Origin of the hydrodynamic Lyapunov modes

McNamara, Sean; Mareschal, Michel

doi:10.1103/physreve.64.051103

Cited by 53 publications

(86 citation statements)

References 11 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…The classical spin lattices obviously belong to the latter group. We further remark on the existence of the delocalized Lyapunov-Goldstone modes, which were observed in dilute gases [4,30,31,14] and in some other extended systems [32]. If these modes exist in the spin systems, the projections on single spins of the Lyapunov vectors corresponding to the smallest nonzero Lyapunov exponents should exhibit a sinusoidal dependence on the positions of spins.…”

Section: Lyapunov Spectramentioning

confidence: 95%

Lyapunov instabilities in lattices of interacting classical spins at infinite temperature

Wijn¹,

Hess²,

Fine³

2013

J. Phys. A: Math. Theor.

View full text Add to dashboard Cite

Abstract. We numerically investigate Lyapunov instabilities for one-, two-and three-dimensional lattices of interacting classical spins at infinite temperature. We obtain the largest Lyapunov exponents for a very large variety of nearestneighbor spin-spin interactions and complete Lyapunov spectra in a few selected cases. We investigate the dependence of the largest Lyapunov exponents and whole Lyapunov spectra on the lattice size and find that both quickly become size-independent. Finally, we analyze the dependence of the largest Lyapunov exponents on the anisotropy of spin-spin interaction with the particular focus on the difference between bipartite and nonbipartite lattices.

show abstract

Section: Lyapunov Spectramentioning

confidence: 95%

Lyapunov instabilities in lattices of interacting classical spins at infinite temperature

Wijn¹,

Hess²,

Fine³

2013

J. Phys. A: Math. Theor.

View full text Add to dashboard Cite

show abstract

“…This angle has already been investigated in many-particle systems [7,21]. It should be noted that some analytical approaches give formula to calculate Lyapunov exponents from the spatial part only (or the momentum part only) of the tangent vector [8,32,33], so it is important to investigate the relation between the spatial part and the momentum part of the Lyapunov vector.…”

Section: B Angle Between the Spatial And The Momentum Parts Of The Lmentioning

confidence: 99%

“…For example, the Lyapunov vector was used to characterize a highdimensional chaotic attractor [3] and the clustered motion in symplectic coupled map systems [4]. One may also mention that the wavelike structure of the Lyapunov vectors associated with the stepwise structure of the Lyapunov spectra in the small (in absolute value) Lyapunov exponent region has been reported in many-hard-disk systems [5,6,7,8].…”

Section: Introductionmentioning

confidence: 99%

Localized behavior in the Lyapunov vectors for quasi-one-dimensional many-hard-disk systems

Taniguchi

Morriss

2003

Phys. Rev. E

View full text Add to dashboard Cite

We introduce a definition of a "localization width" whose logarithm is given by the entropy of the distribution of particle component amplitudes in the Lyapunov vector. Different types of localization widths are observed, for example, a minimum localization width where the components of only two particles are dominant. We can distinguish a delocalization associated with a random distribution of particle contributions, a delocalization associated with a uniform distribution and a delocalization associated with a wave-like structure in the Lyapunov vector. Using the localization width we show that in quasi-one-dimensional systems of many hard disks there are two kinds of dependence of the localization width on the Lyapunov exponent index for the larger exponents: one is exponential, and the other is linear. Differences, due to these kinds of localizations also appear in the shapes of the localized peaks of the Lyapunov vectors, the Lyapunov spectra and the angle between the spatial and momentum parts of the Lyapunov vectors. We show that the Krylov relation for the largest Lyapunov exponent λ ∼ −ρ ln ρ as a function of the density ρ is satisfied (apart from a factor) in the same density region as the linear dependence of the localization widths is observed. It is also shown that there are asymmetries in the spatial and momentum parts of the Lyapunov vectors, as well as in their x and y-components.

show abstract

“…Originally, it was observed in systems with hard-core particle interactions, but very recently numerical evidence for Lyapunov modes in a system with soft-core interactions was reported [9]. Some analytical approaches, such as random matrix theory [10,11], kinetic theory [12] and periodic orbit theory [13], have been used in an attempt to understand this phenomenon.…”

mentioning

confidence: 99%

Time-Oscillating Lyapunov Modes and the Momentum Autocorrelation Function

Taniguchi

Morriss

2005

Phys. Rev. Lett.

View full text Add to dashboard Cite

The time-dependent structure of the Lyapunov vectors corresponding to the steps of Lyapunov spectra and their basis set representation are discussed for a quasi-one-dimensional many-hard-disk systems. Time-oscillating behavior is observed in two types of Lyapunov modes, one associated with the time translational invariance and another with the spatial translational invariance, and their phase relation is specified. It is shown that the longest period of the Lyapunov modes is twice as long as the period of the longitudinal momentum auto-correlation function. A simple explanation for this relation is proposed. This result gives the first quantitative connection between the Lyapunov modes and an experimentally accessible quantity.

show abstract

Origin of the hydrodynamic Lyapunov modes

Cited by 53 publications

References 11 publications

Lyapunov instabilities in lattices of interacting classical spins at infinite temperature

Lyapunov instabilities in lattices of interacting classical spins at infinite temperature

Localized behavior in the Lyapunov vectors for quasi-one-dimensional many-hard-disk systems

Time-Oscillating Lyapunov Modes and the Momentum Autocorrelation Function

Contact Info

Product

Resources

About