Renormalized dispersion relations of<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mi>β</mml:mi></mml:math>-Fermi-Pasta-Ulam chains in equilibrium and nonequilibrium states

Jiang, Shi; Lu, Hai Hao; Zhou, Douglas; Cai, David

doi:10.1103/physreve.90.032925

Cited by 8 publications

(8 citation statements)

References 38 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Here, ( )  w Q k is the temporal Fourier transform of Q k (t). It is important to note that for both thermal equilibrium and nonequilibrium steady state, the theoretical prediction (4) agrees very well with W k meas and these renormalized dispersion relations are induced by wave-wave resonances, instead of inherited from their linear dispersive dynamics [6,9]. More specifically, the contribution of the trivial and nontrivial resonances is significant to the renormalization of the dispersion relation [9].…”

Section: Renormalized Dispersion Relationsupporting

confidence: 59%

“…It has been found that such relations, referred to as renormalized dispersion relations, often arise from wave-wave interactions, and they can deviate substantially from the bare linear dispersion relation [2][3][4][5][6]. The pioneering Fermi-Pasta-Ulam (FPU) lattice is an example exhibiting such phenomenon even in strongly nonlinear regimes [2,3,[6][7][8][9]. The FPU lattice problem has spurred a great number of important developments in physics and mathematics [10,11].…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Stochastic linearization of turbulent dynamics of dispersive waves in equilibrium and non-equilibrium state

Jiang

Zhou

et al. 2016

New J. Phys.

Self Cite

View full text Add to dashboard Cite

Characterizing dispersive wave turbulence in the long time dynamics is central to understanding of many natural phenomena, e.g., in atmosphere ocean dynamics, nonlinear optics, and plasma physics. Using the β-Fermi-Pasta-Ulam nonlinear system as a prototypical example, we show that in thermal equilibrium and non-equilibrium steady state the turbulent state even in the strongly nonlinear regime possesses an effective linear stochastic structure in renormalized normal variables. In this framework, we can well characterize the spatiotemporal dynamics, which are dominated by longwavelength renormalized waves. We further demonstrate that the energy flux is nearly saturated by the long-wavelength renormalized waves in non-equilibrium steady state. The scenario of such effective linear stochastic dynamics can be extended to study turbulent states in other nonlinear wave systems.

show abstract

Section: Renormalized Dispersion Relationsupporting

confidence: 59%

Section: Introductionmentioning

confidence: 99%

Stochastic linearization of turbulent dynamics of dispersive waves in equilibrium and non-equilibrium state

Jiang

Zhou

et al. 2016

New J. Phys.

Self Cite

View full text Add to dashboard Cite

show abstract

“…The paradox of the Fermi-Pasta-Ulam recurrence had a deep impact on the development of nonlinear science [2][3][4][5][6], in particular, in the context of ergodic theory, soliton theory, and integrability [7][8][9][10][11][12][13][14][15]. Aside from the specific model equation originally considered by Fermi, Pasta, and Ulam [1], the recurrence effect is a general phenomenon found in a variety of almost integrable models whose phase space is strongly segmented by the existence of a large number…”

Section: Introductionmentioning

confidence: 99%

“…There is an intuitive appeal in the idea that weakly nonlinear random waves should not exhibit reversible recurrences, but instead a monotonic irreversible process of thermalization to equilibrium. Such irreversible processes can be precisely formulated by using the welldeveloped wave turbulence theory [36][37][38][39][40][41], which has been successfully applied to a huge variety of physical systems [7][8][9]11,[42][43][44][45][46][47][48]. The wave turbulence theory is formally based on irreversible kinetic equations that describe an irreversible process of thermalization to equilibrium, as expressed by the fundamental H theorem of entropy growth.…”

