Book o abs ac s. Quodons in Mica 2013
Nonlinea localized a elling exci a ions in c ys als.
Al ea, Alican e, Spain, Sep embe 18-21, 2013.
Mee ing in honou o P o . F ancis Michael Russell.
E-mail: in oquodons@up .es, u l: h p://www.quodons.webs.up .es
Hono a y chai man
F ancis Michael Russell
Chai men
Juan FR A chilla and V´ıc o S´anchez-Mo cillo
Scien i ic commi ee
Yu iy Kose ich, Yu y Gaididei, Vladimi Dubinko, V´ıc o S´anchez-Mo cillo and
Juan FR A chilla
O ganizing commi ee
Luis Miguel Ga c´ıa-Ra i, No´e Jim´enez, V´ıc o S´anchez-Mo cillo,
Juan FR A chilla and Jes´us Cue as.
Uni e si a Poli `ecnica de Val`encia:
Ins i u o Uni e si a io de Ma em´a ica Pu a y Aplicada
Ins i u o pa a la Ges i´on In eg ada de las Zonas Cos e as
Uni e sidad de Se illa
G oup o Nonlinea Physics
ISBN: 978-84-09-05975-1
Quodons in Mica 2013
Mee ing in honou o P o . Mike Russell.
Index
1. In oduc ion.
3. JFR A chilla, SMM Coelho, FD Au e , V Dubinko and V Hizhnyako . Expe imen al ob-
se a ion o mo ing disc e e b ea he s in ge manium.
5. L B zihik. Bisolec ons in ha monic and anha monic la ices.
6. AP Che e iko . Soli ons and cha ge anspo in iangula and quad a ic Mo se la ices.
7. LA Cisne os-Ake. T a elling cohe en s uc u es in he elec on anspo in 2D anha monic c ys al
la ices.
8. SMM Coelho, FD Au e , JM Nel and JFR A chilla. The o igin o de ec s induced in ul a-pu e
ge manium by Elec on Beam Deposi ion.
10. S Como osan and M Apos ol. Theo y s. Reali y - Localized exci a ions induced by op ical
manipula ion o p o eins, as a di e en app oach o link expe imen s wi h heo y.
12. L C uzei o. The amide I band o c ys alline ace anilide: old da a unde new ligh .
13. SV Dmi ie and AA Kis ano . Mo ing disc e e b ea he s in c ys als wi h NaCl s uc u e.
15. V Dubinko, JFR A chilla, SMM Coelho and V Hizhnyako . Modeling o he annealing o
adia ion-induced de ec s in ge manium by mo ing disc e e b ea he s.
16. JC Eilbeck. Nume ical simula ions o nonlinea modes in mica: pas , p esen and u u e.
17. A Fe ando, C Mili´an, DE Ceballos-He e a and Dmi y V. Sk yabin. Soliplasmon eso-
nances a me al-dielec ic in e aces.
19. YuB Gaididei. Ene gy localiza ion in nonlinea sys ems wi h lexible geome y.
20. D Hennig. Exis ence and non-exis ence o b ea he solu ions in damped and d i en nonlinea la -
ices.
21. P Jason and M Johansson. Exis ence, dynamics and mobili y o Quan um Compac ons in an
ex ended Bose-Hubba d model.
22. N. Jim´enez, JFR A chilla, Y. Kose ich, V. S´anchez-Mo cillo and LM Ga c´ıa-Ra i. A
c owdion in mica. Be ween K40 ecoil and ansmission spu e ing.
24. M Johansson. S ongly localized mo ing disc e e soli ons (b ea he s): new ways o bea he Peie ls-
Naba o ba ie .
26. YA Kose ich and AV Sa in. Ene gy anspo in molecula chains wi h combined anha monic
po en ials o pai in e a omic in e ac ion.
28. B Malomed, C Mej´ıa-Co ´es and RA Vicencio. Mobile disc e e soli ons in he one-dimensional
la ice wi h he cubic-quin ic nonlinea i y.
29. FM Russell. Reco ding p ocess in i on- ich musco i e c ys als.
30. L Salasnich. B igh soli ons o a ac i e Bose-Eins ein condensa es con ined in quasi-1D op ical
la ice.
31. V S´anchez-Mo cillo, LM Ga c´ıa-Ra i, V. Rome o-Ga c´ıa, R. Pic´o, A. Ceb ecos, and
Kes u is S aliunas. Wa e localiza ion in chi ped sonic c ys als.
32. P Selysche , V Sugako and T Didenko. Peculia i ies o he change o empe a u e and hea
ans e unde i adia ion.
33. K S aliunas. Taming o Modula ion Ins abili y: Manipula ion, and Comple e Supp ession o Ins a-
bili y by Spa io-Tempo al Pe iodic Modula ion.
34. G Tsi onis. Gain-D i en B ea he s in PT −Symme ic Me ama e ials.
36. JAD Wa is and IA Bu . Mo ing b ea he modes in wo-dimensional la ices.
ISBN: 978-84-09-05975-1, Al ea, Spain, 18/09/2013.
c
CC-BY-ND 4.0 by Quodons in Mica 2013 and he au ho s o each abs ac .
Quodons in Mica 2013
Mee ing in honou o P o . Mike Russell.
Expe imen al obse a ion o mo ing disc e e b ea he s in
Ge manium
Juan FR A chilla1, Se gio M. M. Coelho2, F. Danie Au e 2, Vladimi Dubinko3and Vladimi
Hizhnyako 4
1G oup o Nonlinea Physics, Uni e si y o Se illa, Spain, Email: a chil[email p o ec ed]
2Depa men o Physics, Uni e si y o P e o ia, P e o ia, Sou h A ica
3Kha ko Physical-Technical Ins i u e, Kha ko , Uk aine
4Ins i u e o Physics, Uni e si y o Ta u, Es onia
Keywo ds: ILM, b ea he , elec ic aps, ge manium, DLTS
Abs ac
Los ene gy ICP Plasma p oduce A oms ha a i e a a semiconduc o su ace wi h e y low ene gy
(2-8 eV) bu a e able o anneal de ec s deep inside he semiconduc o [1], as shown in he igu e. The
numbe o de ec s be o e and a e plasma i adia ion is ob ained h ough he well p o en echnique o
Deep Le el T ansien Spec oscopy (DLTS) [2].
Se e al di e en de ec s we e emo ed o modi ied in Sb-doped ge manium, some o he hem a e
known, such as he E cen e , which has he highes concen a ion. A e elimina ing o he possibili ies
(elec ic ield, ligh , hea ) we now conclude ha mo ing disc e e b ea he s (DBs)[3], as a mechanism o
long-dis ance ene gy anspo , a e he mos likely cause. S a iona y and mo ing b ea he s ha e been
ound ecen ly by molecula dynamics in di e en ma e ials wi h ene gies om 0.1 eV o a ew eV [4,5].
The mechanism o annealing is an ac i a ed p ocess, and disc e e b ea he s ha e al eady been shown o
accele a e his ype o p ocesses [6].
This would be a s iking e idence o he impo ance o DBs in c ys als and opens he way o u he
expe imen s o p obe DB p ope ies bo h in semiconduc o s and in he me als used o con ac s. Mos
o he measu emen s ha e been done in ge manium, bu also i ha e been shown ha simila e ec s ake
place in silicon.
Acknowledgemen s: The au ho s’ esea ch was unded by he ollowing ins i u ions: JFRA by p ojec
FIS2008-04848 om MICINN. SMM and FDA by he Sou h A ican Na ional Resea ch Founda ion.
