281:21–25, 2001. [3] J. L. Mar´ın, J. C. Eilbeck, and F. M. Russell. 2-D breathers and applications. In P. L. Christiansen and M. P. Soerensen, editors, Nonlinear Science at the Dawn of the 21th Century, pages 293–306, Berlin, 2000. Springer. [4] F. M. Russell and J. C. Eilbeck. Evidence for moving breathers in a layered crystal insulator at 300k. Europhysics Letters, 78:10004, 2007. [5] Q. Dou, J. Cuevas, J. C. Eilbeck, and F. M. Russell, Breathers and kinks in a simulated crystal experiment, Discrete and Continuous Dynamical Systems - Series S, 4, 1107–1118 (2011). 16 Quodons in Mica 2013 Meeting in honour of Prof. Mike Russell. Soliplasmon resonances at metal-dielectric interfaces Albert Ferrando1, Carles Mili´an2, Daniel E. Ceballos-Herrera3and Dmitry V. Skryabin4 1Departament d’ ` Optica, Interdisciplinary Modeling Group InterTech, Universitat de Val`encia, Dr. Moliner 50, 46100 Burjassot (Val`encia), Spain E-mail: albert.ferr[email protected] 2Centre de Physique Th´eorique, CNRS, ´ Ecole Polytechnique, F-91128 Palaiseau, France 3Universidad Aut´onoma de Nuevo Le´on, Facultad de Ciencias F´ısico Matem´aticas, Avenida Universidad S/N, Cd. Universitaria, Nuevo Le´on 66450, M´exico 4Centre for Photonics and Photonic Materials, Department of Physics, University of Bath, Bath BA2 7AY, United Kingdom Keywords: Plasmonics, Nonlinear Optics, Solitons Abstract Nonlinear effects are a natural scenario in the world of plasmonic resonances. The peculiarities of the dispersion properties of surface plasmonic resonances (SPP) along with the high intensities that can be achieved close to the metal/dielectric surface open the way to interesting and peculiar nonlinear phenomena. In this presentation we will review and analyze the role played by dielectric Kerr nonlinearities and how they affect the propagation of continuous wave SPPs. We will present a variational theory that will reveal itself very useful for the physical understanding of the interplay between the dispersion properties of the SPP and Kerr nonlinearities [1]. Within the previous context, the key concept of our approach will be the soliplasmon resonance, a quasi-particle constituted by a bound state of a spatial soliton and a SPP [2] (see Figure 1). By means of our variational model, we will visualize the principal physical properties of these states: dispersion properties, classification of stationary states, soliton-plasmon coupling, etc [3]. We will compare these results with those obtained by numerically solving the full nonlinear Maxwell’s equations [4]. We will also take advantage of our variational model to clarify the different ways Kerr nonlinearities can affect SPP propagation by distinguishing soliplasmon resonances from different types of nonlinear plasmonic states. Acknowledgements: The work of AF was supported by the MINECO under the TEC2010-15327 grant. References [1] A. V. Zayats, I. I. Smolyaninov, and A. A. Maradudin. Nano-optics of surface plasmon polaritons. Phys. Rep., 408, 34 (2005) 131–314. [2] K. Y. Bliokh, Y. P. Bliokh, and A. Ferrando. Resonant plasmon-soliton interaction. Phys. Rev. A,79, 4 (2009) 041803. [3] A. Ferrando, C. Mili´an, and D. V. Skryabin. Variational theory of soliplasmon resonances. http://arxiv.org/abs/1301.4526v1. [4] C. Mili´an, D. E. Ceballos-Herrera, D. V. Skryabin and A. Ferrando. Soliton-plasmon resonances as Maxwell nonlinear bound states. Opt. Lett. ,37, 20 (2012) 4421–4423. 17 Figure 1: Characteristic example of a soliplasmon resonance propagating along a metal/Kerr interface. 