Monte Carlo calculation of the current-voltage characteristi(19)

We have studied the nonlinear current-voltage characteristic of a two dimensional lattice Coulomb gas by Monte Carlo simulation. We present three different determinations of the power-law exponent $a(T)$ of the nonlinear current-voltage characteristic, $V

rangeoftemperatures.Thisprovidesalinkbetweentheequilibriumandnonequilibrium

responsepropertiesofthesystem:A nitemesoscopiclinearresistanceina nitesample

belowTcisduetothermallyactivatedvortexmotionacrosssomepotentialbarrier,generated

byinteractionswithallothervorticesinthesystem.Whena nitecurrentisimposedacross

thesystem,newnonequilibriumcon gurationsareaccessedwherevorticesaredrivenaway

fromtheirequilibriumpositionsbythe niteLorentzforce,thusgivingnonlinearresponse.

OurdatashowsthatthebarrierovercomebytheLorentzforce,givingnonlinearresponse,

isessentiallythesamebarrierasintheequilibriumcase,i.e.,thepotentialbarrierinthe

caseofa nitecurrentappearstobedeterminedbyequilibriumstatesinthesystem.This

isconsistentwiththescalingansatz,discussedabove,ofacertaincurrentlengthscale(r )

associatedwiththe nitecurrent,suchthatforlengthsshorterthanthecurrentlengthscale

anequilibriumstateisstillattained,whichgivesapotentialbarrieressentiallyequaltothat

intheequilibriumcase.

Aninterestingpossibilityarisesheretomeasure nitesizee ectsonthelinearresistance

inlithographicJosephsonjunctionarrays.Theideawouldheretotakeadvantageof nite

sizeroundings,ratherthanasusualwantthemtobeassmallaspossible,andtryingto

texperimentaldataonverysmallarraystoour nitesizescalingformulas.Thiswould

provideanunusualexperimentaltestof nitesizescaling.Itisalsoimportanttoanalyze

thedataintermsofthereducedtemperaturescale,asTcissampledependent.Accordingto

Eq.(17)itshouldbepossibletoscalethelinearresistanceofsamplesofdi erentsizesonto

asinglescalingfunctionusingtheexponenta(X)fromthenonlinearIVcharacteristics.

Ourconclusionsare:(1)Simulationofnonequilibriumvortexdynamicsallowcalculation

ofalatticesizeindependentIVexponenta(T)asafunctionoftemperatureT.(2)This

curvefora(T)agreesnicelywithexperimentsinanintervalaroundTc,andthisappearsto

bereportedhereforthe rsttime.(3)Thiscurvecanbeobtainedfromasimplephenomeno-

logicaltheoryforthenonlinearIVcharacteristic.(4)Thiscurvecanalsobeobtainedfrom

asimulationoftheequilibriumvortexdynamics.Thisprovidesausefullinkbetweendriven

di usionandequilibriumdynamicsoftwo-dimensionalvortexsystems.