Radionov Sergey, Aberg Sven, Guhr Thomas
Matematisk Fysik, LTH, Lunds Universitet, Lund, Sweden and Kiev Institute for Nuclear Research, Kiev, Ukraine.
Phys Rev E Stat Nonlin Soft Matter Phys. 2004 Sep;70(3 Pt 2):036207. doi: 10.1103/PhysRevE.70.036207. Epub 2004 Sep 15.
We study classical and quantum chaos for two interacting particles on the plane. This is the simplest nontrivial case which sheds light on chaos in interacting many-body systems. The system consists of a confining one-body potential, assumed to be a deformed harmonic oscillator, and a two-body interaction of Coulomb type. In general, the dynamics is mixed with regular and chaotic trajectories. The relative roles of the one-body field and the two-body interaction are investigated. Chaos sets in as the strength of the two-body interaction increases. However, the degree of chaoticity strongly depends on the shape of the one-body potential and, for some shapes of the harmonic oscillator, the dynamics remains regular for all values of the two-body interaction. Scaling properties are found for the classical as well as for the quantum mechanical problem.
我们研究平面上两个相互作用粒子的经典混沌和量子混沌。这是最简单的非平凡情形，它为相互作用多体系统中的混沌现象提供了启示。该系统由一个限制单粒子的势（假定为变形的谐振子）和一个库仑型的两体相互作用组成。一般来说，动力学是规则轨迹和混沌轨迹的混合。我们研究了单粒子场和两体相互作用的相对作用。随着两体相互作用强度的增加，混沌出现。然而，混沌程度强烈依赖于单粒子势的形状，并且对于某些谐振子形状，对于两体相互作用的所有值，动力学都保持规则。我们发现了经典问题和量子力学问题的标度性质。