18 Quodons in Mica 2013 Meeting in honour of Prof. Mike Russell. Energy localization in nonlinear systems with flexible geometry Yuri Gaididei1 1Bogolyubov Institute for Theoretical Physics,Metrologichna str. 14 B, 01413, Kiev, Ukrai E-mail: yb[email protected] Keywords: energy localization, charge-curvature interaction, shape transformation Abstract Shape transformations in driven and damped micro-electromechanical arrays are considered. Closed chains of weakly coupled charge-controlled capacitors under the action of spatially homogeneous timeperiodic external electric field are studied. The capacitors are modeled as electric dipoles which under an action of the external electric field periodically change their amplitude. The coupling between the vibrating dipoles and the bending degrees of freedom of the chain modifies the local bending rigidity of the chain. In the absence of driving the array takes a circular shape. When the driving intensity exceeds some critical level the circular shape of the aggregate becomes unstable and the chain takes the shape of an ellipse or, in general, of a polygon. The excitation energy is localized in such places where the chain is more flat. Acknowledgements: I’m grateful for inviting me to the scientific committee of the conference. 19 Quodons in Mica 2013 Meeting in honour of Prof. Mike Russell. Existence and non-existence of breather solutions in damped and driven nonlinear lattices Dirk Hennig, Department of Mathematics, University of Portsmouth, Portsmouth, PO1 3HF, UK E-mail: [email protected] Keywords: nonlinear lattices, breather solutions, localisation, pattern formation and synchronisation Abstract We investigate the existence of spatially localised solutions, in the form of discrete breathers, in general damped and driven nonlinear lattice systems of coupled oscillators. Conditions for the exponential decay of the difference between the maximal and minimal amplitudes of the oscillators are provided which proves that initial non-uniform spatial patterns representing breathers attain exponentially fast a spatially uniform state preventing the formation and/or preservation of any breather solution at all. Strikingly our results are generic in the sense that they hold for any, attractive interaction, coupling strength and on-site potential and general driving fields. Furthermore, our rigorous quantitative results establish conditions under which discrete breathers in general damped and driven nonlinear lattices can exist at all and open the way for further research on the emergent dynamical scenarios, in particular features of pattern formation, localisation and synchronisation, in coupled cell networks. 20 Quodons in Mica 2013 Meeting in honour of Prof. Mike Russell. Existence, dynamics and mobility of Quantum Compactons in an extended Bose-Hubbard model Peter Jason1, Magnus Johansson2 1Department of Physics, Chemistry and Biology (IFM), Link¨oping University, SE-581 83 Link¨oping, Sweden E-mail: p[email protected] 2Department of Physics, Chemistry and Biology (IFM), Link¨oping University, SE-581 83 Link¨oping, Sweden E-mail: [email protected] Keywords: Compacton, extended Bose-Hubbard model, Bose-Einstein condensate Abstract Lattice Compactons, discrete breathers with compact support, were found for a discrete nonlinear Schr¨odinger (DNLS) equation extended with nearest neighbour intersite nonlinearities [1], a model originally studied with waveguide arrays in mind. These compactons were shown to exhibit very good mobility if the parameters are tuned close to the compactons stability boundary. The DNLS can also be used to model the behaviour of Bose-Einstein condensates in optical lattices, and the remarkable control over the experiments in this field of research has made it possible to study the quantum mechanics of strongly correlated atoms. We will define the concept of a Quantum Lattice Compacton [2] and discuss the existence and dynamics, with special emphasis on mobility, of these in an extended Bose-Hubbard model corresponding to above-mentioned extended DNLS equation in the quantum mechanical limit. The compactons is given ’a kick’ by means of a phase-gradient and it is shown that the size of this phase is crucial for the mobility of the compactons. For small phase-gradients, corresponding to a slow coherent motion in the classical model, the time-scales of the quantum tunnelings become of the same order as the time-scale of the translational motion and the classical mobility is destroyed by quantum fluctuations. For large phase-gradients, corresponding to rapid classical motion, the classical and quantum time-scales separate so that a mobile, localized coherent quantum state can be translated many sites in the lattice already for small particle numbers of the order of 10. Acknowledgements: This project has been financed by the Swedish Research Council. References [1] M. ¨ Oster, M. Johansson, and A. Eriksson, Phys. Rev. E 67, 056606 (2003). [2] P. Jason and M. Johansson, Phys. Rev. A 85, 011603(R) (2012). 