The DOI matches its Crossref record; 44 of the 44 references it cites were found in a registry or an index.
Collective Non-Abelian Instabilities in a Melting Color Glass Condensate
Open accessAbstract
We present first results for ($3+1$)D simulations of SU(2) Yang-Mills equations for matter expanding into the vacuum after a heavy ion collision. Violations of boost invariance cause a non-Abelian Weibel instability leading soft modes to grow with proper time $\ensuremath{\tau}$ as $\mathrm{exp}(\ensuremath{\Gamma}\sqrt{{g}^{2}\ensuremath{\mu}\ensuremath{\tau}})$, where ${g}^{2}\ensuremath{\mu}$ is a scale arising from the saturation of gluons in the nuclear wave function. The scale for the growth rate $\ensuremath{\Gamma}$ is set by a plasmon mass, defined as ${\ensuremath{\omega}}_{\mathrm{pl}}={\ensuremath{\kappa}}_{0}\sqrt{{g}^{2}\ensuremath{\mu}/\ensuremath{\tau}}$, generated dynamically in the collision. We compare the numerical ratio $\ensuremath{\Gamma}/{\ensuremath{\kappa}}_{0}$ to the corresponding value predicted by the hard thermal loop formalism for anisotropic plasmas.
Overview
The claims and statistics of this paper haven’t been checked yet.
Run the check — free, no account needed. It reads the open-access text and checks the sources it cites.
Integrity signals
Registry
Cites
Statistics
Verification
Claims the paper makes
The claims and statistics of this paper haven’t been checked yet.
Run the check — free, no account needed. It reads the open-access text and checks the sources it cites.
Claims other papers make about this one
Each is checked against this paper’s own text: does it say what the citing paper says it does?
The check wasn’t confident either way, so it gives no verdict — never disputed.
In the citing paper
“There is now a substantial body of experimental data[158, 159] that seems to confirm the presence of such large fluctuations with an impressive identification capability thanks to high performance 4 π detectors.”
From Phase Transitions in the Early and Present Universe (2006) · cites this paper as [158]
Experimental — accuracy not yet measured
Self-check
Percentages, sums and reported differences re-computed from the paper’s own numbers.
The self-check needs the paper’s full text.
Citations
Cites
Adams, J. R., Aggarwal, M. M., Ahammed, Z., Amonett, J., Anderson, B. D., Arkhipkin, D., Averichev, G. S., Badyal, S. K., Bai, Y., Balewski, J. T., et al. (2005) · Nuclear Physics A · doi:10.1016/j.nuclphysa.2005.03.085 · Cited by 3,381
Adcox, K., Adler, S. S., Afanasiev, S., Aidala, C., Ajitanand, N. N., Akiba, Y., Al-Jamel, A., Alexander, J., Amirikas, R., Aoki, K., et al. (2005) · Nuclear Physics A · doi:10.1016/j.nuclphysa.2005.03.086 · Cited by 3,025
Quark–gluon plasma and color glass condensate at RHIC? The perspective from the BRAHMS experiment
Arsene, I. C., Bearden, I. G., Beavis, D., Beşliu, C., Budick, B., Boggild, H., Chasman, C., Christensen, C. H., Christiansen, P., Cibor, J., et al. (2005) · Nuclear Physics A · doi:10.1016/j.nuclphysa.2005.02.130 · Cited by 2,256
The PHOBOS perspective on discoveries at RHIC
Back, B. B., Baker, M. D., Ballintijn, M., Barton, D. S., Becker, B., Betts, R. R., Bickley, A. A., Bindel, R., Budzanowski, A., Busza, W., et al. (2005) · Nuclear Physics A · doi:10.1016/j.nuclphysa.2005.03.084 · Cited by 2,242
Computing quark and gluon distribution functions for very large nuclei
McLerran, L., & Raju Venugopalan, B. (1994) · Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D. Particles and fields · doi:10.1103/physrevd.49.2233 · Cited by 2,044
Spontaneously Growing Transverse Waves in a Plasma Due to an Anisotropic Velocity Distribution
Weibel, E. S. (1959) · Physical Review Letters · doi:10.1103/physrevlett.2.83 · Cited by 1,713
Green’s function in the color field of a large nucleus
