Radiation damping of a quantum harmonic oscillator

Comments on the Interaction Energy of a Quantum Oscillator in the Blackbody Radiation Field

“…-< ...)r = 0), <Hint>£ does not exist in the limit y oo. In the high-and-low-temperature approximation we find the results (we only consider the leading terms; see also the results in [3] which coincide with my results):…”

“…The model Hamiltonian describes a linear charged oscillator in the blackbody radiation field (in the min imal coupling Hamiltonian the A2-term is neglected; dipol-approximation; see formula (1) in [1], which corresponds to the one dimensional version of for mula (1) in [2]; see also [3]): 2 k \ m V atk 1 + Hpi + a iq i: k cok qkQ (1) In (1) the generalized canonical variables P and Q are related with the original variables p and x of the oscillator by the canonical transformation p = -(m Wo)1 2 Q, x = (m col)"1,2 P; pk and qk denote the canonical variables of the field. The averages <)h are taken on the assumption that the Hamiltonian (1) is in thermal equilibrium (i.e.…”

“…I assume that the finite result for A in [2] is due to an inconsistent renormalization procedure with re spect to U on the one hand and <P2) H/2 on the other hand (of course, in [2,3] also a twofold renormaliza tion had to be performed, which essentially corre sponds to (7) and (14)). …”

“…At last I emphasize that due to the neglection of the A2-term the model (7), which was considered in [1][2][3], cannot reveal the well known ^-depen dent energy shift in the high temperature regime (kBT$> h£Oq) [8]-The inclusion of the /42-term in (1) would cause the additional term ri = ^nehco0 (kBT/hoj0)2 in Uth. Consequently, the low-temper ature T 2-shifts in (13) cancel out whereas in the hightemperature regime q represents the most important correction to the free oscillator result.…”