Critical initial-slip scaling for the noisy complex Ginzburg-Landau equation
We employ the perturbative fieldtheoretic 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 wi...
Saved in:
Published in | Journal of physics. A, Mathematical and theoretical Vol. 49; no. 43; pp. 434001 - 434017 |
---|---|
Main Authors | , |
Format | Journal Article |
Language | English |
Published |
United Kingdom
IOP Publishing
03.10.2016
|
Subjects | |
Online Access | Get full text |
ISSN | 1751-8113 1751-8121 |
DOI | 10.1088/1751-8113/49/43/434001 |
Cover
Abstract | We employ the perturbative fieldtheoretic 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 nonlinear 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 nonlinear Schrödinger 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. |
---|---|
AbstractList | We employ the perturbative fieldtheoretic 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 nonlinear 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 nonlinear Schrödinger 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. |
Author | Täuber, Uwe C Liu, Weigang |
Author_xml | – sequence: 1 givenname: Weigang surname: Liu fullname: Liu, Weigang email: qfsdy@vt.edu organization: Department of Physics & Center for Soft Matter and Biological Physics, MC 0435, Robeson Hall, 850 West Campus Drive, Virginia Tech, Blacksburg, VA 24061, USA – sequence: 2 givenname: Uwe C surname: Täuber fullname: Täuber, Uwe C email: tauber@vt.edu organization: Department of Physics & Center for Soft Matter and Biological Physics, MC 0435, Robeson Hall, 850 West Campus Drive, Virginia Tech, Blacksburg, VA 24061, USA |
BackLink | https://www.osti.gov/biblio/1328220$$D View this record in Osti.gov |
BookMark | eNqFkMtKAzEUhoNUsK2-ggQX7sbmNjdwI0WrMOBG1yHNpU2ZJmMyBevTm14QFKGbk8PJ_yWcbwQGzjsNwDVGdxhV1QSXOc4qjOmE1ROWKmUI4TMwPF4QPPjpMb0AoxhXCOUM1WQImmmwvZWihdalRrRZbG0HY5pYt4DGB9gvNXTexi2Uft21-hPOrPuab8Iia4RTYgP1x0b01rtLcG5EG_XV8RyD96fHt-lz1rzOXqYPTSZpXvRZUc4p00hSUZvKzMsas7yWWBSF0QWrsEEKMyMFUqSoVK0ZrUrFiFAlIophTcfg5vCuj73lUdpey6X0zmnZc0xJRQhKoeIQksHHGLThXbBrEbYcI74Tx3dO-M4JZzVnqe7FJfD-D5g-2O_XB2Hb0zg54NZ3fOU3wSUVp6HbfyDxK8Q7Zeg3gESQlQ |
CODEN | JPHAC5 |
CitedBy_id | crossref_primary_10_1103_PhysRevE_108_024219 crossref_primary_10_1103_PhysRevB_96_094304 crossref_primary_10_1103_PhysRevB_96_054442 crossref_primary_10_1088_1751_8121_adbc51 crossref_primary_10_1007_s10958_021_05492_2 crossref_primary_10_1103_PhysRevB_102_104425 |
