Dynamical slowing down in nonequilibrium phase...
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Dynamical slowing down in nonequilibrium phase transitions Fine Group Meeting October 15, 2018 [email protected] Alfred Zong GEDIK GROUP
Transcript of Dynamical slowing down in nonequilibrium phase...
Dynamicalslowingdowninnonequilibriumphasetransitions
FineGroup Meeting October15,2018 [email protected]
AlfredZong
GEDIK GROUP
Inphysics…Freeenergy
ψ
T >Tc
T =Tc
T <Tc
“Asthecorrelationlengthdiverges,theregionsofthesystem,whichrepresentfluctuations abouttheequilibriumstate,getlargerandlarger;correspondingly,theytakelongerandlongertorelaxbywhateveristheequilibrationmechanism(oftendiffusion).”
– NigelGoldenfeld,LecturesonPhaseTransitionsandtheRenormalizationGroup
⌧ ⇠ ⇠(T )z
@ (r)
@t= ��
�F
� (r)+ ⇣(r, t)
Time-dependentGinzburg-Landauequation:
Dynamiccriticalexponent
Fluctuations
Criticalslowingdowninequilibriumphasetransition
FrequencyTime
Cailleau etal.,J.Phys.C 12,L411(1979)
Criticalquasi-elasticscattering- Neutronscatteringonp-terphenyl- Antiferrodistorsivestructural
transitionatTc = 179.5 K- Slowing down of orientational
fluctuation
Criticalslowingdowninequilibriumphasetransition
FrequencyTime
Maschek etal.,PRB 91,235146 (2015)
Softening of collective mode- Kohn anomaly in TbTe3, TCDW = 330 K
Criticalslowingdowninequilibriumphasetransition
FrequencyTime
Iizumi,Phys. B+C 136,36 (1986)
- First-order structural transition in Sn: Tβ-α = 260 K
§ Signaturesofdynamicalslowingdownintheultrafast meltingofachargedensitywave
§ Slowingdowninothernonequilibriumregimes
EquilibriumNonequilibrium
Photo-inducedmeltingofCDWinLaTe3
e– densitylattice
Photo-inducedmeltingofCDWinLaTe3
Thresholdexcitationdensity
6420
Excitation density ( 1020 cm-3)
Slowingdownatthethreshold
Slowingdownatthethreshold
⌧edx
dt
� ↵(t)x+ x
3 + ⇣0(x� y) = 0
1
!
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d
2y
dt
2+ (y � x) = 0
Electron(x):
Lattice(y):
↵(t) = ↵0 �⇥(t)Fe�t/⌧0
Slowingdownatthethreshold
⌧edx
dt
� ↵(t)x+ x
3 + ⇣0(x� y) = 0
1
!
20
d
2y
dt
2+ (y � x) = 0
Electron(x):
Lattice(y):
↵(t) = ↵0 �⇥(t)Fe�t/⌧0
Electron(x) Lattice(y)
§ Signaturesofdynamicalslowingdownintheultrafastmeltingofachargedensitywave
§ Slowingdowninothernonequilibriumregimes
EquilibriumNonequilibrium
Inlivingsystems...
Schefferetal.,“Early-warningsignalsforcriticaltransitions”,Nature 461,53(2009)
Veraartetal.,Nature 481,357(2012)
Asimplerinteractingdynamicalsystem
Pantaleone,Am.J.Phys. 70,992(2002)Yangetal., Eur.J.Phys. 39,055004(2018)
Huygens(1665):“anoddkindofsympathy”
Phasediagramofmetronomesynchronization
Pantaleone,Am.J.Phys. 70,992(2002)
Measuringthesynchronizationtimescale
Labtime(sec)14201 204
…
Criticalbehaviornearthephaseboundary• Timetosynchronizethesystemdivergesasapowerlaw?• Therecoverytimedivergesafterperturbingasinglemetronomeinthesynchronizedstate?• Softeningofacollectivemode,ifthereisany?…...
§ Universalityofslowingdownnearaphasetransition–eveninthehighlynonequilibriumandultrafast regime§ Asimilarframeworkoftime-dependentLandauformalism
mayhelpunderstandotheraspectsofphoto-inducedphasetransitions
§ Fordriveninteractingdynamicalsystems,itmaybeinterestingtostudya“simpler”mechanicalanalogue–metronomesynchronization
• Transientopticalspectroscopy:EmreErgeçenandMehmetYilmaz• Ultrafastelectrondiffraction:TimmRohwer,I-ChengTung,HaidanWen,andtheSLACUEDteam
(XiaozheShen,JieYang,RenkaiLi,Suji Park,MatthiasHoffmann,BenjaminOfori-Okai,MichaelKozina,andXijieWang)
• Samplepreparation:Ya-QingBieandPabloJarillo-Herrero• Samplegrowthandcharacterization:JoshuaStraquadine,PhilipWalmsley,andIanFisher• Theory:PavelDolgirev,AlexanderRozhkov,andBorisFine
Acknowledgements
https://thiscondensedlife.wordpress.com/2018/08/19/critical-slowing-down/
