Coherent Structures and Entropy in Constrained, Modulationally Unstable, Nonintegrable Systems

Rumpf, Benno; Newell, Alan C.

doi:10.1103/physrevlett.87.054102

Cited by 81 publications

(96 citation statements)

References 9 publications

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“…In a similar way, optical wave thermalization through supercontinuum generation is affected by the dissipative Raman effect 25 . We note, in particular, that although wave turbulence theory is independent of the sign of the interactions 11 , in practice modulation instability dominates in the self-focusing case; the dynamics are controlled by the potential (rather than kinetic) energy of the system, the (inverse) momentum cascade is unidirectional, self-similar spectra are transient, and 'condensation' appears in the form of coherent soliton structures 24,26 . Localized intensity structures (zeros in the field) are present here from the random-phase initial conditions, but these did not participate actively in the dynamics.…”

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confidence: 91%

Observation of the kinetic condensation of classical waves

et al. 2012

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The observation of Bose-Einstein condensation, in which particle interactions lead to a thermodynamic transition into a single, macroscopically populated coherent state, is a triumph of modern physics [1][2][3][4][5] . It is commonly assumed that this transition is a quantum process, relying on quantum statistics, but recent studies in wave turbulence theory have suggested that classical waves with random phases can condense in a formally identical manner [6][7][8][9] . In complete analogy with gas kinetics, particle velocities map to wavepacket kvectors, collisions are mimicked by four-wave mixing, and entropy principles drive the system towards an equipartition of energy. Here, we use classical light in a self-defocusing photorefractive crystal to give the first observation of classical wave condensation, including the growth of a coherent state, the spectral redistribution towards equilibrium, and the formal reversibility of the interactions. The results confirm fundamental predictions of kinetic wave theory and hold relevance for a variety of fields, ranging from Bose-Einstein condensation to information transfer and imaging.Weakly interacting bosons may exhibit, under extremely low temperatures, a Bose-Einstein transition [1][2][3][4][5] . This transition is characterized by a macroscopic occupation of the ground state. The quantum nature of the bosons involved is crucial for this process, and indeed Bose-Einstein condensation (BEC) is a wonderful manifestation of quantum mechanics at a macroscopic scale. On the other hand, a growing body of theoretical work has predicted that completely classical waves may undergo an analogous condensation process [6][7][8][9] . The requirements are a random ensemble of waves, so that statistical arguments apply, and a means of interaction between modes. Examples include sea waves stirred by wind, vibrations on elastic plates, interacting oscillators, and diffracting light that propagates in a nonlinear medium 6,10,11 . As these systems evolve, turbulent wave mixing leads to a self-organized redistribution of energy: an inverse cascade increases the 'number of waves' in the lowest allowed mode while a normal cascade transfers energy towards higher momenta. The process is ruled by the natural thermalization of a conservative Hamiltonian wave system. As with the collisions of particles, each wave interaction is formally reversible, yet entropy principles mandate that the ensemble evolves towards an equilibrium state of maximum disorder. In this way, a large-scale coherent structure grows and becomes immersed in a sea of small-scale fluctuations ('uncondensed particles'), which store the information necessary for reversible evolution of the waves. Here, we directly observe this process of wave condensation, as well as its formal reversibility, by imaging classical light dynamics in a photorefractive crystal.

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confidence: 91%

Observation of the kinetic condensation of classical waves

et al. 2012

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“…It is indeed important to note that the spontaneous formation of a homogeneous solution corroborates the general rule discussed above [10,11,13], because the homogenous solution realizes the minimum of the energy (Hamiltonian) in the defocusing case. This analogy between the focusing and defocusing regimes reveals that the formation of a condensate may be viewed as a consequence of the fact that the system naturally tends to increase its disorder (entropy).…”

Section: Introductionmentioning

confidence: 54%

“…However this is not the case, because if n k (t) exhibits the singular behavior given in Eq. (13), then the collision term in Eq. (22) becomes singular at t = t * .…”

Section: The Growth Of a Condensatementioning

confidence: 99%

“…[10], a rigorous theoretical description of the long term evolution of the system would require a thermodynamic approach. It is only recently that statistical equilibrium models have been elaborated in the framework of statistical mechanics [11][12][13]. As a remarkable result, whenever the Hamiltonian system is constrained by an additional integral of motion (e.g., number of particles), the increase of entropy of small-scale turbulent fluctuations requires the formation of coherent structures [11,13], so that it is thermodynamically advantageous for the system to approach the ground state which minimizes the energy [10].…”

Section: Introductionmentioning

confidence: 99%

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Breakdown of weak-turbulence and nonlinear wave condensation

Düring

Picozzi

Rica

2009

Physica D: Nonlinear Phenomena

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“…This means that the KE does not depend on the sign of the dispersion coefficient (normal or anomalous dispersion regime) and thus does not describe coherent soliton states. Note that the fact that the generation of a coherent soliton is quenched by the strong randomness of the incoherent wave in the weakly nonlinear regime (t c ≪ τ 0 ) has been already studied in different cases [90][91][92], in particular through supercontinuum generation [12,93]. It is also important to remark that the instantaneous Kerr nonlinearity does not enter the KE (3).…”

Section: Mean-field Kinetic Equationmentioning

confidence: 99%

Weak Langmuir optical turbulence in a fiber cavity

Garnier

Mussot

et al. 2016

Phys. Rev. A

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We study theoretically and numerically the dynamics of a passive optical fiber ring cavity pumped by a highly incoherent wave -an incoherently injected fiber laser. The theoretical analysis reveals that the turbulent dynamics of the cavity is dominated by the Raman effect. The forced-dissipative nature of the fiber cavity is responsible for a large diversity of turbulent behaviors: Besides nonequilibrium statistical stationary states, we report the formation of a periodic pattern of spectral incoherent solitons, or the formation of different types of spectral singularities, e.g., dispersive shock waves and incoherent spectral collapse behaviors. We derive a mean-field kinetic equation that describes in detail the different turbulent regimes of the cavity and whose structure is formally analogous to the weak Langmuir turbulence kinetic equation in the presence of forcing and damping. A quantitative agreement is obtained between the simulations of the nonlinear Schrödinger equation with cavity boundary conditions and those of the mean-field kinetic equation and the corresponding singular integro-differential reduction, without using adjustable parameters. We discuss the possible realization of a fiber cavity experimental set-up in which the theoretical predictions can be observed and studied.

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Coherent Structures and Entropy in Constrained, Modulationally Unstable, Nonintegrable Systems

Cited by 81 publications

References 9 publications

Observation of the kinetic condensation of classical waves

Observation of the kinetic condensation of classical waves

Breakdown of weak-turbulence and nonlinear wave condensation

Weak Langmuir optical turbulence in a fiber cavity

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