Lu W T, Sridhar S, Zworski Maciej
Department of Physics and Electronic Materials Research Institute, Northeastern University, Boston, Massachusetts 02115, USA.
Phys Rev Lett. 2003 Oct 10;91(15):154101. doi: 10.1103/PhysRevLett.91.154101. Epub 2003 Oct 8.
We present a conjecture relating the density of quantum resonances for an open chaotic system to the fractal dimension of the associated classical repeller. Mathematical arguments justifying this conjecture are discussed. Numerical evidence based on computation of resonances of systems of n disks on a plane are presented supporting this conjecture. The result generalizes the Weyl law for the density of states of a closed system to chaotic open systems.
我们提出了一个关于开放混沌系统的量子共振密度与相关经典排斥子的分形维数之间关系的猜想。讨论了支持该猜想的数学论证。给出了基于平面上n个圆盘系统共振计算的数值证据来支持这一猜想。该结果将封闭系统态密度的魏尔定律推广到了混沌开放系统。
