Iomin A, Zaslavsky G M
Courant Institute of Mathematical Sciences, New York University, 251 Mercer Street, New York, NY 10012, USA.
Phys Rev E Stat Nonlin Soft Matter Phys. 2001 Apr;63(4 Pt 2):047203. doi: 10.1103/PhysRevE.63.047203. Epub 2001 Mar 29.
We show that the breaking time of quantum-classical correspondence depends on the type of kinetics and the dominant origin of stickiness. For sticky dynamics of quantum kicked rotor, when the hierarchical set of islands corresponds to the accelerator mode, we demonstrate by simulation that the breaking time scales as tau(Planck's over 2pi) approximately (1/Planck's over 2pi)(1/mu) with the transport exponent mu>1 that corresponds to superdiffusive dynamics [B. Sundaram and G. M. Zaslavsky, Phys. Rev. E 59, 7231 (1999)]. We discuss also other possibilities for the breaking time scaling and transition to the logarithmic one tau(Planck's over 2pi) approximately ln(1/Planck's over 2pi) with respect to Planck's over 2pi.
我们表明，量子 - 经典对应关系的破缺时间取决于动力学类型和粘性的主要来源。对于量子受驱转子的粘性动力学，当分层岛集对应于加速器模式时，我们通过模拟证明，破缺时间的标度为(\tau(\frac{\hbar}{2\pi})\approx(\frac{1}{\frac{\hbar}{2\pi}})^{\frac{1}{\mu}})，其中输运指数(\mu>1)对应于超扩散动力学[B. 桑达拉姆和G. M. 扎斯拉夫斯基，《物理评论E》59，7231 (1999)]。我们还讨论了破缺时间标度的其他可能性以及相对于(\frac{\hbar}{2\pi})向对数标度(\tau(\frac{\hbar}{2\pi})\approx\ln(\frac{1}{\frac{\hbar}{2\pi}}))的转变。
