Revisiting the Fermi Golden Rule: Quantum Dynamical Phase Transition as a Paradigm Shift

Classical and quantum phase transitions involve observables which are non-analytic as functions of a controlled thermodynamical variable. As occurs with the self-consistent Fermi Golden Rule, one condition to obtain the discontinuous behavior is the proper evaluation of a classical or quantum thermodynamic limit. We show that in presence of an environment, the oscillatory dynamics of a quantum two-level system, in analogy with a classical damped oscillator, can undergo a quantum dynamical phase transition to a non-oscillatory phase. This is obtained from a self-consistent solution of the Generalized Landauer Buettiker Equations, a simplified integral form of the Keldysh formalism. I argue that working at each side of the transition implies standing under different paradigms in the Kuhn's sense of the word. In consequence, paradigms incommensurability obtains a sound mathematical justification as a consequence of the non-analyticity of the observables. A strong case is made upon the need to deepen the public's intuition and understanding on the abrupt transition from static to dynamical friction regimes. Keywords: Self Consistent Fermi Golden Rule, Paradigm Shift, Quantum Dynamical Phase Transition, Decoherence, Energy-time Wigner Function, Dissipative Two-level system, Keldysh Formalisma, Generalized Landauer-Buettiker Equations, Loschmidt Echo, Mesoscopic Echo, Spin Dynamics, Solid State NMR, Dynamical Quantum Zeno Effect, Liquid Crystal NMR.