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Critical initial-slip scaling for the noisy complex Ginzburg-Landau equation

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dc.contributor.authorLiu, W.en
dc.contributor.authorTäuber, Uwe C.en
dc.contributor.departmentPhysicsen
dc.date.accessioned2017-01-06T15:09:46Zen
dc.date.available2017-01-06T15:09:46Zen
dc.date.issued2016-10-28en
dc.description.abstractWe employ the perturbative field-theoretic renormalization group method to investigate the universal critical behavior near the continuous non-equilibrium phase transition in the complex Ginzburg-Landau equation with additive white noise. This stochastic partial differential describes a remarkably wide range of physical systems: coupled non-linear oscillators subject to external noise near a Hopf bifurcation instability; spontaneous structure formation in non-equilibrium systems, e.g., in cyclically competing populations; and driven-dissipative Bose--Einstein condensation, realized in open systems on the interface of quantum optics and many-body physics, such as cold atomic gases and exciton-polaritons in pumped semiconductor quantum wells in optical cavities. Our starting point is a noisy, dissipative Gross-Pitaevski or non-linear Schr\"odinger equation, or equivalently purely relaxational kinetics originating from a complex-valued Landau-Ginzburg functional, which generalizes the standard equilibrium model A critical dynamics of a non-conserved complex order parameter field. We study the universal critical behavior of this system in the early stages of its relaxation from a Gaussian-weighted fully randomized initial state. In this critical aging regime, time translation invariance is broken, and the dynamics is characterized by the stationary static and dynamic critical exponents, as well as an independent `initial-slip' exponent. We show that to first order in the dimensional expansion about the upper critical dimension, this initial-slip exponent in the complex Ginzburg-Landau equation is identical to its equilibrium model A counterpart. We furthermore employ the renormalization group flow equations as well as construct a suitable complex spherical model extension to argue that this conclusion likely remains true to all orders in the perturbation expansion.en
dc.description.versionPublished versionen
dc.format.extent17 pagesen
dc.format.mimetypeapplication/pdfen
dc.identifier.doihttps://doi.org/10.1088/1751-8113/49/43/434001en
dc.identifier.issn1751-8113en
dc.identifier.issue43en
dc.identifier.urihttp://hdl.handle.net/10919/73990en
dc.identifier.volume49en
dc.language.isoenen
dc.publisherIOPen
dc.relation.urihttp://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&KeyUT=WOS:000385765100001&DestLinkType=FullRecord&DestApp=ALL_WOS&UsrCustomerID=930d57c9ac61a043676db62af60056c1en
dc.rightsIn Copyrighten
dc.rights.urihttp://rightsstatements.org/vocab/InC/1.0/en
dc.subjectPhysics, Multidisciplinaryen
dc.subjectPhysics, Mathematicalen
dc.subjectPhysicsen
dc.subjectcritical agingen
dc.subjectnon-equilibrium relaxationen
dc.subjectcomplex Ginzburg-Landau equationen
dc.subjectdriven-dissipative Bose-Einstein condensationen
dc.subjectrenormalization groupen
dc.subjectNONEQUILIBRIUM CRITICAL RELAXATIONen
dc.subjectCRITICAL-DYNAMICSen
dc.subjectSUPERCONDUCTING CIRCUITSen
dc.subjectRENORMALIZATION-GROUPen
dc.subjectQUANTUM SIMULATIONen
dc.subjectMONTE-CARLOen
dc.subjectBEHAVIORen
dc.titleCritical initial-slip scaling for the noisy complex Ginzburg-Landau equationen
dc.title.serialJournal of Physics A-Mathematical And Theoreticalen
dc.typeArticle - Refereeden
dc.type.dcmitypeTexten
pubs.organisational-group/Virginia Techen
pubs.organisational-group/Virginia Tech/All T&R Facultyen
pubs.organisational-group/Virginia Tech/Scienceen
pubs.organisational-group/Virginia Tech/Science/COS T&R Facultyen
pubs.organisational-group/Virginia Tech/Science/Physicsen

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