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

J. E. Avron·A. Elgart
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Abstract

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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J. E. Avron, A. Elgart. 1998-08-20. An Adiabatic Theorem without a Gap Condition: Two level system coupled to quantized radiation field. https://doi.org/10.1103/physreva.58.4300

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