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By H. Haken (auth.), L. Genzel (eds.)

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3 M. LAx: Phys. Rev. 129, 2342 (1963). Quantum mechanical Langevin equations. Sect. 3. 9) becomes db+ ~ " =iw0 b+-xb+ +i~g! Bt (t0) . F+(t) where the last term is evidently the fluctuating force. 15) Q) iiw is the occupation number of the mode corresponding to frequency w of the heatbath. 15) can be directly expressed by the damping constant x only for the temperature T=O. 18) w and (F(t) F+(t')) w always appear under an integral which contains a factor eiw,t, where w 0 is the frequency of the harmonic oscillator (light field).

5) nwo b+b. 6) we arrive at a:; Jb+(T) t =iwob+- 4 lgwl2 eiw{t-T)dl'+i Lg! B;t (to) eiwt. 10) +oo I lgl 2 eiw{t-r) dw = 2x <5 (t- T) . 11) has certain computational advantages. The actual difference between (IV. 11) is in practical calculations negligible. 4) are the important ones. For a discussion of the terms dropped see R. BoNIFACIO and F. HAAKE: Z. Physik 200, 526 (1967). 1 For a coupling of the harmonic oscillator to a general heatbath (treated approximately) see J. R. SENITZKY: Phys. Rev.

15) means derivation with respect to the argument. 15) we have neglected terms of the order (1 -r)f(kD). 18) where already for n ~ 1 the asymptotic formulas of the Fresnel integrals have been used (for more details see RISKEN, 1. c. 4 on p. 11}. 15) leading to Dl0 g'(l0 A}I00 =g(l0 A) IX -----'!!.. 19} reads l0 A = x,. 20) 100 ) where x~' is one of the zeros of g. c. 3 on p. 11}. It is, however, a simple matter to calculate higher approximations. 15), we find for the field distribution in the interior of the resonator: l ~ = {c~s q z}g(lo A 1]) IXo sm q z _ ~g'(x) 2n ~' 1-i ~ L {cos q,.

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