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

摘要

Classical and quantum phase transitions involve observables which arenon-analytic as functions of a controlled thermodynamical variable. As occurswith the self-consistent Fermi Golden Rule, one condition to obtain thediscontinuous behavior is the proper evaluation of a classical or quantumthermodynamic limit. We show that in presence of an environment, theoscillatory dynamics of a quantum two-level system, in analogy with a classicaldamped oscillator, can undergo a quantum dynamical phase transition to anon-oscillatory phase. This is obtained from a self-consistent solution of theGeneralized Landauer Buettiker Equations, a simplified integral form of theKeldysh formalism. I argue that working at each side of the transition impliesstanding under different paradigms in the Kuhn's sense of the word. Inconsequence, paradigms incommensurability obtains a sound mathematicaljustification as a consequence of the non-analyticity of the observables. Astrong case is made upon the need to deepen the public's intuition andunderstanding on the abrupt transition from static to dynamical frictionregimes. Keywords: Self Consistent Fermi Golden Rule, Paradigm Shift, QuantumDynamical Phase Transition, Decoherence, Energy-time Wigner Function,Dissipative Two-level system, Keldysh Formalisma, GeneralizedLandauer-Buettiker Equations, Loschmidt Echo, Mesoscopic Echo, Spin Dynamics,Solid State NMR, Dynamical Quantum Zeno Effect, Liquid Crystal NMR.