Loschmidt Echo for edge of chaos and chaotic sea in Standard Map: Cases Study

Abstract

Using the Standard Map model, this study explores the quantum Loschmidt Echo (LE) decay laws for mixed-type phase spaces, including edge of chaos and chaotic sea regimes. A universal decay law is proposed and numerically verified, characterizing the intricate dynamics of LE decay processes with a semi-classical statistical approach. Key findings include three typical decay stages and time-scale relations as well as the critical perturbations for comparing the decay extent, with critical insights into classical-quantum correspondences through the construction of classical ensemble from the uncertainty of quantum state. This work provides analytical and numerical advancements in understanding dynamical stability in quantum systems.

104 pages, 61 figures. arXiv admin note: text overlap with arXiv:0908.0702 by other authors