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Fractional Langevin Equation in Quantum Systems with Memory Effect

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DOI: 10.4236/am.2014.512167    2,292 Downloads   2,877 Views   Citations

ABSTRACT

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.

Conflicts of Interest

The authors declare no conflicts of interest.

Cite this paper

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.

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