Cites_doi | 10.1017/CBO9780511721687 10.1209/0295-5075/105/50001 10.1038/nature07128 10.1103/PhysRevE.72.016130 10.1007/BF01316547 10.1103/PhysRevE.85.030102 10.1088/0305-4470/26/14/006 10.1017/CBO9780511627200 10.1051/jphyscol:1976138 10.1088/0305-4470/39/24/R01 10.1103/PhysRevE.89.032146 10.1103/PhysRevX.4.021010 10.1088/0305-4470/26/20/016 10.1088/1478-3975/13/2/025005 10.1016/j.physa.2010.02.047 10.1103/PhysRevA.53.4250 10.1142/S021797929800288X 10.1038/nature05131 10.1103/RevModPhys.65.851 10.1017/CBO9781139046213 10.1103/PhysRevLett.110.195301 10.1103/RevModPhys.85.553 10.1088/1742-5468/2015/05/P05022 10.1002/andp.201200261 10.1007/BF01319383 10.1017/CBO9781139003667 10.1007/978-90-481-2869-3 10.1103/PhysRevE.83.051107 10.1007/BF01017663 10.1103/physrevx.5.011017 10.1103/PhysRevLett.111.073603 10.1038/nphys1034 10.1088/0305-4470/37/44/003 10.1088/1367-2630/13/2/023003 10.1073/pnas.1107970109 10.1103/PhysRevB.82.245315 10.1103/RevModPhys.85.299 10.1038/nature09009 10.1103/PhysRevLett.105.020602 10.1142/4733 10.1002/lpor.200810046 10.1088/0305-4470/38/18/R01 10.1103/PhysRevLett.108.110602 10.1103/RevModPhys.49.435 10.1007/BF01312880 10.1103/Physics.2.40 10.1103/PhysRevB.89.134310 10.1038/nphys1051 10.1073/pnas.1306993110 10.1103/PhysRevE.55.668 10.1038/nphys2251 10.1103/PhysRevLett.88.045702 |
ContentType | Journal Article |
Copyright | 2016 IOP Publishing Ltd |
Copyright_xml | – notice: 2016 IOP Publishing Ltd |
DBID | AAYXX CITATION OTOTI |
DOI | 10.1088/1751-8113/49/43/434001 |
DatabaseName | CrossRef OSTI.GOV |
DatabaseTitle | CrossRef |
DatabaseTitleList | |
DeliveryMethod | fulltext_linktorsrc |
Discipline | Physics |
DocumentTitleAlternate | Critical initial-slip scaling for the noisy complex Ginzburg-Landau equation |
EISSN | 1751-8121 |
ExternalDocumentID | 1328220 10_1088_1751_8113_49_43_434001 jpaaa3d9a |
GrantInformation_xml | – fundername: Basic Energy Sciences grantid: DE-FG02-09ER46613 funderid: http://dx.doi.org/10.13039/100006151 |
GroupedDBID | 1JI 4.4 5B3 5GY 5VS 5ZH 6TJ 7.M 7.Q AAGCD AAGID AAJIO AAJKP AALHV AATNI ABCXL ABHWH ABQJV ABVAM ACAFW ACGFS ACHIP ACNCT AEFHF AFYNE AKPSB ALMA_UNASSIGNED_HOLDINGS AOAED ASPBG ATQHT AVWKF AZFZN CBCFC CEBXE CJUJL CRLBU CS3 EBS EDWGO EJD EMSAF EPQRW EQZZN HAK IHE IJHAN IOP IZVLO KOT LAP M45 N5L NT- NT. PJBAE RIN RNS RO9 ROL RPA SY9 TN5 W28 AAYXX ADEQX AEINN CITATION KNG OTOTI RW3 |
ID | FETCH-LOGICAL-c356t-67b34e0c3a9f8fb791459c1a66fe6481f0d14fca0d268d9e4387d42ad702d41e3 |
IEDL.DBID | IOP |
ISSN | 1751-8113 |
IngestDate | Fri May 19 00:39:27 EDT 2023 Wed Oct 01 03:14:15 EDT 2025 Thu Apr 24 23:00:39 EDT 2025 Wed Aug 21 03:33:54 EDT 2024 Fri Jan 08 09:41:19 EST 2021 |
IsPeerReviewed | true |
IsScholarly | true |
Issue | 43 |
Language | English |
LinkModel | DirectLink |
MergedId | FETCHMERGED-LOGICAL-c356t-67b34e0c3a9f8fb791459c1a66fe6481f0d14fca0d268d9e4387d42ad702d41e3 |
Notes | JPhysA-106176.R1 USDOE Office of Science (SC), Basic Energy Sciences (BES) FG02-09ER46613; SC0002308 |
PageCount | 17 |
ParticipantIDs | iop_journals_10_1088_1751_8113_49_43_434001 crossref_citationtrail_10_1088_1751_8113_49_43_434001 crossref_primary_10_1088_1751_8113_49_43_434001 osti_scitechconnect_1328220 |