21 Quodons in Mica 2013 Meeting in honour of Prof. Mike Russell. A crowdion in mica. Between K40 recoil and transmission sputtering No´e Jim´enez1, Juan FR Archilla2, Yuriy Kosevich3, V´ıctor S´anchez-Morcillo1and Luis Miguel Garc´ıa-Raffi1 1Polytechnic University of Valencia, Spain, , E-mail: [email protected] 2Group of Nonlinear Physics, University of Sevilla, Spain 3Semenov Institute of Chemical Physics, Russian Academy of Sciences, Moscow, Russia Keywords: Kinks, lattice kinks, crowdion, silicates, muscovite, mica Abstract Tracks in mica muscovite which apparently are caused by some kind of lattice excitation [1] may have been produced by the recoil of K40. The isotope K40 can decay emitting an electron or a positron with the corresponding neutrino, the recoil energy of K40 is of about 40 eV. The experiment by Russell and Eilbeck [2] proved the transmission of localized energy along lattice lines in the K+layer. The impact of an αparticle on one side of a mica specimen led to the ejection of an unidentified atoms from the other side. Typical surface binding energies for silicates are between 3 and 5 eV. We construct a 1D model for mica, taking into account that the K+is a repulsive one, finding supersonic kinks [3] with a large range of energies and velocities, both with next-neighbour interaction and with many neighbours. The distances between ions are extremely small, but with the introduction of the ZBL repulsive short range potential, similar kinks are found again but with reasonable ion distances∼[4]. However, when a substrate potential obtained from empirical potentials is introduced there is an enormous change in kink properties. Below some characteristic energy Ecand velocity Vcthe kinks are dispersed in phonons. Above that energy, kinks loose energy into phonons until they achieve Ecand Vc, thereafter propagating without radiation. This lattice kink also called crowdion has a self-selected energy Ec30 eV, which is exactly between the recoil energy of K40 and the surface binding energy of atoms in silicates. Crowdion have been found with molecular dynamics in different materials as Ni [5] showing exceptional robustness and self-focusing properties. Acknowledgements: JFRA acknowledges financial support from the project FIS2008-04848. The work of VSM and LMGR was also supported by projects FIS2011-29731-C02-02 and MTM2012-36740-c02-02 respectively. All projects are granted by the Spanish Ministerio de Ciencia e Innovaci´on. All authors acknowledge Mike Russell for continuous discussions. 22 020 40 60 80 100 2 4 6 8 10 12 14 16 18 time (s.u.) Kink energy (s.u.) Figure 1: Large energies bring about the emission of phonons until a non-radiating lattice kink or crowdion is formed. The scaled units are equivalent to 2.8 eV. References [1] K. Kroneberger, M. Schosnig, F. M. Russell, and K.O. Groeneveld. Search for solitons in solids. Rad. Meas, 23:209–213, 1994. [2] F. M. Russell and J. C. Eilbeck. Evidence for moving breathers in a layered crystal insulator at 300K. Europhys. Lett., 78:10004, 2007. [3] Yu. A. Kosevich, R. Khomeriki, and S. Ruffo. Supersonic discrete kink-solitons and sinusoidal patterns with magic wave number in anharmonic lattices. Europhys. Lett., 66:21–27, 2004. [4] J. F. R. Archilla, Yu. A. Kosevich, N. Jim´enez, V. S´anchez-Morcillo and L.M. Garc´ı-Raffi Moving excitations in cation lattices. Ukr. Jou. Phys., 58(7):647–657, 2013. [5] A.M. Iskandarov, N. N. Medvedev, P. V. Zakharov, S. V. Dmitriev Crowdion mobility and self-focusing in 3D and 2D nickel. Comp. Mat. Sci.., 47:429, 2009. 