Minimum-Time Transitions between Thermal Equilibrium States of the   Quantum Parametric Oscillator
  In this article, we use geometric optimal control to completely solve the problem of minimum-time transitions between thermal equilibrium states of the quantum parametric oscillator, which finds applications in various physical contexts. We discover a new kind of optimal solutions, absent from all the previous treatments of the problem. 
Dionisis Stefanatos
math.OC cs.SY quant-ph