ProviderPackageCode | CITATION AAYXX |
PublicationCentury | 2000 |
PublicationDate | 2016-10-03 |
PublicationDateYYYYMMDD | 2016-10-03 |
PublicationDate_xml | – month: 10 year: 2016 text: 2016-10-03 day: 03 |
PublicationDecade | 2010 |
PublicationPlace | United Kingdom |
PublicationPlace_xml | – name: United Kingdom |
PublicationTitle | Journal of physics. A, Mathematical and theoretical |
PublicationTitleAbbrev | JPA |
PublicationTitleAlternate | J. Phys. A: Math. Theor |
PublicationYear | 2016 |
Publisher | IOP Publishing |
Publisher_xml | – name: IOP Publishing |
References | 44 45 46 47 48 Oerding K (43) 1993; 26 Gambassi A (40) 2005; 38 50 53 10 54 11 55 12 13 14 58 15 59 16 17 18 19 Vasil’ev A N (6) 2004 Diehl H W ed Domb C (56) 1986; 10 Chen S (52) 2016; 13 Keeling J (27) 2010 Folk R (7) 2006; 39 3 5 Henkel M (57) 2015; 2015 9 21 22 23 24 25 Amit D J (1) 1984 26 28 29 Ramasco J J (51) 2004; 37 Halpin-Healy T (49) 2014; 105 Chiocchetta A (41) 2016 30 Chang D E (20) 2011; 13 31 32 33 34 Zinn-Justin J (4) 2005 35 36 37 38 39 Oerding K (42) 1993; 26 Gardiner C W (60) 1999 Täuber U C (8) 2014 Itzykson C (2) 1989; vols 1, 2 |
References_xml | – year: 1984 ident: 1 publication-title: Field Theory, the Renomalization Group, and Critical Phenomenona – ident: 26 doi: 10.1017/CBO9780511721687 – volume: 105 issn: 0295-5075 year: 2014 ident: 49 publication-title: Europhys. Lett. doi: 10.1209/0295-5075/105/50001 – ident: 15 doi: 10.1038/nature07128 – ident: 36 doi: 10.1103/PhysRevE.72.016130 – year: 1999 ident: 60 publication-title: Quantum Noise – ident: 53 doi: 10.1007/BF01316547 – volume: vols 1, 2 year: 1989 ident: 2 publication-title: Statistical Field Theory – ident: 47 doi: 10.1103/PhysRevE.85.030102 – volume: 26 start-page: 3369 issn: 0305-4470 year: 1993 ident: 42 publication-title: J. Phys. A: Math. Gen. doi: 10.1088/0305-4470/26/14/006 – ident: 34 doi: 10.1017/CBO9780511627200 – ident: 54 doi: 10.1051/jphyscol:1976138 – volume: 39 start-page: R207 issn: 0305-4470 year: 2006 ident: 7 publication-title: J. Phys. A: Math. Gen. doi: 10.1088/0305-4470/39/24/R01 – ident: 48 doi: 10.1103/PhysRevE.89.032146 – ident: 28 doi: 10.1103/PhysRevX.4.021010 – volume: 26 start-page: 5295 issn: 0305-4470 year: 1993 ident: 43 publication-title: J. Phys. A: Math. Gen. doi: 10.1088/0305-4470/26/20/016 – volume: 13 issn: 1478-3975 year: 2016 ident: 52 publication-title: Phys. Biol. doi: 10.1088/1478-3975/13/2/025005 – ident: 35 doi: 10.1016/j.physa.2010.02.047 – ident: 22 doi: 10.1103/PhysRevA.53.4250 – ident: 44 doi: 10.1142/S021797929800288X – ident: 23 doi: 10.1038/nature05131 – ident: 33 doi: 10.1103/RevModPhys.65.851 – year: 2014 ident: 8 publication-title: Critical Dynamics—A Field Theory Approach to Equilibrium and Non-Equilibrium Scaling Behavior doi: 10.1017/CBO9781139046213 – ident: 