dynamical slowing down in nonequilibrium phase...

Dynamicalslowingdowninnonequilibriumphasetransitions

FineGroup Meeting October15,2018 alfredz@mit.edu

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

!

20

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/