Fractional Langevin Equation in Quantum Systems with Memory Effect

摘要

In this paper, we introduce the fractional generalized Langevin equation (FGLE) in quantum systems with memory effect. For a particular form of memory kernel that characterizes the quantum system, we obtain the analytical solution of the FGLE in terms of the two-parameter Mittag-Leffler function. Based on this solution, we study the time evolution of this system including the qubit excited-state energy, polarization and von Neumann entropy. Memory effect of this system is observed directly through the trapping states of these dynamics.