23 Quodons in Mica 2013 Meeting in honour of Prof. Mike Russell. Bright solitons of attractive Bose-Einstein condensates confined in quasi-1D optical lattice Luca Salasnich Dipartimento di Fisica e Astronomia “Galileo Galilei”, Universita di Padova, Via Marzolo 8, 35131 Padova, Italy E-mail: [email protected] Keywords: Bose-Einstein Condensates, Bright Solitons, Optical Lattices Abstract We investigate a self-attractive Bose-Einstein condensate confined in a combination of a cigar-shaped trap and deep optical lattice acting in the axial direction by using a 1D discrete nonpolynomial Schrodinger equation (DNPSE). This 1D DNPSE, which is derived from the 3D Gross-Pitaevskii equation, admits onsite collapse unlike previously considered varieties of one-dimensional equations. We show that persistently moving bright solitons can be readily created by the application of the kick to stable on-site unstaggered solitons while staggered solitons are immobile. Acknowledgements: The fruitfull collaboration with Boris Malomed, Ljupco Hadzievski, Aleksandra Maluckov and Goran Gligoric is acknowledged. The author thanks for partial support University of Padova (Research Project ”Quantum Information with Ultracold Atoms in Optical Lattices”), Cariparo Foundation (Excellence Project ”Macroscopic Quantum Properties of Ultracold Atoms under Optical Confinement”), and Ministero Istruzione Universita Ricerca (PRIN Project ”Collective Quantum Phenomena: from Strongly-Correlated Systems to Quantum Simulators”). References [1] A. Maluckov, L. Hadzievski, B.A. Malomed, L. Salasnich, Phys. Rev. A 78, 013616 (2008). [2] G. Gligoric, A. Maluckov, L. Salasnich, B. A. Malomed, L. Hadzievski, Chaos 19, 043105 (2009). [3] L. Salasnich, J. Phys. A: Math. Theor. 42, 335205 (2009). 30 Quodons in Mica 2013 Meeting in honour of Prof. Mike Russell. Wave localization in chirped sonic crystals V´ıctor S´anchez-Morcillo1, Luis Miguel Garc´ıa-Raffi1, V. Romero-Garc´ıa1, R. Pic´o1, A. Cebrecos1, and Kestutis Staliunas2 1Universidad Politcnica de Valencia, Spain, E-mail: [email protected] 2ICREA, Departament de Fsica i Enginyeria Nuclear, UniversitatPolitcnica de Catalunya, Spain Abstract The study of wave propagation in periodic media has a long history in the field of vibrations and acoustics [1]. In recent years, after the pioneering works of Yablonovitch [2] and John [3], who discovered simultaneously the possibilities to control the light flow in periodic distribution of dielectric materials, an increasing interest appeared in the analogous structures to control both the elastic and acoustic waves using the wellknown phononic crystals (PC). By analogy with the photonic case, these periodic arrangements present acoustic band gaps (BGs), defined as frequency ranges where vibrations, sound and phonons are forbidden. A particular case of PC, is the sonic crystal (SC) [4,5] which consist of solid scatterers embedded in a fluid host medium. In this work we consider propagation in chirped sonic crystals, systems in which the lattice constant, i.e. the distance between scatterers gradually changes along the propagation direction. We propose and experimentally demonstrate a mechanism of sound wave concentration based on soft reflections in chirped sonic crystals. The reported field enhancement occurs at around particular (bright) planes in the crystal and is related to a progressive slowing down of the sound wave as it propagates along the material. At these bright planes, a substantial concentration of the energy (with a local increase up to 20 times) was obtained for a linear chirp and for frequencies around the first band gap. A simple couple mode theory is proposed that interprets and estimates the observed effects. Wave concentration energy can be applied to increase the efficiency of detectors and absorbers Acknowledgements: The work of VSM and LMGR was also supported by projects FIS2011-29731- C02-02 and MTM2012-36740-c02-02 respectively. All projects are granted by the Spanish Ministerio de Ciencia e Innovaci´on. References [1] Brillouin, L., Wave Propagation in Periodic Structures, 2nd ed. Dover,New York (1953). [2] Yablonovitch, E. , Inhibited Spontaneous Emission in Solid-State Physics and Electronics, Phys. Rev. Lett., 58, 