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...

Full description

Saved in:
Bibliographic Details
Published inJournal of physics. A, Mathematical and theoretical Vol. 49; no. 43; pp. 434001 - 434017
Main Authors Liu, Weigang, Täuber, Uwe C
Format Journal Article
LanguageEnglish
Published United Kingdom IOP Publishing 03.10.2016
Subjects
Online AccessGet full text
ISSN1751-8113
1751-8121
DOI10.1088/1751-8113/49/43/434001

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