Explicit solution of diffusion master equation under the action of linear resonance force via the thermal entangled state representation**Project supported by the National Natural Science Foundation of China (Grant Nos. 11347026, 11147009, and 11244005), the Natural Science Foundation of Shandong Province, China (Grant Nos. ZR2013AM012 and ZR2012AM004), and the Scientific Research Project of Liaocheng, China.

Abstract

Using the well-behaved features of the thermal entangled state representation, we solve the diffusion master equation under the action of a linear resonance force, and then obtain the infinitive operator-sum representation of the density operator. This approach may also be effective for treating other master equations. Moreover, we find that the initial pure coherent state evolves into a mixed thermal state after passing through the diffusion process under the action of the linear resonance force.