2059 (1987). [3] John, S., Strong Localization of Photons in Certain Disordered Dielectric Superlattices,Phys. Rev. Lett., 58, 2486 (1987). [4] Mart´ınez-Sala, R., Sancho, J., S´anchez, J. V., G´omez, V., Llinares, J., and Meseguer, F., Sound Attenuation by Sculpture, Nature, 378, 241 (1995). [5] S´anchez-Perez, J. V., Caballero, D., Mart´ınez-Sala, R., Rubio, C., S´anchez-Dehesa, J., Meseguer, F., Llinares, J., and Galvez, F., Sound Attenuation by a Two-Dimensional Array of Rigid Cylinders, Phys. Rev. Lett., 80, 5325 (1998). [6] V. Romero-Garc´ıa, R. Pic´o, A. Cebrecos, V. J. S´anchez-Morcillo, and K. Staliunas, Sound enhancement in chirped sonic crystals. App. Phys. Lett. 102, 091906 (2013) 31 Quodons in Mica 2013 Meeting in honour of Prof. Mike Russell. Peculiarities of the change of temperature and heat transfer under irradiation Pavel Selyshchev1, Vladimir Sugakov2and Tatiana Didenko3 1Department of Physics, University of Pretoria, 2 Lynnwood Rd, Pretoria 0002 South Africa, E-mail: [email protected]om 2Department of Theoretical Physics, Institute for Nuclear Research, b.47, prospekt Nauky, Kiev 03680 Ukraine. Ukraine 3Physics Department, Taras Shevchenko National University of Kyiv, Volodymyr street 60,Kyiv, Ukraine Keywords: Irradiation, defects, heating, self-oscillation, auto-wave Abstract Theoretical approach to manifestation of non-linear thermoconcentration feedback in a material under irradiation is developed. This thermo-concentration nonlinear feedback is a mechanism of instability that leads to development of self-oscillations and auto-waves. The nature of the feedback is the following. The thermal energy of material increases under irradiation due to irradiation heating.At the same time the significant non-thermal energy is accumulated in the material as a result of accumulation of the radiation-induced defects (vacancies, interstitial atoms, their complexes etc.). The value of the nonthermal energy is equal to the energy of defects formation multiplied by the defect concentration. The accumulated energy is converted into thermal energy when the defects disappear as result of defect annealing (decay, recombination, and absorption by sinks). Rate of annealing is a strong (exponential) function of temperature. Let a small increase of the temperature arises as a result of small fluctuation. So the defect annealing increases, the energy that is stored by radiation defects is released into heat and the temperature of the material increases further. Thus the positive feed-back is formed. Change of materials temperature and evolution of radiation damage of material are described with a system of nonlinear differential equations. The variables of the system which describe material under irradiation are densities of different radiation defects, defect characteristics and temperature of the material. The qualitative analysis of this non-linear dynamical system is carried out. It is obtained a frequency of the self-oscillations and speed of the auto-wave. It is found conditions for which they arise and develop. The physical interpretation of obtained results is given. Acknowledgements: This project has been financed by NRF of South Africa 32 Quodons in Mica 2013 Meeting in honour of Prof. Mike Russell. Taming of Modulation Instability: Manipulation, and Complete Suppression of Instability by Spatio-Temporal Periodic Modulation Kestutis Staliunas ICREA & UPC, Barcelona, Spain, E-mail: [email protected] Keywords: Modulation instability, pattern formation. Abstract Modulation instability is at the basis of spontaneous pattern formation in many nonlinear spatially extended systems in Nature, technology, and everyday live. A variety of spatial patterns can be observed, like regular and stationary dissipative patterns, nonstationary (periodic and chaotic) patterns, fractal, and turbulent patterns. However in all cases, the very onset of the spatial patterns and of the spatiotemporal dynamics, the very initial break-up of the spatial symmetry, occurs via modulation instability: the homogeneous, the maximally symmetric state loses its