A generalized<i>G</i>‐function for the Quantum Rabi Model

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  • Daniel Braak
    EP VI and Center for Electronic Correlations and Magnetism University of Augsburg 86135 Augsburg Germany

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<jats:p>The analytical solution of the quantum Rabi model is based on a transcendental function<jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="graphic/andp201200270-math-0001.png" xlink:title="urn:x-wiley:00033804:andp201200270:equation:andp201200270-math-0001"/>, the zeros of which determine the eigenenergies.<jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="graphic/andp201200270-math-0002.png" xlink:title="urn:x-wiley:00033804:andp201200270:equation:andp201200270-math-0002"/>is generalized here to a function<jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="graphic/andp201200270-math-0003.png" xlink:title="urn:x-wiley:00033804:andp201200270:equation:andp201200270-math-0003"/>, which allows a much better numerical control of the high‐energy part of the spectrum by an appropriate choice of the complex parameter<jats:italic>z</jats:italic>. Additionally, it is shown that all zeros of<jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="graphic/andp201200270-math-0004.png" xlink:title="urn:x-wiley:00033804:andp201200270:equation:andp201200270-math-0004"/>correspond to eigenvalues of the Hamiltonian as well as the zeros of<jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="graphic/andp201200270-math-0005.png" xlink:title="urn:x-wiley:00033804:andp201200270:equation:andp201200270-math-0005"/>for imaginary<jats:italic>z</jats:italic>.</jats:p>

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