Equation 84 · The Entry a Relabeling Cannot Write
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Symbol H_f
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subscript
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Because conserves total excitation number, the dynamics starting from a single excitation stays confined to the two-dimensional subspace spanned by |e,g (system excited, bath in its ground state) and |g,e (the reverse). On resonance, both basis states carry the same bare energy, +/2 - /2 = 0 , so restricted to this subspace is proportional to the swap operator between the two, and the Schrödinger equation solves in closed form. Starting from | = |e,g ,
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