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arXiv · 0905.2448

Infinite operator-sum representation of density operator for a dissipative cavity with Kerr medium derived by virtue of entangled state representation

Li-yun Hu·Hong-yi Fan
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Abstract

By using the thermo entangled state representation we solve the master equation for a dissipative cavity with Kerr medium to obtain density operators' infinite operator-sum representation}$ρ(t) =\sum_{m,n,l=0}^{\infty}M_{m,n,l}ρ_{0}\mathcal{M}_{m,n,l}^{\dagger}.$ It is noticeable that}$M_{m,n,l}$ is not hermite conjugate to $\mathcal{M}_{m,n,l}^{\dagger}$, nevertheless the normalization}$\sum_{m,n,l=0}^{\infty}\mathcal{M}_{nm,,l}^{\dagger}M_{m,n,l}=1$ still holds}, i.e., they are trace-preserving in a general sense. This example may stimulate further studying if general superoperator theory needs modification.

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Li-yun Hu, Hong-yi Fan. 2010-03-25. Infinite operator-sum representation of density operator for a dissipative cavity with Kerr medium derived by virtue of entangled state representation. https://doi.org/10.1007/s10773-009-0144-5

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