The time and spatial variation of the y-component of the P-mode.

Dynamical instability is characterized by the Lyapunov exponents which give the rate of separation of nearby trajectories. In general, there is one exponent for each independent direction in phase space. While for many exponents the direction of separation varies rapidly, for some exponents the direction is either fixed or slowly varying. These fixed or slowly varying directions are called the Lyapunov modes. Here we show that the frequency of the slowest time variation of the Lyapunov modes is connected with oscillation frequency of the tail of the velocity autocorrelation function, an experimentally measurable quantity.

The figure shows the time and spatial variation of one of the key Lyapunov modes for a quasi-one-dimensional system of hard disks. In chaotic particle systems dynamical instability means that the system is unpredictable and a statistical treatment is required. The importance of this phenomenon is that it connects stability properties and macroscopic collective movement (phonons) in a many-body system. The form of the Lyapunov mode is connected to the invariant properties of the system.

Tooru Taniguchi and Gary Morriss