Section: Introductionmentioning

confidence: 99%

“…For this purpose, we develop a nonequilibrium kinetic theory that accounts for the existence of phase correlations among the random waves. Phase correlations are known to play a role in different cases [7][8][9][49][50][51][52][53][54][55][56][57][58]; in particular, they lead to the formation of large-scale coherent structures (solitons or condensates) emerging from a strongly nonlinear turbulent regime [38][39][40][41][42][43][44][45][46]59-65]-a coherent structure being inherently a phase-correlated object. Also note that stochastic recurrences of random waves have been predicted recently for water waves governed by Alber's equation when nonlinear effects are stronger than linear dispersive effects [66].…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Incoherent Fermi-Pasta-Ulam Recurrences and Unconstrained Thermalization Mediated by Strong Phase Correlations

et al. 2017

View full text Add to dashboard Cite

The long-standing and controversial Fermi-Pasta-Ulam problem addresses fundamental issues of statistical physics, and the attempt to resolve the mystery of the recurrences has led to many great discoveries, such as chaos, integrable systems, and soliton theory. From a general perspective, the recurrence is commonly considered as a coherent phase-sensitive effect that originates in the property of integrability of the system. In contrast to this interpretation, we show that convection among a pair of waves is responsible for a new recurrence phenomenon that takes place for strongly incoherent waves far from integrability. We explain the incoherent recurrence by developing a nonequilibrium spatiotemporal kinetic formulation that accounts for the existence of phase correlations among incoherent waves. The theory reveals that the recurrence originates in a novel form of modulational instability, which shows that strongly correlated fluctuations are spontaneously created among the random waves. Contrary to conventional incoherent modulational instabilities, we find that Landau damping can be completely suppressed, which unexpectedly removes the threshold of the instability. Consequently, the recurrence can take place for strongly incoherent waves and is thus characterized by a reduction of nonequilibrium entropy that violates the H theorem of entropy growth. In its long-term evolution, the system enters a secondary turbulent regime characterized by an irreversible process of relaxation to equilibrium. At variance with the expected thermalization described by standard Gibbsian statistical mechanics, our thermalization process is not dictated by the usual constraints of energy and momentum conservation: The inverse temperatures associated with energy and momentum are zero. This unveils a previously unrecognized scenario of unconstrained thermalization, which is relevant to a variety of weakly dispersive wave systems. Our work should stimulate the development of new experiments aimed at observing recurrence behaviors with random waves. From a broader perspective, the spatiotemporal kinetic formulation we develop here paves the way to the study of novel forms of global incoherent collective behaviors in wave turbulence, such as the formation of incoherent breather structures.

show abstract

Stability of topological edge states under strong nonlinear effects

Chaunsali

Yang

et al. 2021

Phys. Rev. B

View full text Add to dashboard Cite

We examine the role of strong nonlinearity on the topologically robust edge state in a one-dimensional system. We consider a chain inspired from the Su-Schrieffer-Heeger model but with a finite-frequency edge state and the dynamics governed by second-order differential equations. We introduce a cubic onsite nonlinearity and study this nonlinear effect on the edge state's frequency and linear stability. Nonlinear continuation reveals that the edge state loses its typical shape enforced by the chiral symmetry and becomes generally unstable due to various types of instabilities that we analyze using a combination of spectral stability and Krein signature analysis. This results in an initially excited nonlinear-edge state shedding its energy into the bulk over a long time. However, the stability trends differ both qualitatively and quantitatively when softening and stiffening types of nonlinearity are considered. In the latter, we find a frequency regime where nonlinear edge states can be linearly stable. This enables high-amplitude edge states to remain spatially localized without shedding their energy, a feature that we have confirmed via long-time dynamical simulations. Finally, we examine the robustness of frequency and stability of nonlinear edge states against disorder, and find that those are more robust under a chiral disorder compared to a nonchiral disorder. Moreover, the frequency-regime where high-amplitude edge states were found to be linearly stable remains intact in the presence of a small amount of disorder of both types.

show abstract

Renormalized dispersion relations ofβ-Fermi-Pasta-Ulam chains in equilibrium and nonequilibrium states

Cited by 8 publications

References 38 publications

Stochastic linearization of turbulent dynamics of dispersive waves in equilibrium and non-equilibrium state

Stochastic linearization of turbulent dynamics of dispersive waves in equilibrium and non-equilibrium state

Incoherent Fermi-Pasta-Ulam Recurrences and Unconstrained Thermalization Mediated by Strong Phase Correlations

Stability of topological edge states under strong nonlinear effects

Contact Info

Product

Resources

About