Zi-Gang Yuan1,2**, Xin-Yu Zhang1, He Zhao1, Yan-Chao Li3
1College of Mathematics and Physics, Beijing University of Chemical Technology, P. O. Box 26, Beijing 100029 2Centre for Quantum Technologies, National University of Singapore, 3 Science Drive 2, Singapore 117543, Singapore 3Center of Materials Science and Optoelectronics Engineering, College of Materials Science and Opto-Electronic Technology, University of Chinese Academy of Sciences, Beijing 100049
Abstract：We study the effect of the initial-state energy variance to the short-time behavior of the Loschmidt echo (LE) in a purely dephasing model. We find that the short-time LE behaves as a Gaussian function with the width determined by the initial-state energy variance of the interaction Hamiltonian, while it is a quartic decaying function with the width determined by the initial-state energy variance of the commutator between the interaction Hamiltonian and the environmental Hamiltonian when the initial state is an eigenstate of the interaction Hamiltonian. Furthermore, the Gaussian envelope in the temporal evolution of LE in strong coupling regime is determined by the inband variance. We will also verify the above conclusion in the XY spin model (as environment).
2020, Vol. 37 