VH by he Eu opean Union h ough he Eu opean Regional De elopmen Fund (Cen e o Excellence
Mesosys ems: Theo y and Applica ions.
Re e ences
[1] J. F. R. A chilla, S. M. M. Coelho, F. D. Au e , V. I. Dubinko, and V. Hizhnyako , Expe imen al obse a ion
o mo ing disc e e b ea he s in Ge manium. To be published.
[2] F. D. Au e , S. Coelho, G. Mybu g, P. J. Janse an Rensbu g and W. E. Meye , De ec in oduc ion in Ge
du ing induc i ely coupled plasma e ching and Scho ky ba ie diode ab ica ion p ocesses Thin. Solid. Films.
518:2485, 2010.
[3] S. Flach and A. Go bach, Disc e e B ea he s: Ad ances in Theo y and Applica ions Phys. Rep. 467:1-116, 2008.
[4] M. Hass, V. Hizhnyako , A. Shelkan, M. Klopo , and A. J. Sie e s, P edic ion o high- equency in insic
localised modes in Ni and Nb, Phys. Re . B 84:144303, 2011.
[5] V. Hizhnyako , M Haas, A Shelkan and M Klopo , 2013, Theo y and MD simula ions o in insic localized
modes and de ec o ma ion in solids Phys. Sc ip . To appea .
[6] V. I. Dubinko, P. A. Selyshche , and J. F. R. A chilla, Reac ion a e heo y wi h accoun o he c ys al
anha monici y, Phys. Re . E 83:041124, 2011.
3

Figu e 1: Th ee DLTS spec a pe o med in Sb-doped Ge a e being damaged by 5 MeV αpa icles
ollowed by 24 hou s o oom empe a u e annealing. The labels a he igh Y-axis indica e he de ec
concen a ion a he espec i e peaks and a e meaningless o he wise. Black ( hin line): be o e ICP; ed
(dashed): a e 30’ ICP h ough an Au con ac ; blue ( hick line): a e 30’ ICP di ec ly on Ge. See ex
o explana ion. The highes peak a 185 K co esponds o he E cen e de ec .
4
Quodons in Mica 2013
Mee ing in honou o P o . Mike Russell.
Bisolec ons in ha monic and anha monic la ices
La issa B zihik1,2,3
1Bogolyubo Ins i u e o Theo e ical Physics, Me olohichna S ., 14b, Kyi 03680, Uk aine
2Ins i u o Plu idisciplina , Uni e sidad Complu ense, Paseo Juan XXIII, 1, Mad id 28040, Spain
3Wessex Ins i u e o Technology, Ashu s , Sou hamp on SO40 7AA, UK
E-mail: [email p o ec ed]
Keywo ds: bisoli ons, bisolec ons, anha monic la ice, elec on-la ice in e ac ion
Abs ac
I is shown ha elec on-la ice in e ac ion leads o binding o wo ex a elec ons (holes) wi h an ipa allel
spins in a molecula la ice in o a bound bisoli on s a e a he in e media e alues o elec on-la ice cou-
pling, when he adiaba ic app oxima ion is alid [1,2]. I he po en ial ene gy o he in e -si e in e ac ions
in he la ice is ha monic, such bisoli ons a e s able a eloci ies less han he eloci y o he sound. I
is p o ed ha he accoun o he la ice anha monici y esul s in he o ma ion o he bound bisolec on
s a e [3-4] which is s able in he whole ange o i s eloci ies up o he eloci y o he sound. Such a
bisolec on p opaga es along he chain p ac ically wi hou ene gy dissipa ion and is an ideal cha ge ca ie
in quasi-one-dimensional molecula sys ems wi h mode a ely s ong elec on-la ice coupling. We show
also ha supe sonic bisolec ons can exis in an anha monic la ice.
Acco ding o he analy ical s udy, he en elope unc ion o a bisolec on can ha e one o wo maxima
depending on he s eng h o he Coulomb epulsion be ween he elec ons. This esul is shown o
explain he esul s o he nume ical modeling o wo elec ons in an anha monic la ice wi h Mo se- ype
in e ac ions be ween uni si es [5] wi hin a wide ange o he Coulomb in e ac ion s eng h. I also ag ees
wi h o he nume ical da a [6].
Acknowledgemen s:The au ho acknowledges he inancial suppo om COFAA-IPN, IPN-CGPI-
20130803 and UPM.
Re e ences
[1] . S. B izhik, A. S. Da ydo . The elec osoli on pai ing in so molecula chains. J. Low Temp. Phys.,10, (1984)
748–753.
[2] . S. B izhik. Bisoli ons in one-dimensional molecula sys ems. J. Low Temp. Phys.,12, (1986) 437–438.
[3] . G. Vela de, L. B izhik, A. P. Che e iko , L. C uzei o, V. Ebeling, G. Roepke. On Elec on Pai ing In One-
Dimensional Anha monic La ices. In . J. Q. Chem.,112 (2012) 551–565.
[4] . B izhik, A. P. Che e iko , V. Ebeling, G. Roepke, M. G. Vela de. Elec on pai ing and Coulomb epulsion in
one-dimensional anha monic la ices. Phys. Re . B 85 (2012) 245105 (9 pp).
[5] . Hennig, M. G. Vela de, W. Ebeling, A. P. Che e iko . Compounds o pai ed elec ons and la ice soli ons
mo ing wi h supe sonic eloci y. Phys. Re . E 78 (2008), 066606 (9 pp).
[6] . S. Dias, M. L. Ly a, and F. A. B. F. de Mou a. Sel - apping o in e ac ing elec ons in c ys alline nonlinea
chains Eu . Phys. J. B,85 (2012) 7–15.
5
Quodons in Mica 2013
Mee ing in honou o P o . Mike Russell.
Soli ons and cha ge anspo in iangula and quad a ic Mo se
la ices
Alexande P. Che e iko 1,2
1Dep . o Physics, Sa a o S a e Uni e si y, As akhanskaya 83, Sa a o -410012, Russia
E-mail: [email p o ec ed]
2Ins i u o Plu idisciplina , Uni e sidad Complu ense, Paseo Juan XXIII, 1, Mad id-28040, Spain
Keywo ds: 2d-Mo se la ices, quasi-1d and ho se-shoe soli ons, cha ge anspo , solec ons, igh -binding
model
Abs ac
Localized mo ing soli on-like exci a ions a e conside ed o be po en ially e ec i e ca ie s o elec ic
cha ges in one- and wo-dimensional nonlinea la ices o model some eal physical, chemical, biological
subs ances. We s udy he e ia nume ical simula ions he exci a ion and p opaga ion along c ys allog aphic
axes o bo h quasi-1d and ho se-shoe supe sonic soli ons in iangula la ices and in quad a ic la ices
o pa icles in e ac ing ia po en ial Mo se o ces. Also soli on-like exci a ions a e s udied in quad a ic
la ices wi h addi ional on-si e po en ial (cup a e-like la ices). Analysis o dispe sion cha ac e is ics and
solu ions o he Kadom se -Pe iash ili equa ion appea use ul o desc ibe p ope ies o soli ons in 2d-
la ices. Then apping o an added excess elec on due o i s po en ial quasi-elec os a ic in e ac ion
wi h la ice pa icles hus o ming a quasi pa icle soli on-elec on (”solec on”) is s udied in he ame o
igh -binding model (TBM). I is shown ha apping o elec on may be ealized e en i he elec on is
loca ed i s a enough om he soli on and i s wa e unc ion is no localized (“ acuum cleane e ec ”).
