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Freezing Transition in Decaying Burgers Turbulence and Random Matrix Dualities
- Source :
- EPL-Europhysics Letters, EPL-Europhysics Letters, European Physical Society/EDP Sciences/Società Italiana di Fisica/IOP Publishing, 2010, 90, pp.60004, EPL-Europhysics Letters, 2010, 90, pp.60004. ⟨10.1209/0295-5075/90/60004⟩
- Publication Year :
- 2010
- Publisher :
- arXiv, 2010.
-
Abstract
- We reveal a phase transition with decreasing viscosity $\nu$ at \nu=\nu_c>0 in one-dimensional decaying Burgers turbulence with a power-law correlated random profile of Gaussian-distributed initial velocities \sim|x-x'|^{-2}. The low-viscosity phase exhibits non-Gaussian one-point probability density of velocities, continuously dependent on \nu, reflecting a spontaneous one step replica symmetry breaking (RSB) in the associated statistical mechanics problem. We obtain the low orders cumulants analytically. Our results, which are checked numerically, are based on combining insights in the mechanism of the freezing transition in random logarithmic potentials with an extension of duality relations discovered recently in Random Matrix Theory. They are essentially non mean-field in nature as also demonstrated by the shock size distribution computed numerically and different from the short range correlated Kida model, itself well described by a mean field one step RSB ansatz. We also provide some insights for the finite viscosity behaviour of velocities in the latter model.<br />Comment: Published version, essentially restructured & misprints corrected. 6 pages, 5 figures
- Subjects :
- Phase transition
[PHYS.MPHY]Physics [physics]/Mathematical Physics [math-ph]
Phase (waves)
General Physics and Astronomy
Duality (optimization)
FOS: Physical sciences
Probability density function
01 natural sciences
010305 fluids & plasmas
[MATH.MATH-MP]Mathematics [math]/Mathematical Physics [math-ph]
0103 physical sciences
Statistical physics
Symmetry breaking
[PHYS.COND.CM-SM]Physics [physics]/Condensed Matter [cond-mat]/Statistical Mechanics [cond-mat.stat-mech]
010306 general physics
Condensed Matter - Statistical Mechanics
Mathematical Physics
Physics
Statistical Mechanics (cond-mat.stat-mech)
Turbulence
Disordered Systems and Neural Networks (cond-mat.dis-nn)
Mathematical Physics (math-ph)
Condensed Matter - Disordered Systems and Neural Networks
Nonlinear Sciences - Chaotic Dynamics
Distribution (mathematics)
[NLIN.NLIN-CD]Nonlinear Sciences [physics]/Chaotic Dynamics [nlin.CD]
Chaotic Dynamics (nlin.CD)
Random matrix
Subjects
Details
- ISSN :
- 02955075 and 12864854
- Database :
- OpenAIRE
- Journal :
- EPL-Europhysics Letters, EPL-Europhysics Letters, European Physical Society/EDP Sciences/Società Italiana di Fisica/IOP Publishing, 2010, 90, pp.60004, EPL-Europhysics Letters, 2010, 90, pp.60004. ⟨10.1209/0295-5075/90/60004⟩
- Accession number :
- edsair.doi.dedup.....3c0721dbb826c5492ee3ded293590392
- Full Text :
- https://doi.org/10.48550/arxiv.1004.5025