Expectation value based cluster expansion
Held by Alexander
Leymann (Otto von Guericke University of Magdeburg, Germany)
We present a new method to formulate equations of motion for open quantum many-particle systems involving different kinds of particles. This method reformulates and generalizes the well known cluster expansion technique , but uses expectation values instead of correlation functions. The use of expectation values considerably reduces the amount of algebraic effort to derive the equations and increases the flexibility concerning the approximation principles. Neglecting correlations is not a new concept but our formulation allows for a new perspective on various approximation techniques presented recently in [2-5].
To illustrate the efficiency of our scheme we extend the semiconductor model for quantum-dot-based microcavity lasers developed in  to higher order photon auto-correlation functions and confirm the convergence of the cluster expansion, by going up to 10th order in the expectation value based cluster expansion.
 J. Fricke, Ann. Phys. (N.Y.) 252, 479 (1996).
 A. Carmele, M. Richter, W. W. Chow, and A. Knorr, Phys. Rev. Lett. 104, 156801 (2010).
 C. Gies, J. Wiersig, M. Lorke, and F. Jahnke, Phys. Rev. A 75, 013803 (2007).
 M. Richter, A. Carmele, A. Sitek, and A. Knorr, Phys. Rev. Lett. 103, 087407 (2009).
 S. Ritter, P. Gartner, C. Gies, and F. Jahnke, Opt. Express 18, 9909 (2010).