Acknowledgemen s: This esea ch was suppo ed by he Spanish Minis e io de Ciencia e Inno acion, un-
de G an MAT2011-26221 and by he Minis y o Educa ion and Science o he Russian Fede a ion wi hin
FTP Scien i ic and pedagogical pe sonnel o he inno a i e Russia, 2009-2013, g an 14.B37.21.0751.
Re e ences
[1] A.P. Che e iko , W. Ebeling, M.G. Vela de. P ope ies o nano-scale soli on-like exci a ions in wodimensional
la ice laye s.Physica D, 240 (2011) 1954–1959.
[2] A.P. Che e iko , W. Ebeling, M.G. Vela de. Localized nonlinea , soli on-like wa es in wo-dimensional anha -
monic la ices. Wa e Mo ion, 48 (2011) 753–760.
[3] A.P. Che e iko , W. Ebeling, M.G. Vela de. Con olling as elec on ans e a he nano-scale by soli onic
exci a ions along c ys allog aphic axes. Eu . Phys. J. B,85, 291 (2012)1–8.
6
Quodons in Mica 2013
Mee ing in honou o P o . Mike Russell.
T a elling cohe en s uc u es in he elec on anspo in 2D
anha monic c ys al la ices
Luis A. Cisne os-Ake1,2
1Depa men o Ma hema ics,
Escuela Supe io de F´ısica y Ma em´a icas,
Ins i u o Poli ´ecnico Nacional, M´exico.
2Ins i u o Plu idisciplina ,
Uni e sidad Complu ense de Mad id, Spain.
E-mail: cisne [email p o ec ed]
Keywo ds: Anha monic la ice, lump solu ion.
Abs ac
We s udy he easibili y o soli on-media ed elec on anspo in wo dimensional (2D) anha monic squa e
c ys al la ices. To his end we conside cubic and Mo se anha monic in e ac ions in 2D la ices in he
absence o he elec on and nume ically show he possibili y o p opaga ion o lump cohe en s uc u es
simila o hose in he Kadom se -Pe iash ili (KP) equa ion. We inally inse he elec on in o he
la ice o conside he elec on-soli on bound s a e and nume ically show he possibili y o solec on
o ma ion.
Acknowledgemen s: The au ho hanks he inancial suppo om COFAA-IPN, IPN-CGPI-20130803
and UCM.
7
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40 80 120 160 200 240 280
-0,4
-0,2
0,0
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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
( )
u
x
=u
y
,Å
(g)
ux=uy,Å
(h)
u
x
=u
y
,Å
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Figu e 1: Displacemen s ux=uyo ligh a oms loca ed along (110) di ec ion as he unc ions o ime.
Ene gy exchange be ween ligh a oms o he c ys al esul ing in mo ion o he DB along (110) c ys allo-
g aphic di ec ion can be seen.
[3] J. F. R. A chilla, J. Cue as, M. D. Alba, M. Na anjo and J. M. T illo. Disc e e b ea he s o unde s anding
econs uc i e mine al p ocesses a low empe a u es. J. Phys. Chem. B,110, 47 (2006) 24112–24120.
[4] M.E. Manley, A.J. Sie e s, J.W. Lynn, S.A. Kisele , N.I. Agladze, Y. Chen, A. Llobe and A. Ala as. In insic
localized modes obse ed in he high- empe a u e ib a ional spec um o NaI. Phys. Re . B 79 (2009) 134304-
134308.
[5] S. A. Kisele , A. J. Sie e s. Gene a ion o in insic ib a ional gap modes in h ee-dimensional ionic c ys als.
Phys. Re . B 55 (1997) 5755-5758.
[6] M. E. Manley, D. L. Abe na hy, N. I. Agladze and A. J. Sie e s. ymme y-b eaking dynamical pa e n and
localiza ion obse ed in he high- empe a u e ib a ional spec um o NaI. Scien i ic Repo s 1(2011) 4.
[7] D. Chen, S. Aub y and G.P. Tsi onis. B ea he mobili y in disc e e φ4nonlinea la ices. Phys. Re . Le . 77
(1996) 4776-4779.
[8] L. Z. Khadee a, S. V. Dmi ie . Disc e e b ea he s in c ys als wi h NaCl s uc u e. Phys. Re . B 81 (2010)
214306-214313.
14

Quodons in Mica 2013
Mee ing in honou o P o . Mike Russell.
Modeling o he annealing o adia ion-induced de ec s in
Ge manium by mo ing disc e e b ea he s
Vladimi Dubinko1, Juan FR A chilla2, Se gio M. M. Coelho3and Vladimi Hizhnyako 4
1Kha ko Physical-Technical Ins i u e, Kha ko , Uk aine, Email: [email p o ec ed]
2G oup o Nonlinea Physics, Uni e si y o Se illa, Spain
3Depa men o Physics, Uni e si y o P e o ia, P e o ia, Sou h A ica
4Ins i u e o Physics, Uni e si y o Ta u, Es onia
Keywo ds: ILM, b ea he , elec ic aps, ge manium, DLTS
Abs ac
The e is an inc easing in e es in he mechanism and p ope ies o non-linea la ice ib a ions in c ys als,
which may ha e la ge li e imes and p opaga ion dis ances, and a e called in insic localized modes (ILM)
o disc e e b ea he s (DB) [1]. In ecen heo e ical wo ks by some o he p esen au ho s, exis ence o
sessile [2] as well as mobile DBs [3] ha e been demons a ed in me als by means o molecula dynamics
using well de ined MD po en ials. An impo an peculia i y o his phenomenon is i s low ene gy anging
om ac ions o a ew eV, which makes u he in es iga ions o low-ene gy collision e en s especially
app op ia e o a ious applica ions. Deep Le el T ansien Spec oscopy o DLTS is an especially use ul
echnique o di ec expe imen al obse a ion o such phenomena in semiconduc o s, since i allows one
o de ec mic os uc u al changes deep inside he ma e ial p oduced by low-ene gy collision e en s a
he su ace, which a e analyzed in he p esen pape . We assume ha mo ing DB can be apped by
s uc u al de ec s hus c ea ing apped DB (TDB), which a e shown o esul in he ampli ica ion o
he eac ion a es in ol ing he de ec s. The ampli ica ion mechanism has been p oposed o iginally o
explain anomalous low- empe a u e econs uc i e ans o ma ions in laye ed silica es [4]. I is based
on modi ica ion o he classical K ame s escape a e om a po en ial well due o a pe iodic modula ion
o he well dep h (o he eac ion ba ie heigh ). Then, a mac oscopic eac ion a e (a e aged o e a
mac oscopic numbe o de ec s) can be shown o depend on he equency o he DB collisions wi h a
de ec esul ing in he TDB o ma ion (which is p opo ional o he i adia ion lux) and he a e age
TDB li e- ime, τTDB, du ing which he eac ion is accele a ed. Besides, i depends almos exponen ially
on he a e age TDB ene gy, ETDB. A quan i a i e compa ison o he model wi h expe imen al da a on
annealing o E-cen e s in Ge manium by low-ene gy A plasma (∼4 eV) [5] shows an excellen ag eemen
a he ollowing TDB pa ame e s: τTDB = 10−11 s , ETDB = 0.62 eV, which seem o be a easonable
es ima e o he li e- ime and he mean ene gy o TDB p oduced by mo ing DB wi h ene gies anging
om 0.5 o 5 eV.