30 doi: 10.1103/PhysRevLett.110.195301 – ident: 13 doi: 10.1103/RevModPhys.85.553 – volume: 2015 start-page: P05022 issn: 1742-5468 year: 2015 ident: 57 publication-title: J. Stat. Mech. doi: 10.1088/1742-5468/2015/05/P05022 – year: 2005 ident: 4 publication-title: Quantum Field Theory and Critical Phenomenona – ident: 18 doi: 10.1002/andp.201200261 – ident: 39 doi: 10.1007/BF01319383 – ident: 9 doi: 10.1017/CBO9781139003667 – ident: 10 doi: 10.1007/978-90-481-2869-3 – ident: 46 doi: 10.1103/PhysRevE.83.051107 – ident: 37 doi: 10.1007/BF01017663 – ident: 38 doi: 10.1103/physrevx.5.011017 – ident: 21 doi: 10.1103/PhysRevLett.111.073603 – ident: 32 doi: 10.1038/nphys1034 – volume: 37 start-page: 10497 issn: 0305-4470 year: 2004 ident: 51 publication-title: J. Phys. A: Math. Gen. doi: 10.1088/0305-4470/37/44/003 – volume: 13 issn: 1367-2630 year: 2011 ident: 20 publication-title: New J. Phys. doi: 10.1088/1367-2630/13/2/023003 – ident: 25 doi: 10.1073/pnas.1107970109 – volume: 10 start-page: 75 year: 1986 ident: 56 publication-title: Phase Transitions and Critical Phenomena – ident: 59 doi: 10.1103/PhysRevB.82.245315 – ident: 11 doi: 10.1103/RevModPhys.85.299 – ident: 12 doi: 10.1038/nature09009 – ident: 58 doi: 10.1103/PhysRevLett.105.020602 – ident: 3 doi: 10.1142/4733 – ident: 16 doi: 10.1002/lpor.200810046 – volume: 38 start-page: R133 issn: 0305-4470 year: 2005 ident: 40 publication-title: J. Phys. A: Math. Gen. doi: 10.1088/0305-4470/38/18/R01 – ident: 50 doi: 10.1103/PhysRevLett.108.110602 – ident: 5 doi: 10.1103/RevModPhys.49.435 – ident: 55 doi: 10.1007/BF01312880 – ident: 19 doi: 10.1103/Physics.2.40 – ident: 31 doi: 10.1103/PhysRevB.89.134310 – year: 2010 ident: 27 publication-title: Optical Generation and Control of Quantum Coherence in Semiconductor Nanostructures – ident: 24 doi: 10.1038/nphys1051 – ident: 14 doi: 10.1073/pnas.1306993110 – year: 2016 ident: 41 – ident: 45 doi: 10.1103/PhysRevE.55.668 – year: 2004 ident: 6 publication-title: The Field Theoretical Renormalization Group om Critical Behavior Theory and Stochastic Dynamics – ident: 17 doi: 10.1038/nphys2251 – ident: 29 doi: 10.1103/PhysRevLett.88.045702 |
SSID | ssj0054092 |
Score | 2.2428682 |
Snippet | We employ the perturbative fieldtheoretic renormalization group method to investigate the universal critical behavior near the continuous non-equilibrium phase... |
SourceID | osti crossref iop |
SourceType | Open Access Repository Enrichment Source Index Database Publisher |
StartPage | 434001 |
SubjectTerms | complex Ginzburg-Landau equation critical aging driven-dissipative Bose-Einstein condensation non-equilibrium relaxation renormalization group |
Title | Critical initial-slip scaling for the noisy complex Ginzburg-Landau equation |
URI | https://iopscience.iop.org/article/10.1088/1751-8113/49/43/434001 https://www.osti.gov/biblio/1328220 |
