By M. Szymanska
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Additional resources for Bose Condensation and Lasing in Optical Microstructures - Part I [thesis]
14) studied for an isolated condensate by Eastham and Littlewood [38, 40]. 2. 17)), contains all interactions with an environment. 17)): gκ (k)(ψ † dk + d†k ψ) + HSB = j,k α † gγ↑ (j, k)(b†j aj cα† j,k + cj,k aj bj ) + j,k † gγ↓ (j, k)(b†j aj cβj,k + cβ† j,k aj bj ) j,k + j,k b gγb (j, k)b†j bj (cb† j,k + cj,k ) − a gγa (j, k)a†j aj (ca† j,k + cj,k ). 4) which is the sum of photons and excited two-level oscillators, is conserved in a steady state. 18). e. aj b†k with k = j) as their influence would be small in comparison to the coupling within the same site.
They can be high energy phonons, collisions or impurities. In the case of electrons and holes even the normal impurities could be pair-breaking processes as the electric charge of the impurity acts with the opposite sign on the electron and the hole . 5) contains interactions which are the same for both levels and are analogous to normal, non-magnetic, impurities in superconductors. We will call them type 2 processes. This processes correspond to potentials which vary very slowly in space in comparison to the size of excitons or in time.
At zero temperature the system is always condensed as the decoherence processes are not included in the model. The condensate has a gap in the excitation spectrum of magnitude 4g|λ|, where λ is an amplitude of the coherent photon field and g, as usual, is the coupling 18 M. 3). 3: The photon spectral functions A(ω) for polariton system (+ve values mean absorption, and -ve emission) at different excitation densities ρex . The top row of plots (red curves) are in the normal state, the bottom left hand plot (green curve) at the transition and the remaining plots (blue curves) in the condensed state, taken from the reference .