stability with respect to the growing modes of spatial modulation. Therefore, a possibility of control and of suppression of modulation instability, i.e. a possibility of control of formation of spatial patterns in many systems, could be of a tremendous importance. We propose, and we show, very generally, that a proper spatio-temporal periodic modulation of the parameters of the extended system can modify, and can eventually suppress the modulation instability. We show the phenomena on a model of Complex Ginzburg-Landau Equation which is a paradigmatic model for the long-wave modulation instability. We show the effect by linear stability analysis (more precisely, by a modification of Floquet analysis), as well as by direct numerical integration of the modulated Complex Ginzburg-Landau Equation in one and two space dimensions. We discuss also a possible extension of the idea beyond the long-wave instability in Complex Ginzburg-Landau Equation: we consider the other types of spatial instabilities (Turing and short-wave parametric instabilities), and we show that the developed concept of taming of spatial instabilities work also in these cases. 33 Quodons in Mica 2013 Meeting in honour of Prof. Mike Russell. Gain-Driven Breathers in PT −Symmetric Metamaterials Giorgos P. Tsironis1, Nikos Lazarides1 1Department of Physics, University of Crete, P. O. Box 2208, 71003 Heraklion, Greece & Institute of Electronic Structure and Laser, Foundation for Research and Technology-Hellas, P.O. Box 1527, 71110 Heraklion, Greece E-mail: [email protected] Keywords: PT −Symmetry, Discrete Breathers, Loss Compensation Abstract Great research efforts have been recently focused on the development and investigation of synthetic materials that exhibit a combined PT −symmetry [1]. Naturally, the concepts and notions of PT −symmetric systems have been extended to dynamical lattices, particularly in optics [2]. However, the realization of PT −symmetric electronic circuits [3] provides a convenient platform for testing these ideas in easily accessible experimental configurations. In metamaterials, the PT −symmetry relies on balanced gain and loss that also provides loss compensation [4]. It has been demonstrated that nonlinear metamaterials support localized excitations of the breather type [5,6]. A model metamaterial that combines PT −symmetry with balanced gain and loss and in addition nonlinearity, made of split-ring resonators with alternatingly gain and loss in a dimer chain configuration, has been investigated numerically [7,8]. The particular structure of that class of nonlinear PT −metamaterials allows the generation of novel breather excitations with very long life-times that are driven solely by the gain, in a subttle balance between gain and loss. Gain-driven breathers can be excited in nonlinear PT −metamaterials either by proper initialization of the system, or by frequency chirping of an alternating external field [9]. In the latter case, the field is applied only temporarily, in order to induce instability and create several localized waveforms that will dynamically evolve into gain-driven breathers. Importantly, the energy of fundamental gain-driven breathers is concentrated predominantly on two neighboring sites, one with gain and the other with loss, while single-site breathers cannot exist. A typical fundamental breather generated by properly initializing the PT −metamaterial is shown in Fig.1, where energy oscillations that are peculiar to PT −symmetric systems can be also observed. Acknowledgements: This research was partially supported by the THALES Project ANEMOS, cofinanced by the European Union (European Social Fund - ESF) and Greek National Funds through the Operational Program ”Education and Lifelong Learning” of the National Strategic Reference Framework (NSRF) ”Investing in knowledge society through the European Social Fund”. Also supported by the Crete Center for Quantum Complexity and Nanotechnology funded by the European Union. References [1] D. W. Hook. Non-hermittian potentials and real eigenvalues. Ann. Phys. (Berlin),524 (2012) A106. 