 
Summary: Adiabatic theorem without a gap condition: Twolevel system coupled
to quantized radiation field
J. E. Avron and A. Elgart
Department of Physics, Technion, 32000 Haifa, Israel
Received 8 July 1998
We prove an adiabatic theorem for the ground state of the Dicke model Phys. Rev. 93, 99 1954 in a
slowly rotating magnetic field and show that for weak electronphoton coupling, the adiabatic time scale is
close to the time scale of the corresponding twolevel system without the quantized radiation field. There is a
correction to this time scale, which is the Lamb shift of the model. The photon field affects the rate of approach
to the adiabatic limit through a logarithmic correction originating from an infrared singularity characteristic of
QED. S10502947 98 02112X
PACS number s : 12.20. m, 03.65.Db, 32.80. t
I. INTRODUCTION
In this work we investigate the relation between adiabatic
theorems for models that, like QED, allow for the creation
and annihilation of photons and the corresponding quantum
mechanical models where the electron is decoupled from the
photon field. We study this problem in the context of a spe
cific and essentially soluble model: the Dicke model 1 . The
corresponding quantummechanical model is a twolevel