Acknowledgemen s: VD and JFRA acknowledge he hospi ali y o he Ins i u e o Physics in Ta u,
Es onia. JFRA acknowledges inancial suppo om he p ojec FIS2008-04848.
Re e ences
[1] S. Flach and A. Go bach, Phys. Rep. 467:1, 2008.
[2] M. Hass, V. Hizhnyako , A. Shelkan, M. Klopo , and A. J. Sie e s, Phys. Re . B 84:144303, 2011.
[3] V. Hizhnyako , 2013. P i a e communica ion. To be published.
[4] V. I. Dubinko, P. A. Selyshche , and J. F. R. A chilla, Phys. Re . E 83:041124, 2011.
[5] J. F. R. A chilla, S. M. M. Coelho, F. D. Au e , V. I. Dubinko, and V. Hizhnyako , Expe imen al obse a ion
o mo ing disc e e b ea he s in Ge manium. To be published.
15
1
Quodons in Mica 2013
Mee ing in honou o P o . Mike Russell.
Nume ical simula ions o nonlinea modes in mica: pas , p esen
and u u e
J. Ch is Eilbeck
Depa men o Ma hema ics and Maxwell Ins i u e, He io -Wa Uni e si y, Edinbu gh EH14 4AS, UK
E-mail: J.C.Eilbe[email p o ec ed]
Keywo ds: nonlinea la ice exci a ions, nume ical simula ions
Abs ac
Mike’s wo k on mica goes back o he la e 60’s, bu I i s me him a he 1995 Soli ons con e ence a
He io -Wa . A ha ime, soli on esea ch seemed o be ge ing mo e and mo e abs ac , so i was
e eshing o ind an applied p oblem in nonlinea wa es. Fo una ely I had some pos doc money om
he LOCNET EU collabo a ion, and we we e able o enlis a e y gi ed Spanish pos -doc, Jos´e Ma ´ın,
o wo k on he hexagonal and cubic la ice p oblems. I is now 15 yea s since he o iginal 1D and 2D
calcula ions om his ime we e ca ied ou [1-3], so I hough i migh be wo hwhile o e iew wha
was achie ed a ha ime, and wha we e he limi a ions in unde s anding Mike’s obse a ions o acks
in eal mica c ys als.
I will also look a he simple 1D nume ical simula ions o Mike’s g oundb eaking ansmission/ejec ion
expe imen s a ound 2005 [4,5]. Al hough a numbe o o he esea che s ha e come up wi h new nume ical
simula ions and expe imen al wo k in his a ea, I eel much mo e emains o be done o pin down he link
be ween heo y and expe imen s. I will e iew a p og am o wo k in hand o imp o e hese esul s wi h
highe dimensional and mo e de ailed simula ions.
Re e ences
[1] J. L. Ma ´ın, J. C. Eilbeck, and F. M. Russell. Localized mo ing b ea he s in a 2-D hexagonal la ice. Phys.
Le s. A, 248:225–229, 1998.
[2] J. L. Ma ´ın, F. M. Russell, and J. C. Eilbeck. B ea he s in cup a e-like la ices. Phys. Le s. A, 281:21–25,
2001.
[3] J. L. Ma ´ın, J. C. Eilbeck, and F. M. Russell. 2-D b ea he s and applica ions. In P. L. Ch is iansen and M. P.
Soe ensen, edi o s, Nonlinea Science a he Dawn o he 21 h Cen u y, pages 293–306, Be lin, 2000. Sp inge .
[4] F. M. Russell and J. C. Eilbeck. E idence o mo ing b ea he s in a laye ed c ys al insula o a 300k. Eu ophysics
Le e s, 78:10004, 2007.
[5] Q. Dou, J. Cue as, J. C. Eilbeck, and F. M. Russell, B ea he s and kinks in a simula ed c ys al expe imen ,
Disc e e and Con inuous Dynamical Sys ems - Se ies S, 4, 1107–1118 (2011).
16
Quodons in Mica 2013
Mee ing in honou o P o . Mike Russell.
Soliplasmon esonances a me al-dielec ic in e aces
Albe Fe ando1, Ca les Mili´an2, Daniel E. Ceballos-He e a3and Dmi y V. Sk yabin4
1Depa amen d’ `
Op ica, In e disciplina y Modeling G oup In e Tech, Uni e si a de Val`encia, D . Moline 50,
46100 Bu jasso (Val`encia), Spain
E-mail: albe . e [email p o ec ed]
2Cen e de Physique Th´eo ique, CNRS, ´
Ecole Poly echnique, F-91128 Palaiseau, F ance
3Uni e sidad Au ´onoma de Nue o Le´on, Facul ad de Ciencias F´ısico Ma em´a icas, A enida Uni e sidad S/N, Cd.
Uni e si a ia, Nue o Le´on 66450, M´exico
4Cen e o Pho onics and Pho onic Ma e ials, Depa men o Physics, Uni e si y o Ba h, Ba h BA2 7AY,
Uni ed Kingdom
Keywo ds: Plasmonics, Nonlinea Op ics, Soli ons
Abs ac
Nonlinea e ec s a e a na u al scena io in he wo ld o plasmonic esonances. The peculia i ies o he
dispe sion p ope ies o su ace plasmonic esonances (SPP) along wi h he high in ensi ies ha can be
achie ed close o he me al/dielec ic su ace open he way o in e es ing and peculia nonlinea phenom-
ena. In his p esen a ion we will e iew and analyze he ole played by dielec ic Ke nonlinea i ies and
how hey a ec he p opaga ion o con inuous wa e SPPs. We will p esen a a ia ional heo y ha will
e eal i sel e y use ul o he physical unde s anding o he in e play be ween he dispe sion p ope ies o
he SPP and Ke nonlinea i ies [1]. Wi hin he p e ious con ex , he key concep o ou app oach will be
he soliplasmon esonance, a quasi-pa icle cons i u ed by a bound s a e o a spa ial soli on and a SPP [2]
(see Figu e 1). By means o ou a ia ional model, we will isualize he p incipal physical p ope ies o
hese s a es: dispe sion p ope ies, classi ica ion o s a iona y s a es, soli on-plasmon coupling, e c [3].
We will compa e hese esul s wi h hose ob ained by nume ically sol ing he ull nonlinea Maxwell’s
equa ions [4]. We will also ake ad an age o ou a ia ional model o cla i y he di e en ways Ke
nonlinea i ies can a ec SPP p opaga ion by dis inguishing soliplasmon esonances om di e en ypes
o nonlinea plasmonic s a es.
Acknowledgemen s: The wo k o AF was suppo ed by he MINECO unde he TEC2010-15327 g an .
Re e ences
[1] A. V. Zaya s, I. I. Smolyanino , and A. A. Ma adudin. Nano-op ics o su ace plasmon pola i ons. Phys. Rep.,
408, 34 (2005) 131–314.
[2] K. Y. Bliokh, Y. P. Bliokh, and A. Fe ando. Resonan plasmon-soli on in e ac ion. Phys. Re . A,79, 4 (2009)
041803.
[3] A. Fe ando, C. Mili´an, and D. V. Sk yabin. Va ia ional heo y o soliplasmon esonances.
h p://a xi .o g/abs/1301.4526 1.
[4] C. Mili´an, D. E. Ceballos-He e a, D. V. Sk yabin and A. Fe ando. Soli on-plasmon esonances as Maxwell
nonlinea bound s a es. Op . Le . ,37, 20 (2012) 4421–4423.
