dorsal/arxiv
View SchemaClassical evolution of fractal measures on the lattice
| Authors | N. G. Antoniou, F. K. Diakonos, E. N. Saridakis, G. A. Tsolias |
|---|---|
| Categories | |
| ArXiv ID | physics/0610111 |
| URL | https://arxiv.org/abs/physics/0610111 |
| DOI | 10.1103/PhysRevE.75.041111 |
| Journal | Phys.Rev.E75:041111,2007 |
Abstract
We consider the classical evolution of a lattice of non-linear coupled oscillators for a special case of initial conditions resembling the equilibrium state of a macroscopic thermal system at the critical point. The displacements of the oscillators define initially a fractal measure on the lattice associated with the scaling properties of the order parameter fluctuations in the corresponding critical system. Assuming a sudden symmetry breaking (quench), leading to a change in the equilibrium position of each oscillator, we investigate in some detail the deformation of the initial fractal geometry as time evolves. In particular we show that traces of the critical fractal measure can sustain for large times and we extract the properties of the chain which determine the associated time-scales. Our analysis applies generally to critical systems for which, after a slow developing phase where equilibrium conditions are justified, a rapid evolution, induced by a sudden symmetry breaking, emerges in time scales much shorter than the corresponding relaxation or observation time. In particular, it can be used in the fireball evolution in a heavy-ion collision experiment, where the QCD critical point emerges, or in the study of evolving fractals of astrophysical and cosmological scales, and may lead to determination of the initial critical properties of the Universe through observations in the symmetry broken phase.
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"abstract": "We consider the classical evolution of a lattice of non-linear coupled\noscillators for a special case of initial conditions resembling the equilibrium\nstate of a macroscopic thermal system at the critical point. The displacements\nof the oscillators define initially a fractal measure on the lattice associated\nwith the scaling properties of the order parameter fluctuations in the\ncorresponding critical system. Assuming a sudden symmetry breaking (quench),\nleading to a change in the equilibrium position of each oscillator, we\ninvestigate in some detail the deformation of the initial fractal geometry as\ntime evolves. In particular we show that traces of the critical fractal measure\ncan sustain for large times and we extract the properties of the chain which\ndetermine the associated time-scales. Our analysis applies generally to\ncritical systems for which, after a slow developing phase where equilibrium\nconditions are justified, a rapid evolution, induced by a sudden symmetry\nbreaking, emerges in time scales much shorter than the corresponding relaxation\nor observation time. In particular, it can be used in the fireball evolution in\na heavy-ion collision experiment, where the QCD critical point emerges, or in\nthe study of evolving fractals of astrophysical and cosmological scales, and\nmay lead to determination of the initial critical properties of the Universe\nthrough observations in the symmetry broken phase.",
"arxiv_id": "physics/0610111",
"authors": [
"N. G. Antoniou",
"F. K. Diakonos",
"E. N. Saridakis",
"G. A. Tsolias"
],
"categories": [
"physics.comp-ph",
"hep-ph"
],
"doi": "10.1103/PhysRevE.75.041111",
"journal_ref": "Phys.Rev.E75:041111,2007",
"title": "Classical evolution of fractal measures on the lattice",
"url": "https://arxiv.org/abs/physics/0610111"
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