Fractional Langevin Equation in Quantum Systems with Memory Effect


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.

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Wu, J. , Huang, H. , Cheng, S. and Hsieh, W. (2014) Fractional Langevin Equation in Quantum Systems with Memory Effect. Applied Mathematics, 5, 1741-1749. doi: 10.4236/am.2014.512167.

Conflicts of Interest

The authors declare no conflicts of interest.


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