17
Figu e 1: Cha ac e is ic example o a soliplasmon esonance p opaga ing along a me al/Ke in e ace.
18
Quodons in Mica 2013
Mee ing in honou o P o . Mike Russell.
Ene gy localiza ion in nonlinea sys ems wi h lexible geome y
Yu i Gaididei1
1Bogolyubo Ins i u e o Theo e ical Physics,Me ologichna s . 14 B, 01413, Kie , Uk ai
E-mail: yb[email p o ec ed]
Keywo ds: ene gy localiza ion, cha ge-cu a u e in e ac ion, shape ans o ma ion
Abs ac
Shape ans o ma ions in d i en and damped mic o-elec omechanical a ays a e conside ed. Closed
chains o weakly coupled cha ge-con olled capaci o s unde he ac ion o spa ially homogeneous ime-
pe iodic ex e nal elec ic ield a e s udied. The capaci o s a e modeled as elec ic dipoles which unde
an ac ion o he ex e nal elec ic ield pe iodically change hei ampli ude. The coupling be ween he
ib a ing dipoles and he bending deg ees o eedom o he chain modi ies he local bending igidi y o
he chain. In he absence o d i ing he a ay akes a ci cula shape. When he d i ing in ensi y exceeds
some c i ical le el he ci cula shape o he agg ega e becomes uns able and he chain akes he shape o
an ellipse o , in gene al, o a polygon. The exci a ion ene gy is localized in such places whe e he chain
is mo e la .
Acknowledgemen s: I’m g a e ul o in i ing me o he scien i ic commi ee o he con e ence.
19

Quodons in Mica 2013
Mee ing in honou o P o . Mike Russell.
Exis ence and non-exis ence o b ea he solu ions in damped and
d i en nonlinea la ices
Di k Hennig,
Depa men o Ma hema ics, Uni e si y o Po smou h, Po smou h, PO1 3HF, UK
E-mail: di k.hennig@po .ac.uk
Keywo ds: nonlinea la ices, b ea he solu ions, localisa ion, pa e n o ma ion and synch onisa ion
Abs ac
We in es iga e he exis ence o spa ially localised solu ions, in he o m o disc e e b ea he s, in gene al
damped and d i en nonlinea la ice sys ems o coupled oscilla o s. Condi ions o he exponen ial decay
o he di e ence be ween he maximal and minimal ampli udes o he oscilla o s a e p o ided which
p o es ha ini ial non-uni o m spa ial pa e ns ep esen ing b ea he s a ain exponen ially as a spa ially
uni o m s a e p e en ing he o ma ion and/o p ese a ion o any b ea he solu ion a all. S ikingly ou
esul s a e gene ic in he sense ha hey hold o any, a ac i e in e ac ion, coupling s eng h and on-si e
po en ial and gene al d i ing ields. Fu he mo e, ou igo ous quan i a i e esul s es ablish condi ions
unde which disc e e b ea he s in gene al damped and d i en nonlinea la ices can exis a all and
open he way o u he esea ch on he eme gen dynamical scena ios, in pa icula ea u es o pa e n
o ma ion, localisa ion and synch onisa ion, in coupled cell ne wo ks.
20
Quodons in Mica 2013
Mee ing in honou o P o . Mike Russell.
Exis ence, dynamics and mobili y o Quan um Compac ons in an
ex ended Bose-Hubba d model
Pe e Jason1, Magnus Johansson2
1Depa men o Physics, Chemis y and Biology (IFM), Link¨oping Uni e si y, SE-581 83 Link¨oping, Sweden
E-mail: p[email p o ec ed]
2Depa men o Physics, Chemis y and Biology (IFM), Link¨oping Uni e si y, SE-581 83 Link¨oping, Sweden
E-mail: [email p o ec ed]
Keywo ds: Compac on, ex ended Bose-Hubba d model, Bose-Eins ein condensa e
Abs ac
La ice Compac ons, disc e e b ea he s wi h compac suppo , we e ound o a disc e e nonlinea Sch ¨odinge
(DNLS) equa ion ex ended wi h nea es neighbou in e si e nonlinea i ies [1], a model o iginally s udied
wi h wa eguide a ays in mind. These compac ons we e shown o exhibi e y good mobili y i he pa-
ame e s a e uned close o he compac ons s abili y bounda y. The DNLS can also be used o model he
beha iou o Bose-Eins ein condensa es in op ical la ices, and he ema kable con ol o e he expe i-
men s in his ield o esea ch has made i possible o s udy he quan um mechanics o s ongly co ela ed
a oms.
We will de ine he concep o a Quan um La ice Compac on [2] and discuss he exis ence and dy-
namics, wi h special emphasis on mobili y, o hese in an ex ended Bose-Hubba d model co esponding
o abo e-men ioned ex ended DNLS equa ion in he quan um mechanical limi .
The compac ons is gi en ’a kick’ by means o a phase-g adien and i is shown ha he size o his
phase is c ucial o he mobili y o he compac ons. Fo small phase-g adien s, co esponding o a slow
cohe en mo ion in he classical model, he ime-scales o he quan um unnelings become o he same
o de as he ime-scale o he ansla ional mo ion and he classical mobili y is des oyed by quan um
luc ua ions. Fo la ge phase-g adien s, co esponding o apid classical mo ion, he classical and quan um
ime-scales sepa a e so ha a mobile, localized cohe en quan um s a e can be ansla ed many si es in
he la ice al eady o small pa icle numbe s o he o de o 10.
Acknowledgemen s: This p ojec has been inanced by he Swedish Resea ch Council.
Re e ences
[1] M. ¨
Os e , M. Johansson, and A. E iksson, Phys. Re . E 67, 056606 (2003).
[2] P. Jason and M. Johansson, Phys. Re . A 85, 011603(R) (2012).
21
Quodons in Mica 2013
Mee ing in honou o P o . Mike Russell.
A c owdion in mica. Be ween K40 ecoil and ansmission
spu e ing
No´e Jim´enez1, Juan FR A chilla2, Yu iy Kose ich3, V´ıc o S´anchez-Mo cillo1and Luis Miguel
Ga c´ıa-Ra i1
1Poly echnic Uni e si y o Valencia, Spain, , E-mail: [email p o ec ed]
2G oup o Nonlinea Physics, Uni e si y o Se illa, Spain
3Semeno Ins i u e o Chemical Physics, Russian Academy o Sciences, Moscow, Russia
Keywo ds: Kinks, la ice kinks, c owdion, silica es, musco i e, mica
Abs ac
T acks in mica musco i e which appa en ly a e caused by some kind o la ice exci a ion [1] may ha e
been p oduced by he ecoil o K40. The iso ope K40 can decay emi ing an elec on o a posi on wi h
he co esponding neu ino, he ecoil ene gy o K40 is o abou 40 eV. The expe imen by Russell and
Eilbeck [2] p o ed he ansmission o localized ene gy along la ice lines in he K+laye . The impac o
an αpa icle on one side o a mica specimen led o he ejec ion o an uniden i ied a oms om he o he
side. Typical su ace binding ene gies o silica es a e be ween 3 and 5 eV.
We cons uc a 1D model o mica, aking in o accoun ha he K+is a epulsi e one, inding
supe sonic kinks [3] wi h a la ge ange o ene gies and eloci ies, bo h wi h nex -neighbou in e ac ion and
wi h many neighbou s. The dis ances be ween ions a e ex emely small, bu wi h he in oduc ion o he
ZBL epulsi e sho ange po en ial, simila kinks a e ound again bu wi h easonable ion dis ances∼[4].
