相关论文: Goldstone modes in Lyapunov spectra of hard sphere…
The Lyapunov spectrum describes the exponential growth, or decay, of infinitesimal phase-space perturbations. The perturbation associated with the maximum Lyapunov exponent is strongly localized in space, and only a small fraction of all…
We consider a general method for computing the sum of positive Lyapunov exponents for moderately dense gases. This method is based upon hierarchy techniques used previously to derive the generalized Boltzmann equation for the time dependent…
Recent work on many particle system reveals the existence of regular collective perturbations corresponding to the smallest positive Lyapunov exponents (LEs), called hydrodynamic Lyapunov modes. Until now, however, these modes are only…
We demonstrate the preservation of the Lyapunov modes by the underlying tangent space dynamics of hard disks. This result is exact for the zero modes and correct to order $\epsilon$ for the transverse and LP modes where $\epsilon$ is linear…
Lyapunov modes are periodic spatial perturbations of phase-space states of many-particle systems, which are associated with the small positive or negative Lyapunov exponents. Although familiar for hard-particle systems in one, two, and…
The phase space trajectories of many body systems charateristic of simple fluids are highly unstable. We quantify this instability by a set of Lyapunov exponents, which are the rates of exponential divergence, or convergence, of initial…
We consider simulations of a 2-dimensional gas of hard disks in a rectangular container and study the Lyapunov spectrum near the vanishing Lyapunov exponents. To this spectrum are associated ``eigen-directions'', called Lyapunov modes. We…
Time dependent mode structure for the Lyapunov vectors associated with the stepwise structure of the Lyapunov spectra and its relation to the momentum auto-correlation function are discussed in quasi-one-dimensional many-hard-disk systems.…
The Lyapunov exponent spectrum and covariant Lyapunov vectors are studied for a quasi-one-dimensional system of hard disks as a function of density and system size. We characterize the system using the angle distributions between covariant…
The Goldstone theorem implies the appearance of an ungapped mode whenever a continuous global symmetry is spontaneously broken. In general it does not say anything about the precise form of the dispersion relation nor does it imply that…
We present the first numerical observation of Lyapunov modes (mode structure of Lyapunov vectors) in a system maintained in a nonequilibrium steady state. The modes show some similarities and some differences when compared with the results…
The covariant Lyapunov analysis is generalised to systems attached to deterministic thermal reservoirs that create a heat current across the system and perturb it away from equilibrium. The change in the Lyapunov exponents as a function of…
In nonuniform Larkin-Ovchinnikov-Fulde-Ferrell (LOFF) superconductors, both the gauge symmetry and the continuous translational symmetry of the normal state are spontaneously broken. This leads to additional bosonic excitations, or…
We compute Lyapunov spectra for Coulombic and gravitational versions of the one-dimensional systems of parallel sheets with periodic boundary conditions. Exact time evolution of tangent-space vectors are derived and are utilized toward…
We study the Lyapunov instability of a two-dimensional fluid composed of rigid diatomic molecules, with two interaction sites each, and interacting with a WCA site-site potential. We compute full spectra of Lyapunov exponents for such a…
Recent studies on the phase-space dynamics of a one-dimensional Lennard-Jones fluid reveal the existence of regular collective perturbations associated with the smallest positive Lyapunov exponents of the system, called hydrodynamic…
We study the implications of translation invariance on the tangent dynamics of extended dynamical systems, within a random matrix approximation. In a model system, we show the existence of hydrodynamic modes in the slowly growing part of…
A kinetic approach is adopted to describe the exponential growth of a small deviation of the initial phase space point, measured by the largest Lyapunov exponent, for a dilute system of hard disks, both in equilibrium and in a uniform shear…
We show that the third Goldstone mode in the two-species condensate mixtures, which emerges at phase-separation, gets hardened when the confining potentials have separated trap centers. The {\em sandwich} type condensate density profiles,…
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…