McLerran, L., & Raju Venugopalan, B. (1994) · Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D. Particles and fields · doi:10.1103/physrevd.50.2225 · Cited by 975
“Bottom-up” thermalization in heavy ion collisions
Baier, R., Mueller, A. H., Schiff, D., & Son, D. T. (2001) · Physics Letters B · doi:10.1016/s0370-2693(01)00191-5 · Cited by 594
Collective modes of an anisotropic quark-gluon plasma
Romatschke, P., & Strickland, M. T. (2003) · Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D. Particles and fields · doi:10.1103/physrevd.68.036004 · Cited by 477
Self-citationXu, Z., & Greiner, C. (2005) · Physical Review C · doi:10.1103/physrevc.71.064901 · Cited by 467
Flagged first, then by citations
Research works printed but not linked: 1
- P. Houvinen, 2004, Quark-Gluon Plasma 3
Cited by
Sorted by citations
Items 201–251 of 251
Multiparticle production in the Glasma at NLO and plasma instabilitiesPreprint
Venugopalan, R. (2007) · Cited by 3
Self-citationEkpyrosis and inflationary dynamics in heavy ion collisions: the role of quantum fluctuations
Dusling, K., Gelis, F., & Venugopalan, R. (2011) · Journal of Physics G Nuclear and Particle Physics · doi:10.1088/0954-3899/38/12/124120 · Cited by 2
Self-citationInitial state, parton saturation and thermalization
McLerran, L. (2014) · Nuclear Physics A · doi:10.1016/j.nuclphysa.2014.02.005 · Cited by 2
Weibel Instability Growth Rate in Magnetized Plasmas with Quasi-Relativistic Distribution Function
Hosseini, S. A., & Mahdavi, M. (2016) · Communications in Theoretical Physics · doi:10.1088/0253-6102/66/6/709 · Cited by 2
Isotropization of a longitudinally expanding system of scalar fields in the 2PI formalism
Gelis, F., & Hauksson, S. (2024) · Journal of High Energy Physics · doi:10.1007/jhep08(2024)135 · Cited by 2
“Beyond zeroth order, some loop corrections to the CGC description exhibit instabilities (i.e., an exponential growth in time) [14, 15] and need to be resummed for a consistent calculation.”
BackgroundGluon dissociation of J/ψ in anisotropic quark-gluon plasma
Mandal, M., & Roy, P. K. (2012) · Physical Review C · doi:10.1103/physrevc.86.024915 · Cited by 2
Quark-pair production in expanding glasma
Iwazaki, A. (2012) · Physical Review C · doi:10.1103/physrevc.85.034909 · Cited by 2
Schwinger mechanism with energy dissipation in “glasma”
Iwazaki, A. (2011) · Physical Review C · doi:10.1103/physrevc.84.065203 · Cited by 2
Anomalous gluon production and condensation in glasma
Iwazaki, A. (2013) · Physical Review C · doi:10.1103/physrevc.87.024903 · Cited by 2
STRONG FIELDS: FROM HIGH Z ATOMS TO THE COLOR GLASS CONDENSATE
McLerran, L. (2007) · International Journal of Modern Physics E · doi:10.1142/s0218301307006290 · Cited by 2
Khanzadeh, H., & Mahdavi, M. (2017) · Contributions to Plasma Physics · doi:10.1002/ctpp.201700010 · Cited by 2
Quantum chaos in the quantum fluid: Spectrum of initial fluctuations in the little bang
Dusling, K., Epelbaum, T., Gelis, F., & Raju Venugopalan, B. (2013) · Nuclear Physics A · doi:10.1016/j.nuclphysa.2013.02.142 · Cited by 2
Non-thermal photons from the pre-equilibrium stages
Garcia-Montero, O. (2020) · Journal of Physics Conference Series · doi:10.1088/1742-6596/1667/1/012008 · Cited by 2
Multiparticle production in the Glasma at NLO and plasma instabilities
Venugopalan, R. (2007) · Journal of Physics G Nuclear and Particle Physics · doi:10.1088/0954-3899/34/8/s56 · Cited by 2
Self-citationAn analytic study towards instabilities of the glasma
Fujii, H., & Kazunori Itakura, A. (2011) · Indian Journal of Physics · doi:10.1007/s12648-011-0021-y · Cited by 2
Visualizing Color Plasma Instabilities
Strickland, M. T. (2005) · CERN Document Server (European Organization for Nuclear Research) · Cited by 2
On the negative coupling O(N) model in 2d at high temperature