Howe e , when a subs a e po en ial ob ained om empi ical po en ials is in oduced he e is an
eno mous change in kink p ope ies. Below some cha ac e is ic ene gy Ecand eloci y Vc he kinks a e
dispe sed in phonons. Abo e ha ene gy, kinks loose ene gy in o phonons un il hey achie e Ecand Vc,
he ea e p opaga ing wi hou adia ion.
This la ice kink also called c owdion has a sel -selec ed ene gy Ec30 eV, which is exac ly be ween
he ecoil ene gy o K40 and he su ace binding ene gy o a oms in silica es.
C owdion ha e been ound wi h molecula dynamics in di e en ma e ials as Ni [5] showing excep ional
obus ness and sel - ocusing p ope ies.
Acknowledgemen s: JFRA acknowledges inancial suppo om he p ojec FIS2008-04848. The wo k
o VSM and LMGR was also suppo ed by p ojec s FIS2011-29731-C02-02 and MTM2012-36740-c02-02
espec i ely. All p ojec s a e g an ed by he Spanish Minis e io de Ciencia e Inno aci´on. All au ho s
acknowledge Mike Russell o con inuous discussions.
22
020 40 60 80 100
2
4
6
8
10
12
14
16
18
ime (s.u.)
Kink ene gy (s.u.)
Figu e 1: La ge ene gies b ing abou he emission o phonons un il a non- adia ing la ice kink o c owdion
is o med. The scaled uni s a e equi alen o 2.8 eV.
Re e ences
[1] K. K onebe ge , M. Schosnig, F. M. Russell, and K.O. G oene eld. Sea ch o soli ons in solids. Rad. Meas,
23:209–213, 1994.
[2] F. M. Russell and J. C. Eilbeck. E idence o mo ing b ea he s in a laye ed c ys al insula o a 300K. Eu ophys.
Le ., 78:10004, 2007.
[3] Yu. A. Kose ich, R. Khome iki, and S. Ru o. Supe sonic disc e e kink-soli ons and sinusoidal pa e ns wi h
magic wa e numbe in anha monic la ices. Eu ophys. Le ., 66:21–27, 2004.
[4] J. F. R. A chilla, Yu. A. Kose ich, N. Jim´enez, V. S´anchez-Mo cillo and L.M. Ga c´ı-Ra i Mo ing exci a ions
in ca ion la ices. Uk . Jou. Phys., 58(7):647–657, 2013.
[5] A.M. Iskanda o , N. N. Med ede , P. V. Zakha o , S. V. Dmi ie C owdion mobili y and sel - ocusing in 3D
and 2D nickel. Comp. Ma . Sci.., 47:429, 2009.
23
Quodons in Mica 2013
Mee ing in honou o P o . Mike Russell.
B igh soli ons o a ac i e Bose-Eins ein condensa es
con ined in quasi-1D op ical la ice
Luca Salasnich
Dipa imen o di Fisica e As onomia “Galileo Galilei”,
Uni e si a di Pado a, Via Ma zolo 8, 35131 Pado a, I aly
E-mail: [email protected]
Keywo ds: Bose-Eins ein Condensa es, B igh Soli ons, Op ical La ices
Abs ac
We in es iga e a sel -a ac i e Bose-Eins ein condensa e con ined in a combina ion o a ciga -shaped ap
and deep op ical la ice ac ing in he axial di ec ion by using a 1D disc e e nonpolynomial Sch odinge
equa ion (DNPSE). This 1D DNPSE, which is de i ed om he 3D G oss-Pi ae skii equa ion, admi s on-
si e collapse unlike p e iously conside ed a ie ies o one-dimensional equa ions. We show ha pe sis en ly
mo ing b igh soli ons can be eadily c ea ed by he applica ion o he kick o s able on-si e uns agge ed
soli ons while s agge ed soli ons a e immobile.
Acknowledgemen s: The ui ull collabo a ion wi h Bo is Malomed, Ljupco Hadzie ski, Aleksand a
Malucko and Go an Gligo ic is acknowledged. The au ho hanks o pa ial suppo Uni e si y o
Pado a (Resea ch P ojec ”Quan um In o ma ion wi h Ul acold A oms in Op ical La ices”), Ca ipa o
Founda ion (Excellence P ojec ”Mac oscopic Quan um P ope ies o Ul acold A oms unde Op ical
Con inemen ”), and Minis e o Is uzione Uni e si a Rice ca (PRIN P ojec ”Collec i e Quan um Phe-
nomena: om S ongly-Co ela ed Sys ems o Quan um Simula o s”).
Re e ences
[1] A. Malucko , L. Hadzie ski, B.A. Malomed, L. Salasnich, Phys. Re . A 78, 013616 (2008).
[2] G. Gligo ic, A. Malucko , L. Salasnich, B. A. Malomed, L. Hadzie ski, Chaos 19, 043105 (2009).
[3] L. Salasnich, J. Phys. A: Ma h. Theo . 42, 335205 (2009).
30

Quodons in Mica 2013
Mee ing in honou o P o . Mike Russell.
Wa e localiza ion in chi ped sonic c ys als
V´ıc o S´anchez-Mo cillo1, Luis Miguel Ga c´ıa-Ra i1, V. Rome o-Ga c´ıa1, R. Pic´o1, A. Ceb ecos1,
and Kes u is S aliunas2
1Uni e sidad Poli cnica de Valencia, Spain, E-mail: [email p o ec ed]
2ICREA, Depa amen de Fsica i Enginye ia Nuclea , Uni e si a Poli cnica de Ca alunya, Spain
Abs ac
The s udy o wa e p opaga ion in pe iodic media has a long his o y in he ield o ib a ions and acous ics
[1]. In ecen yea s, a e he pionee ing wo ks o Yablono i ch [2] and John [3], who disco e ed simul ane-
ously he possibili ies o con ol he ligh low in pe iodic dis ibu ion o dielec ic ma e ials, an inc easing
in e es appea ed in he analogous s uc u es o con ol bo h he elas ic and acous ic wa es using he well-
known phononic c ys als (PC). By analogy wi h he pho onic case, hese pe iodic a angemen s p esen
acous ic band gaps (BGs), de ined as equency anges whe e ib a ions, sound and phonons a e o bid-
den. A pa icula case o PC, is he sonic c ys al (SC) [4,5] which consis o solid sca e e s embedded in
a luid hos medium. In his wo k we conside p opaga ion in chi ped sonic c ys als, sys ems in which he
la ice cons an , i.e. he dis ance be ween sca e e s g adually changes along he p opaga ion di ec ion.
We p opose and expe imen ally demons a e a mechanism o sound wa e concen a ion based on so
e lec ions in chi ped sonic c ys als. The epo ed ield enhancemen occu s a a ound pa icula (b igh )
planes in he c ys al and is ela ed o a p og essi e slowing down o he sound wa e as i p opaga es along
he ma e ial. A hese b igh planes, a subs an ial concen a ion o he ene gy (wi h a local inc ease up o
20 imes) was ob ained o a linea chi p and o equencies a ound he i s band gap. A simple couple
mode heo y is p oposed ha in e p e s and es ima es he obse ed e ec s. Wa e concen a ion ene gy
can be applied o inc ease he e iciency o de ec o s and abso be s
Acknowledgemen s: The wo k o VSM and LMGR was also suppo ed by p ojec s FIS2011-29731-
C02-02 and MTM2012-36740-c02-02 espec i ely. All p ojec s a e g an ed by he Spanish Minis e io de
Ciencia e Inno aci´on.
