Free-energy transition in a gas of non-interacting nonlinear wave-particles
arXiv:0808.0882 · doi:10.1103/PhysRevLett.101.044101
Abstract
We investigate the dynamics of a gas of non-interacting particle-like soliton waves, demonstrating that phase transitions originate from their collective behavior. This is predicted by solving exactly the nonlinear equations and by employing methods of the statistical mechanics of chaos. In particular, we show that a suitable free energy undergoes a metamorphosis as the input excitation is increased, thereby developing a first order phase transition whose measurable manifestation is the formation of shock waves. This demonstrates that even the simplest phase-space dynamics, involving independent (uncoupled) degrees of freedom, can sustain critical phenomena.
arXiv comment4 pages, 3 figures
References in corpus (8)
- Dispersive, superfluid-like shock waves in nonlinear optics
- On Dispersive and Classical Shock Waves in Bose-Einstein Condensates and Gas Dynamics
- Shocks in nonlocal media
- Kinetic equation for a dense soliton gas
- Statistical mechanics of a nonlinear discrete system
- Formation of shock waves in a Bose-Einstein condensate
- Dissipationless shock waves in repulsive Bose-Einstein condensates
- The theory of optical dispersive shock waves in photorefractive media
Cited by in corpus (11)
- Dark solitons in atomic Bose-Einstein condensates: from theory to experiments
- Observation of a gradient catastrophe generating solitons
- Nonlinear random optical waves: integrable turbulence, rogue waves and intermittency
- Suppression of transverse instabilities of dark solitons and their dispersive shock waves
- Multiple hydrodynamical shocks induced by Raman effect in photonic crystal fibres
- Statistical physics of nonlinear wave interaction
- Time-reversal focusing of an expanding soliton gas in disordered replicas
- Breaking mechanism from a vacuum point in the defocusing nonlinear Schroedinger equation
- Solitons as candidates for energy carriers in Fermi-Pasta-Ulam lattices
- Elliptic finite-band potentials of a non-self-adjoint Dirac operator
- Statistical analysis of complex systems with nonclassical invariant measures