Non-thermal fluctuation and correlation of chaos in conservative systems

研究了混沌哈密顿系统的动力学和平衡性质。特别地，我们研究了链式系统，其中质量由刚性连杆或弹簧连接。对于质量由刚性连杆连接的系统，在链的末端处，质量的平均动能过大。对于质量由弹簧连接的系统，在末端附近的平均动能会瞬时地取过大的值。随着弹簧常数k的增大，到方程的松弛时间τ迅速增大，这与由Boltzmann-Jeans理论得到的表达式τ∝exp（√^<ck>）一致。结果表明，链型系统，如聚合物、DNA、蛋白质、人工物体，在链的末端也显示出过量的平均能量。

Dynamical and equilibrium properties of chaotic Hamiltonian systems are investigated. In particular, we studied chain-type systems where masses are connected by rigid links or springs. For systems where masses are connected by rigid links, average kinetic energies of masses take excessive large values near the ends of chain. For systems where masses are connected by springs, average kinetic energies near the ends transiently take excessive values. The relaxation time to equipartitionτgrows rapidly with the increase of the spring constant k. It is in agreement with the expressionτ∝exp(√^<ck>) obtained from Boltzmann-Jeans theory. The results imply that chain-type systems such as polymers, DNA, protein, artificial objects also show excess average energy near ends of the chain.