Re e ences
[1] B illouin, L., Wa e P opaga ion in Pe iodic S uc u es, 2nd ed. Do e ,New Yo k (1953).
[2] Yablono i ch, E. , Inhibi ed Spon aneous Emission in Solid-S a e Physics and Elec onics, Phys. Re . Le ., 58,
2059 (1987).
[3] John, S., S ong Localiza ion o Pho ons in Ce ain Diso de ed Dielec ic Supe la ices,Phys. Re . Le ., 58,
2486 (1987).
[4] Ma ´ınez-Sala, R., Sancho, J., S´anchez, J. V., G´omez, V., Llina es, J., and Mesegue , F., Sound A enua ion by
Sculp u e, Na u e, 378, 241 (1995).
[5] S´anchez-Pe ez, J. V., Caballe o, D., Ma ´ınez-Sala, R., Rubio, C., S´anchez-Dehesa, J., Mesegue , F., Llina es,
J., and Gal ez, F., Sound A enua ion by a Two-Dimensional A ay o Rigid Cylinde s, Phys. Re . Le ., 80,
5325 (1998).
[6] V. Rome o-Ga c´ıa, R. Pic´o, A. Ceb ecos, V. J. S´anchez-Mo cillo, and K. S aliunas, Sound enhancemen in
chi ped sonic c ys als. App. Phys. Le . 102, 091906 (2013)
31
Quodons in Mica 2013
Mee ing in honou o P o . Mike Russell.
Peculia i ies o he change o empe a u e and hea ans e
unde i adia ion
Pa el Selyshche 1, Vladimi Sugako 2and Ta iana Didenko3
1Depa men o Physics, Uni e si y o P e o ia, 2 Lynnwood Rd, P e o ia 0002 Sou h A ica, E-mail:
[email p o ec ed]om
2Depa men o Theo e ical Physics, Ins i u e o Nuclea Resea ch, b.47, p ospek Nauky, Kie 03680 Uk aine.
Uk aine
3Physics Depa men , Ta as She chenko Na ional Uni e si y o Kyi , Volodymy s ee 60,Kyi , Uk aine
Keywo ds: I adia ion, de ec s, hea ing, sel -oscilla ion, au o-wa e
Abs ac
Theo e ical app oach o mani es a ion o non-linea he moconcen a ion eedback in a ma e ial unde
i adia ion is de eloped. This he mo-concen a ion nonlinea eedback is a mechanism o ins abili y ha
leads o de elopmen o sel -oscilla ions and au o-wa es. The na u e o he eedback is he ollowing.
The he mal ene gy o ma e ial inc eases unde i adia ion due o i adia ion hea ing.A he same ime
he signi ican non- he mal ene gy is accumula ed in he ma e ial as a esul o accumula ion o he
adia ion-induced de ec s ( acancies, in e s i ial a oms, hei complexes e c.). The alue o he non-
he mal ene gy is equal o he ene gy o de ec s o ma ion mul iplied by he de ec concen a ion. The
accumula ed ene gy is con e ed in o he mal ene gy when he de ec s disappea as esul o de ec
annealing (decay, ecombina ion, and abso p ion by sinks). Ra e o annealing is a s ong (exponen ial)
unc ion o empe a u e. Le a small inc ease o he empe a u e a ises as a esul o small luc ua ion.
So he de ec annealing inc eases, he ene gy ha is s o ed by adia ion de ec s is eleased in o hea and
he empe a u e o he ma e ial inc eases u he . Thus he posi i e eed-back is o med.
Change o ma e ials empe a u e and e olu ion o adia ion damage o ma e ial a e desc ibed wi h a
sys em o nonlinea di e en ial equa ions. The a iables o he sys em which desc ibe ma e ial unde
i adia ion a e densi ies o di e en adia ion de ec s, de ec cha ac e is ics and empe a u e o he ma-
e ial.
The quali a i e analysis o his non-linea dynamical sys em is ca ied ou . I is ob ained a equency o
he sel -oscilla ions and speed o he au o-wa e. I is ound condi ions o which hey a ise and de elop.
The physical in e p e a ion o ob ained esul s is gi en.
Acknowledgemen s: This p ojec has been inanced by NRF o Sou h A ica
32
Quodons in Mica 2013
Mee ing in honou o P o . Mike Russell.
Taming o Modula ion Ins abili y:
Manipula ion, and Comple e Supp ession o Ins abili y by
Spa io-Tempo al Pe iodic Modula ion
Kes u is S aliunas
ICREA & UPC, Ba celona, Spain, E-mail: kes u is.s aliunas@ic ea.ca
Keywo ds: Modula ion ins abili y, pa e n o ma ion.
Abs ac
Modula ion ins abili y is a he basis o spon aneous pa e n o ma ion in many nonlinea spa ially ex-
ended sys ems in Na u e, echnology, and e e yday li e. A a ie y o spa ial pa e ns can be obse ed,
like egula and s a iona y dissipa i e pa e ns, nons a iona y (pe iodic and chao ic) pa e ns, ac al,
and u bulen pa e ns. Howe e in all cases, he e y onse o he spa ial pa e ns and o he spa io-
empo al dynamics, he e y ini ial b eak-up o he spa ial symme y, occu s ia modula ion ins abili y:
he homogeneous, he maximally symme ic s a e loses i s s abili y wi h espec o he g owing modes
o spa ial modula ion. The e o e, a possibili y o con ol and o supp ession o modula ion ins abili y,
i.e. a possibili y o con ol o o ma ion o spa ial pa e ns in many sys ems, could be o a emendous
impo ance.
We p opose, and we show, e y gene ally, ha a p ope spa io- empo al pe iodic modula ion o he
pa ame e s o he ex ended sys em can modi y, and can e en ually supp ess he modula ion ins abili y. We
show he phenomena on a model o Complex Ginzbu g-Landau Equa ion which is a pa adigma ic model
o he long-wa e modula ion ins abili y. We show he e ec by linea s abili y analysis (mo e p ecisely, by
a modi ica ion o Floque analysis), as well as by di ec nume ical in eg a ion o he modula ed Complex
Ginzbu g-Landau Equa ion in one and wo space dimensions. We discuss also a possible ex ension o he
idea beyond he long-wa e ins abili y in Complex Ginzbu g-Landau Equa ion: we conside he o he ypes
o spa ial ins abili ies (Tu ing and sho -wa e pa ame ic ins abili ies), and we show ha he de eloped
concep o aming o spa ial ins abili ies wo k also in hese cases.
33
Quodons in Mica 2013
Mee ing in honou o P o . Mike Russell.
Gain-D i en B ea he s in PT −Symme ic Me ama e ials
Gio gos P. Tsi onis1, Nikos Laza ides1
1Depa men o Physics, Uni e si y o C e e, P. O. Box 2208, 71003 He aklion, G eece
&
Ins i u e o Elec onic S uc u e and Lase , Founda ion o Resea ch and Technology-Hellas, P.O. Box 1527,
71110 He aklion, G eece
E-mail: g [email protected]
Keywo ds: PT −Symme y, Disc e e B ea he s, Loss Compensa ion
Abs ac
G ea esea ch e o s ha e been ecen ly ocused on he de elopmen and in es iga ion o syn he ic ma e-
ials ha exhibi a combined PT −symme y [1]. Na u ally, he concep s and no ions o PT −symme ic
sys ems ha e been ex ended o dynamical la ices, pa icula ly in op ics [2]. Howe e , he ealiza ion
o PT −symme ic elec onic ci cui s [3] p o ides a con enien pla o m o es ing hese ideas in easily
accessible expe imen al con igu a ions. In me ama e ials, he PT −symme y elies on balanced gain and
loss ha also p o ides loss compensa ion [4].
