The magnitude of an adiabatic invariant of quantum mechanics

L. M. Garrido

L. M. Garrido, F.J. Sancho

F. Leyvraz, T. H. Seligman

E. Gozzi

S. González-Resines, David Guéry-Odelin, Ander Tobalina +3 more

In physics, similarities can crop up in the most unexpected places. This study, for example, exploits the striking analogy between single ions in microscopic moving traps and the loads moved by mechanical cranes. Though the systems are separated by many orders of magnitude in mass and shuttling distance, results and concepts may be translated from the microscopic domain to the macroscopic, and $v\phantom{\rule{0}{0ex}}i\phantom{\rule{0}{0ex}}c\phantom{\rule{0}{0ex}}e$ $v\phantom{\rule{0}{0ex}}e\phantom{\rule{0}{0ex}}r\phantom{\rule{0}{0ex}}s\phantom{\rule{0}{0ex}}a$. ``Shortcuts to adiabaticity'' techniques based on dynamical invariants of motion allow for fast, ultrarobust load control for unknown initial conditions for cranes, while the analysis of energy consumption for cranes can be translated to ion traps.

L.D. Faddeev, L.A. Khalfin, I.V. Komarov

In old quantum mechanics the adiabatic theorem established by Ehrenfest had the meaning that the quantized action variables J = n are invariant relative to an infinitely slow (adiabatic) change of a mechanical system.1 From this one can guess that if the system is in a state with definite quantum numbers before the adiabatic change started, then after the changes it will be characterized by the same quantum numbers.