Wang Wen-ge
Department of Modern Physics, University of Science and Technology of China, Hefei, China.
Phys Rev E Stat Nonlin Soft Matter Phys. 2008 Mar;77(3 Pt 2):036206. doi: 10.1103/PhysRevE.77.036206. Epub 2008 Mar 13.
We study quantum Loschmidt echo, or fidelity, in the triangle map whose classical counterpart has linear instability and weak chaos. Numerically, three regimes of fidelity decay have been found with respect to the perturbation strength epsilon. In the regime of weak perturbation, the fidelity decays as exp(-c epsilon(2)t(gamma)) with gamma approximately 1.7. In the regime of strong perturbation, the fidelity is approximately a function of epsilont(2.5), which is predicted for the classical fidelity [G. Casati, Phys. Rev. Lett. 94, 114101 (2005)], and decays slower than power-law decay for long times. In an intermediate regime, the fidelity has approximately an exponential decay exp(-c' epsilont).
我们研究了三角形映射中的量子洛施密特回波或保真度，其经典对应物具有线性不稳定性和弱混沌。通过数值计算，发现了关于微扰强度ε的三种保真度衰减 regime。在弱微扰 regime 中，保真度按 exp(-cε²t^γ)衰减，其中γ约为1.7。在强微扰 regime 中，保真度近似为εt^2.5的函数，这是经典保真度所预测的[G. 卡萨蒂，《物理评论快报》94, 114101 (2005)]，并且在长时间下衰减比幂律衰减慢。在中间 regime 中，保真度近似呈指数衰减 exp(-c'εt) 。