I has been demons a ed ha nonlinea me ama e ials suppo localized exci a ions o he b ea he
ype [5,6]. A model me ama e ial ha combines PT −symme y wi h balanced gain and loss and in
addi ion nonlinea i y, made o spli - ing esona o s wi h al e na ingly gain and loss in a dime chain
con igu a ion, has been in es iga ed nume ically [7,8]. The pa icula s uc u e o ha class o nonlinea
PT −me ama e ials allows he gene a ion o no el b ea he exci a ions wi h e y long li e- imes ha a e
d i en solely by he gain, in a sub le balance be ween gain and loss.
Gain-d i en b ea he s can be exci ed in nonlinea PT −me ama e ials ei he by p ope ini ializa ion
o he sys em, o by equency chi ping o an al e na ing ex e nal ield [9]. In he la e case, he ield
is applied only empo a ily, in o de o induce ins abili y and c ea e se e al localized wa e o ms ha
will dynamically e ol e in o gain-d i en b ea he s. Impo an ly, he ene gy o undamen al gain-d i en
b ea he s is concen a ed p edominan ly on wo neighbo ing si es, one wi h gain and he o he wi h loss,
while single-si e b ea he s canno exis . A ypical undamen al b ea he gene a ed by p ope ly ini ializing
he PT −me ama e ial is shown in Fig.1, whe e ene gy oscilla ions ha a e peculia o PT −symme ic
sys ems can be also obse ed.
Acknowledgemen s: This esea ch was pa ially suppo ed by he THALES P ojec ANEMOS, co-
inanced by he Eu opean Union (Eu opean Social Fund - ESF) and G eek Na ional Funds h ough he
Ope a ional P og am ”Educa ion and Li elong Lea ning” o he Na ional S a egic Re e ence F amewo k
(NSRF) ”In es ing in knowledge socie y h ough he Eu opean Social Fund”. Also suppo ed by he
C e e Cen e o Quan um Complexi y and Nano echnology unded by he Eu opean Union.
Re e ences
[1] D. W. Hook. Non-he mi ian po en ials and eal eigen alues. Ann. Phys. (Be lin),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
Figu e 1: Spa io empo al e olu ion o he ene gy densi y Eno a gain-d i en b ea he exci a ion du ing
wo pe iods o he b ea he oscilla ion equency..
[2] R. El-Ganainy, K. G. Mak is, D. N. Ch is odoulides and Z. H. Musslimani. Theo y o coupled op ical
PT −symme ic s uc u es. Op . Le .,32 (2007) 2632–2634.
[3] J. Schindle , A. Li, M. C. Zheng, F. M. Ellis and T. Ko os. Expe imen al s udy o ac i e RLC ci cui s wi h
PT symme ies. Phys. Re . A,84 (2011) 040101(R).
[4] A. D. Boa dman, V. V. G imalsky, Yu. S. Ki sha , S. V. Koshe aya, M. Lapine, N. M. Li chini se , V. N.
Malne , M. Nogino , Y. G. Rapopo and V. M. Shalae . Ac i e and unable me ama e ials. Lase Pho onics
Re .,5(2010) 287–307.
[5] N. Laza ides, M. Ele he iou and G. P. Tsi onis. Disc e e b ea he s in nonlinea magne ic me ama e ials. Phys.
Re . Le .,97 (2006) 157406 (4pp).
[6] N. Laza ides, M. I. Molina and G. P. Tsi onis. B ea he s in one-dimensional bina y me ama e ial models.
Physica B,405 (2010) 3007–3011.
[7] N. Laza ides and G. P. Tsi onis. Gain-d i en disc e e b ea he s in PT −symme ic nonlinea me ama e ials.
Phys. Re . Le .,110 (2013) 053901 (5pp).
[8] G. P. Tsi onis and N. Laza ides. PT −Symme ic Nonlinea Me ama e ials and Ze o-Dimensional Sys ems.
a Xi :1304.0556 1 [nlin.PS]
[9] M. Sa o, B. E. Hubba d, A. J. Sie e s, B. Ilic, D. A. Czaplewski and H. G. G aighead. Obse a ion o locked
in insic localized ib a ional modes in a mic omechanical oscilla o a ay. Phys. Re . Le . 90 (2003) 044102
(4pp).
35

Quodons in Mica 2013
Mee ing in honou o P o . Mike Russell.
Mo ing b ea he modes in wo-dimensional la ices
Jona han AD Wa is1and Im an A Bu
1School o Ma hema ical Sciences, Uni e si y o No ingham, Uni e si y Pa k, No ingham, NG7 2RD, UK
E-mail: [email p o ec ed]
Keywo ds: disc e e b ea he s
Abs ac
We in es iga e wo-dimensional FPU la ices which model he p opaga ion o elec ical cha ge h ough
nonlinea capaci o s and induc o s. As well as he squa e la ice [1], we analyse he iangula -hexagonal
la ice [2] and he mo e open honeycomb s uc u e [5,6]; see igu e 1 o illus a ions. In each case we de i e
he 2D NLS equa ions which go e n he shape o a b ea he in he slowly- a ying small ampli ude limi o
he sys em. Al hough hese la ices a e simple han hei mo e common 2D mechanical coun e pa s [3],
hey ha e a numbe o in e es ing ea u es no p esen in he 1D chain. Fo example, he e is an ellip ici y
cons ain equi ed o b ea he s o exis . In 2D he e is a minimum ene gy h eshold o b ea he s [4],
which we show is maximised o s a iona y b ea he s, and educes as he speed o he b ea he inc eases.
Also as hei speed inc eases, he b ea he s change om being ci cula ly symme ic o ellipsoidal in p o ile.
In addi ion, he gene a ion o highe ha monic modes and he iso opy is seen o depend on he geome y
o he la ice.
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(a) (b) (c)
Figu e 1: Illus a ions o he la ice s uc u es conside ed: (a) squa e, (b) iangula -hexagonal, (c)
honeycomb.
Acknowledgemen s: I am g a e ul o Lau en James, an unde g adua e s uden who ca ied ou some
o he calcula ions as pa o he inal yea p ojec .
36
Re e ences
[1] IA Bu & JAD Wa is. Disc e e b ea he s in a wo-dimensional Fe mi-Pas a-Ulam la ice. J Phys A; Ma h
Gen,39, 4955–4984, (2006).
[2] IA Bu & JAD Wa is. Disc e e b ea he s in a wo-dimensional hexagonal Fe mi-Pas a-Ulam la ice. J Phys A
Ma h Theo ,40, 1239–1264, (2007).
[3] JL Ma in, JC Eilbeck and FM Russell. Localised mo ing b ea he s in a 2D hexagonal la ice. Phys. Le . A
248, 225, (1998)
[4] S Flach, K Kladko and RS MacKay. Ene gy h esholds o disc e e b ea he s in one-, wo-, and h ee-dimensional
la ices Phys. Re . Le . 78, 1207 (1997).
[5] JAD Wa is & LM James. Disc e e b ea he s in a honeycomb la ice. In p epa a ion, (2013).
[6] JAD Wa is www.ma hs.no ingham.ac.uk/pe sonal/jadw/
37