Fractional Langevin Equation in Quantum Systems with Memory Effect

Jing-Nuo Wu, Hsin-Chien Huang, Szu-Cheng Cheng, Wen-Feng Hsieh

Department of Optoelectric Physics, Chinese Culture University, Taiwan.
Department of Photonics and Institute of Electro-Optical Engineering, Taiwan.

DOI: 10.4236/am.2014.512167                

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.

Keywords

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

Conflicts of Interest

The authors declare no conflicts of interest.

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