Author(s)

Jing-Nuo Wu¹, Hsin-Chien Huang¹, Szu-Cheng Cheng^1*, Wen-Feng Hsieh^2*

¹Department of Optoelectric Physics, Chinese Culture University, Taipei City.
²Department of Photonics and Institute of Electro-Optical Engineering, Hsinchu.

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.

Fractional Generalized Langevin Equation, Memory Effect, Mittag-Leffler Function, Memory Kernel, Trapping States, Polarization, von Neumann Entropy

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.