Editing Quantum tunnelling (section)

=== Chaos-assisted tunnelling ===
[[File:Chaos-assisted tunneling in phase space.gif|left|thumb|upright=1|Chaos-assisted tunnelling oscillations between two regular tori embedded in a chaotic sea, seen in phase space]]

In real life, most systems are not integrable and display various degrees of chaos. Classical dynamics is then said to be mixed and the system phase space is typically composed of islands of regular orbits surrounded by a large sea of chaotic orbits. The existence of the chaotic sea, where transport is classically allowed, between the two symmetric tori then assists the quantum tunnelling between them. This phenomenon is referred as chaos-assisted tunnelling.<ref>{{Cite journal|last1=Tomsovic|first1=Steven|last2=Ullmo|first2=Denis|date=1994-07-01|title=Chaos-assisted tunneling|url=https://link.aps.org/doi/10.1103/PhysRevE.50.145|journal=Physical Review E|volume=50|issue=1|pages=145–162|doi=10.1103/PhysRevE.50.145|pmid=9961952|bibcode=1994PhRvE..50..145T}}</ref> and is characterized by sharp resonances of the tunnelling rate when varying any system parameter.