An Adiabatic Theorem without a Gap Condition: Two level system coupled to quantized radiation field

Details An Adiabatic Theorem without a Gap Condition: Two level system coupled to quantized radiation field An Adiabatic Theorem without a Gap Condition: Two level system coupled to quantized radiation field

1998-03-31

arxiv.org/abs/math/9803153v4

Phys. Rev. A, 58, 4300-4306, (1998)

Mathematics

Functional Analysis

Revised version, 15 pages

Scientific paper

10.1103/PhysRevA.58.4300

We prove an adiabatic theorem for the ground state of the Dicke model in a slowly rotating magnetic field and show that for weak electron-photon coupling, the adiabatic time scale is close to the time scale of the corresponding two level 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 affect the rate of approach to the adiabatic limit through a logarithmic correction originating from an infrared singularity characteristic of QED.

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