Escape Dynamics of Many Hard Disks

Abstract

Many-particle effects in escapes of hard disks from a square box via a hole are discussed in a viewpoint of dynamical systems. Starting from $N$ disks in the box at the initial time, we calculate the probability $P_n(t)$ for at least $n$ disks to remain inside the box at time $t$ for $n=1,2,\cdots ,N$. At early times the probabilities $P_n(t)$, $n=2,3,\cdots ,N-1$, are described by superpositions of exponential decay functions. On the other hand, after a long time the probability $P_n(t)$ shows a power-law decay $\sim t^{-2n}$ for $n\ne 1$, in contrast to the fact that it decays with a different power law $\sim t^{-n}$ for cases without any disk-disk collision. Chaotic or non-chaotic properties of the escape systems are discussed by the dynamics of a finite time largest Lyapunov exponent, whose decay properties are related with those of the probability $P_n(t)$.

14 pages, 11 figures

References in corpus (9)

• Dynamics of Loschmidt echoes and fidelity decay
• Loschmidt Echo
• Decoherence, Entanglement and Irreversibility in Quantum Dynamical Systems with Few Degrees of Freedom
• Poincare recurrences and transient chaos in systems with leaks
• Peeping at chaos: Nondestructive monitoring of chaotic systems by measuring long-time escape rates
• Poincare recurrences from the perspective of transient chaos
• Time-oscillating Lyapunov modes and auto-correlation functions for quasi-one-dimensional systems
• Time-dependent mode structure for Lyapunov vectors as a collective movement in quasi-one-dimensional systems
• Influence of boundary conditions on quantum escape