Abstract
We study the role of Franck-Condon (F-C) principle in the dynamics of a central spin system, which is coupled to an Ising chain in transverse field. The transition process of energy levels caused by the excited central spin is studied to manifest the quantum critical effect through the Franck-Condon principle. The super-sensitivity of this quantum critical system is demonstrated clearly from the properties of Franck-Condon factors. We analytically show how spin numbers, coupling strength and order parameter of the Ising chain sensitively effect on the energy level populations in dynamical evolution near the critical point. This super-sensitivity and criticality are explicitly displayed in absorption spectrum.
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