Volume | 49 |
hasFullText | 1 |
inHoldings | 1 |
isFullTextHit | |
isPrint | |
journalDatabaseRights | – providerCode: PRVIOP databaseName: IOP Science Platform customDbUrl: eissn: 1751-8121 dateEnd: 99991231 omitProxy: false ssIdentifier: ssj0054092 issn: 1751-8113 databaseCode: IOP dateStart: 20070101 isFulltext: true titleUrlDefault: https://iopscience.iop.org/ providerName: IOP Publishing |
link | http://utb.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwpV1LT9wwELYoqFIvlFIQC6X1gRvybpxMHOdYVeUl1HIAiZvlp7RilV3YrAT8-o7zQCwSQqiXKEo8iTMee76JP48JOZDWBQwscmZCahkgfGNlcIKBNqbkNinSNtvnH3FyBWfXec8mbNbCTGfd0D_E0zZRcKvCjhAnR-jwOJOcZyMoR4DHDO0QA6C1OMcVjfz070U_GCMeafZFfpLpFwm_-pwl__QB64Bj9RR72zOvc_SZmL6-LdnkZriozdA-vkjl-F8ftEHWO0xKf7YCX8iKrzbJx4YbaudfyXm_HQIdR6aRnjDEpjM6xyvo9yiiXoooklbT8fyBNhR1f0-Px9VjnMFh5_FXxYL62zan-Ba5Ovp9-euEdZswMJvlomaiMBn4xGa6DDKYouSQl5ZrIYIXIHlIHIdgdeJSIV3pIZOFg1S7IkkdcJ9tk9VqWvkdQjG0Ai51iAuoIEFjsF4YYazMQXvtxYDkveqV7TKUx40yJqqZKZdSRU2pqCkFpQI8NpoakNGT3KzN0fGmxCE2huq66_zN0j-WSuulu2rmwoDsRRtR2NIx9a6NHCVbK4z0EX8lu-962x75hKBMNITB7BtZre8Wfh-BT22-N6b9D98H8QY |
linkProvider | IOP Publishing |
linkToPdf | http://utb.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwpV1Ja9wwFBZZaOmlTTcySZvo0FvRjGU_y_KxtJksHdIcGshNaIWhwTOpPdDm1-fJ9gyZQAilF2FsPS9Py_tkffpEyCdpXcCBRc5MSC0DhG-sDE4w0MaU3CZF2ql9nouTSzi7yq82yNFqLcxs3nf9QzzshII7F_aEODnCgMeZ5DwbQTkCTDOIOkJzFzbJdo7xMzL7Tn9cLDtkxCTt3sgru-VC4UfvtRajNvE9sL-eYYu7F3nGrzqGSN0KFkbCya_hojFDe_tAzvG_P2qHvOyxKf3SGb0mG756Q561HFFbvyWT5bYIdBoZR_qaIUad0xrPYPyjiH4poklazab1X9pS1f0fejytbuNMDpvEXxYL6m86bfF35HJ89PPrCes3Y2A2y0XDRGEy8InNdBlkMEXJIS8t10IEL0DykDgOwerEpUK60kMmCwepdkWSOuA-e0-2qlnldwnFIRZwqUNcSAUJVgrrhRHGyhy0114MSL50v7K9UnncMONatTPmUqroLRW9paBUgGnrrQEZrezmnVbHkxafsUBU32zrJ3MfruXWa1cVltWA7Md6orC0owSvjVwl2ygc8SMOS_b-6WmH5PnFt7GanJ5_3ycvEKeJlkOYfSBbze-F_4hYqDEHbU2_A1yl9mc |
openUrl | ctx_ver=Z39.88-2004&ctx_enc=info%3Aofi%2Fenc%3AUTF-8&rfr_id=info%3Asid%2Fsummon.serialssolutions.com&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.atitle=Critical+initial-slip+scaling+for+the+noisy+complex+Ginzburg%E2%80%93Landau+equation&rft.jtitle=Journal+of+physics.+A%2C+Mathematical+and+theoretical&rft.au=Liu%2C+Weigang&rft.au=T%C3%A4uber%2C+Uwe+C&rft.date=2016-10-03&rft.issn=1751-8113&rft.eissn=1751-8121&rft.volume=49&rft.issue=43&rft.spage=434001&rft_id=info:doi/10.1088%2F1751-8113%2F49%2F43%2F434001&rft.externalDBID=n%2Fa&rft.externalDocID=10_1088_1751_8113_49_43_434001 |
thumbnail_l | http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/lc.gif&issn=1751-8113&client=summon |
thumbnail_m | http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/mc.gif&issn=1751-8113&client=summon |
thumbnail_s | http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/sc.gif&issn=1751-8113&client=summon |