在本論文中我們探討了在半導體微共振腔中的二維極化子，玻色-愛因斯坦凝聚態(BEC)下的激發譜。 在非平衡的情況下，極化子BEC可由耗散- Gross-Pitaevskii方程式來描述其凝聚態耦合至極化子熱庫的情況。我們也研究在不同條件下，激發譜在穩態下的解析與數值解。我們發現在空間均勻條件下，激發譜存在著擴散Goldstone mode 與動態之不穩定區。
最後,我們考慮極化子BEC耦合至耗散的單一模態，等同於極化子BEC耦合至結構熱庫之Lorentzian態密度。隨著不同耦合強度，激發譜也可給出平坦，類似Bogoliubov，或是能隙之色散關係, 而耦合所產生的影響可增強或減弱系統的不穩定性。

We study the dynamics of Bose-Einstein condensation of weakly interacting exciton-polaritons in a semiconductor microcavity. In the non-equilibrium regime, the dissipative Gross-Pitaevskii Equation is employed to describe the polariton condensate coupled to a polariton reservoir. The spectrum of the elementary excitations around the stationary state is analytically and numerically studied in different situations. There exists a diffusive Goldstone mode and a dynamical instability region for a spatially homogeneous geometry. Finally, the polariton BEC is considered to be coupled to a single-mode dissipative system, which corresponds to a reservoir with Lorentzian-shape density of states. By detuning the single-mode energy, the excitation spectrum exhibits a flat dispersion, a Bogoliubov-like dispersion, or an energy gap when increasing the coupling strength, which can enhance or supress the system instability.

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