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Volume 2 - LENR-CANR

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Figure 3. Energy levels that contribute to indirect coupling between |M,n and |M+1,n-5 in the case of<br />

multi-quantum exchange involving 5 quanta.<br />

The impact of loss on energy exchange can be illustrated through a concrete example. We<br />

consider a finite basis solution constructed from a combination of 12 basis states composed<br />

individually of products of Dicke states and oscillator states<br />

c S, M n<br />

j<br />

j j j<br />

We consider indirect coupling from an initial state |M,n to a final state |M+1,n-5, in which a<br />

single two-level system excitation is matched to a loss of 5 oscillator quanta. The states are<br />

illustrated in Figure 3.<br />

If no loss is present, the indirect matrix element between the initial state and the final state<br />

can be found to lowest-order in perturbation theory to be<br />

5<br />

625 V<br />

V1,12 n n 1 4 n 4 S M S M 1 0<br />

64 E<br />

If loss is present and large for all intermediate states with a basis energy less than E, such that<br />

the associated paths do not contribute, then the indirect coupling matrix element is<br />

1 4 3 2 2<br />

V1,12 1,125 S 10S S 10M 8M 22<br />

V <br />

0<br />

18 <br />

584

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