Romatschke, P. (2025) · Journal of High Energy Physics · doi:10.1007/jhep04(2025)012 · Cited by 1
Self-citationImpact of anisotropy on the QCD phase structure and transport coefficients of quark matter
Singh, D., & Kumar, A. (2026) · Physical review. D/Physical review. D. · doi:10.1103/phyn-xc87 · Cited by 1
The initial stages of heavy-ion collisions in the colour glass condensate framework
Gelis, F. (2015) · Pramana · doi:10.1007/s12043-015-0974-z · Cited by 1
Early isotropization of the Glasma
Epelbaum, T. (2014) · Nuclear Physics A · doi:10.1016/j.nuclphysa.2014.09.038 · Cited by 1
Unstable dynamics of Yang-Mills fields at early times of heavy ion collisions
Ipp, A. (2013) · Journal of Physics Conference Series · doi:10.1088/1742-6596/422/1/012028 · Cited by 1
COMPUTING EARLY-TIME DYNAMICS IN HEAVY ION COLLISIONS: STATUS, PROBLEMS AND PROSPECTS
VENUGOPALAN, R. (2011) · International Journal of Modern Physics Conference Series · doi:10.1142/s2010194511001541 · Cited by 1
Self-citationRaju Venugopalan, B., Dusling, K., & Mace, M. (2018) · doi:10.22323/1.308.0039 · Cited by 1
Replica evolution of classical fields in 4+1D spacetime toward real-time dynamics of quantum fields
Akira Ohnishi, A., Matsuda, H., Kunihiro, T., & TAKAHASHI, T. T. (2020) · Progress of Theoretical and Experimental Physics · doi:10.1093/ptep/ptaa172 · Cited by 1
Nonequilibrium Fermion Production in Quantum Field Theory
Pruschke, J. (2010) · Technischen Universität Darmstadt · doi:10.26083/tuprints-00002209 · Cited by 1
Pair production by boost-invariant fields in comoving coordinates
Tuchin, K. (2007) · Journal of Physics G Nuclear and Particle Physics · doi:10.1088/0954-3899/34/12/008 · Cited by 1
Chaotic thermalization in Yang-Mills-Higgs theory on a spacial lattice
Fariello, R., & Forkel, H. (2009) · Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D. Particles and fields · doi:10.1103/physrevd.80.025021 · Cited by 1
Pair production by boost-invariant fields in comoving coordinates
Tuchin, K. (2006) · CERN Document Server (European Organization for Nuclear Research) · Cited by 1
Gluon Saturation and the Formation Stage of Heavy Ion Collisions
McLerran, L. (2010) · Numerical data and functional relationships in science and technology. Group I, Elementary particles, nuclei and atoms · doi:10.1007/978-3-642-01539-7_11
New Forms of High Energy Density Matter
McLerran, L. (2013) · Springer eBooks · doi:10.1007/978-3-319-00047-3_16
The onset of hydrodynamical flow in high energy heavy ion collisions
Epelbaum, T., & Gelis, F. (2014) · Nuclear Physics A · doi:10.1016/j.nuclphysa.2014.07.014
Chromo-Weibel instabilities in classical Yang-Mills evolution
Attems, M. (2015) · Journal of Physics Conference Series · doi:10.1088/1742-6596/612/1/012015
High-Energy Heavy Ion Collisions
Monnai, A. (2014) · Springer theses · doi:10.1007/978-4-431-54798-3_2
Out-of-equilibrium dynamics of topological an anomalous effects from chiral kinetic theory
Mueller, N. (2019) · Conference on Quark Confinement and the Hadron Spectrum (Confinement) · doi:10.22323/1.336.0277
Theoretical modeling to plasma phase in heavy ion collisions
Saini, A., Bhardwaj, S., Keswani, B., Somani, A. K., & Nemade, P. N. (2020) · AIP conference proceedings · doi:10.1063/5.0001272
Romatschke, P., & Romatschke, U. (2019) · Cambridge University Press eBooks · doi:10.1017/9781108651998.004
Self-citationRiemann, Ricci, Christoffels, and All That
Romatschke, P., & Romatschke, U. (2019) · doi:10.1017/9781108651998.009
Self-citationModern Theory of Fluid Dynamics
Romatschke, P., & Romatschke, U. (2019) · Cambridge University Press eBooks · doi:10.1017/9781108651998.003
Self-citationSimulating Relativistic Nuclear Collisions
Romatschke, P., & Romatschke, U. (2019) · Cambridge University Press eBooks · doi:10.1017/9781108651998.005