34 0 4 8 12 τ25 30 35 40 45 n 0 0.4 0.8 1.2 En 0 0.2 0.4 0.6 0.8 1 1.2 1.4 Figure 1: Spatiotemporal evolution of the energy density Enof a gain-driven breather excitation during two periods of the breather oscillation frequency.. [2] R. El-Ganainy, K. G. Makris, D. N. Christodoulides and Z. H. Musslimani. Theory of coupled optical PT −symmetric structures. Opt. Lett.,32 (2007) 2632–2634. [3] J. Schindler, A. Li, M. C. Zheng, F. M. Ellis and T. Kottos. Experimental study of active RLC circuits with PT symmetries. Phys. Rev. A,84 (2011) 040101(R). [4] A. D. Boardman, V. V. Grimalsky, Yu. S. Kivshar, S. V. Koshevaya, M. Lapine, N. M. Litchinitser, V. N. Malnev, M. Noginov, Y. G. Rapoport and V. M. Shalaev. Active and tunable metamaterials. Laser Photonics Rev.,5(2010) 287–307. [5] N. Lazarides, M. Eleftheriou and G. P. Tsironis. Discrete breathers in nonlinear magnetic metamaterials. Phys. Rev. Lett.,97 (2006) 157406 (4pp). [6] N. Lazarides, M. I. Molina and G. P. Tsironis. Breathers in one-dimensional binary metamaterial models. Physica B,405 (2010) 3007–3011. [7] N. Lazarides and G. P. Tsironis. Gain-driven discrete breathers in PT −symmetric nonlinear metamaterials. Phys. Rev. Lett.,110 (2013) 053901 (5pp). [8] G. P. Tsironis and N. Lazarides. PT −Symmetric Nonlinear Metamaterials and Zero-Dimensional Systems. arXiv:1304.0556v1 [nlin.PS] [9] M. Sato, B. E. Hubbard, A. J. Sievers, B. Ilic, D. A. Czaplewski and H. G. Graighead. Observation of locked intrinsic localized vibrational modes in a micromechanical oscillator array. Phys. Rev. Lett. 90 (2003) 044102 (4pp). 35 Quodons in Mica 2013 Meeting in honour of Prof. Mike Russell. Moving breather modes in two-dimensional lattices Jonathan AD Wattis1and Imran A Butt 1School of Mathematical Sciences, University of Nottingham, University Park, Nottingham, NG7 2RD, UK E-mail: [email protected] Keywords: discrete breathers Abstract We investigate two-dimensional FPU lattices which model the propagation of electrical charge through nonlinear capacitors and inductors. As well as the square lattice [1], we analyse the triangular-hexagonal lattice [2] and the more open honeycomb structure [5,6]; see figure 1 for illustrations. In each case we derive the 2D NLS equations which govern the shape of a breather in the slowly-varying small amplitude limit of the system. Although these lattices are simpler than their more common 2D mechanical counterparts [3], they have a number of interesting features not present in the 1D chain. For example, there is an ellipticity constraint required for breathers to exist. In 2D there is a minimum energy threshold for breathers [4], which we show is maximised for stationary breathers, and reduces as the speed of the breather increases. Also as their speed increases, the breathers change from being circularly symmetric to ellipsoidal in profile. In addition, the generation of higher harmonic modes and the isotropy is seen to depend on the geometry of the lattice.      J J J J J J J J J J J J J J J J J J J J J J J J   J J   J J     J J   J J   J J J J   J J   J J     J J   J J   J J (a) (b) (c) Figure 1: Illustrations of the lattice structures considered: (a) square, (b) triangular-hexagonal, (c) honeycomb. Acknowledgements: I am grateful to Lauren James, an undergraduate student who carried out some of the calculations as part of her final year project. 36 References [1] IA Butt & JAD Wattis. Discrete breathers in a two-dimensional Fermi-Pasta-Ulam lattice. J Phys A; Math Gen,39, 4955–4984, (2006). [2] IA Butt & JAD Wattis. Discrete breathers in a two-dimensional hexagonal Fermi-Pasta-Ulam lattice. J Phys A Math Theor,40, 1239–1264, (2007). [3] JL Marin, JC Eilbeck and FM Russell. Localised moving breathers in a 2D hexagonal lattice. Phys. Lett. A 248, 225, (1998) [4] S Flach, K Kladko and RS MacKay. Energy thresholds for discrete breathers in one-, two-, and three-dimensional lattices Phys. Rev. Lett. 78, 1207 (1997). [5] JAD Wattis & LM James. Discrete breathers in a honeycomb lattice. In preparation, (2013). [6] JAD Wattis www.maths.nottingham.ac.uk/personal/jadw/ 37