Backward and covariant Lyapunov vectors and exponents for hard disk systems with a steady heat current

Abstract

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 heat current is described and explained. Both the nonequilibrium backward and covariant hydrodynamic Lyapunov modes are analysed and compared. The movement of the converged angle between the hydrodynamic stable and unstable conjugate manifolds with the free flight time of the dynamics is accurately predicted for any nonequilibrium system simply as a function of their exponent. The nonequilibrium positive and negative $\LP$ mode frequencies are found to be asymmetrical, causing the negative mode to oscillate between the two functional forms of each mode in the positive conjugate mode pair. This in turn leads to the angular distributions between the conjugate modes to oscillate symmetrically about $\pi /2$ at a rate given by the difference between the positive and negative mode frequencies.

References in corpus (10)

• Characterizing dynamics with covariant Lyapunov vectors
• Structure of characteristic Lyapunov vectors in spatiotemporal chaos
• Spatiotemporal structure of Lyapunov vectors in chaotic coupled-map lattices
• Lyapunov analysis captures the collective dynamics of large chaotic systems
• Covariant Lyapunov vectors for rigid disk systems
• Structure of characteristic Lyapunov vectors in anharmonic Hamiltonian lattices
• Time-dependent mode structure for Lyapunov vectors as a collective movement in quasi-one-dimensional systems
• Lyapunov Modes for a Nonequilibrium System with a Heat Flux
• Lyapunov Mode Dynamics in Hard-Disk Systems
• Covariant hydrodynamic Lyapunov modes and strong stochasticity threshold in Hamiltonian lattices