Self-citationRomatschke, P., & Romatschke, U. (2019) · Cambridge University Press eBooks · doi:10.1017/9781108651998.011
Self-citationRomatschke, P., & Romatschke, U. (2019) · doi:10.1017/9781108651998.008
Self-citationRomatschke, P., & Romatschke, U. (2019) · Cambridge University Press eBooks · doi:10.1017/9781108651998.007
Self-citationRomatschke, P., & Romatschke, U. (2019) · doi:10.1017/9781108651998.010
Self-citationOutline, Notation, Preliminaries
Romatschke, P., & Romatschke, U. (2019) · Cambridge University Press eBooks · doi:10.1017/9781108651998.002
Self-citationRomatschke, P., & Romatschke, U. (2019) · doi:10.1017/9781108651998.001
Self-citationScenario of instabilities driven equilibration of the quark-gluon plasma
Mrówczyński, S. (2008) · Springer eBooks · doi:10.1007/978-3-540-72516-9_126
Romatschke, P., & Romatschke, U. (2019) · Cambridge University Press eBooks · doi:10.1017/9781108651998.012
Self-citationShaikh, W., Mandal, M., Roy, P. K., & Chattopadhyay, S. (2023) · The European Physical Journal Plus · doi:10.1140/epjp/s13360-023-04208-6
Isotropization in heavy ion collisions in the 2PI formalism
Gelis, F. (2025) · Journal of subatomic particles and cosmology. · doi:10.1016/j.jspc.2025.100222
“In the CGC, the next-to-leading order shows some trend towards isotropiza-tion, but is plagued with secular divergences due to instabilities in the solutions of linearized Yang-Mills equations [6].”
Leading Lyapunov exponent in the glasma
Pooja, Avramescu, D., & Lappi, T. (2026) · Physical review. D/Physical review. D. · doi:10.1103/6j35-n7z4
Metadata
- Authors
- Romatschke, P., & Venugopalan, R.
- Affiliations
- Bielefeld University (DE)
- ORCID
- Romatschke, Paul
- Venue
- Physical Review Letters
- Publisher
- American Physical Society (APS)
- Published
- 2006-02-14
- Volume
- 96
- Issue
- 6
- Pages
- 062302-062302
- ISSN
- 0031-9007 (ISSN-L)
- 1079-7114
- OpenAlex
- W2072867672
- Cited by
- 253
- References
- 44
- Citations by year
- 2026: 2 · 2025: 4 · 2024: 5 · 2023: 6 · 2022: 7 · 2021: 8 · 2020: 5 · 2019: 19 · 2018: 7 · 2017: 11 · 2016: 13 · 2015: 10 · 2014: 13 · 2013: 18 · 2012: 14
- FWCI
- 15.92
- Type
- journal article
- Language
- en
- Open access
- green
- arxiv.org
- Locations
- Physical Review Letters (publishedVersion)
- PubMed (publishedVersion)
- arXiv (Cornell University) (submittedVersion)
- CERN Document Server (European Organization for Nuclear Research) (submittedVersion)
- arXiv (Cornell University)
- Topics
- Physical Sciences › Physics and Astronomy › Nuclear and High Energy Physics › High-Energy Particle Collisions Research
- Physical Sciences › Physics and Astronomy › Nuclear and High Energy Physics › Quantum Chromodynamics and Particle Interactions
- Physical Sciences › Physics and Astronomy › Nuclear and High Energy Physics › Particle physics theoretical and experimental studies
- Keywords
- color glass condensate, SU(2) gauge theory, heavy-ion collisions, gluon saturation, collective instabilities, hard thermal loops, anisotropic plasma, quark-gluon plasma
About these checks
Registry, retraction, Cites and statistics results are computed, not judged, with one exception: a printed reference that no index lists is read once by a model before it counts as a citation error. Claims are extracted by a model and kept only when their quote appears verbatim in the text; each cited source is then checked, with a model’s help, for whether it says what the claim relies on. Those verdicts can be wrong — read the claim’s quote and the cited source before relying on one.
Statistics and arithmetic are recomputed, not judged.
Confidence bands are shown only for fields calibrated on our annotated test set. None is calibrated yet, so no band is shown.
What counts as a claim ›How we measure confidence ›How we check this ›
Are you an author, or do you see a problem with this page? Request a review
