Maths HEP Lunchtime Seminars: Resonant tunnelling in the landscape?
6 February 2009 13:00 in CLC407
We discuss resonant tunnelling in quantum mechanics and the application of these idea to the string landscape. Tye had argued that this could lead to dynamical relaxation of the cosmological constant, even though it wasn't known whether resonant tunnelling could occur in quantum field theory. Following the pioneering work of Banks, Bender and Wu, we describe quantum field theory in terms of infinite dimensional quantum mechanics and utilize the ``Most probable escape path'' (MPEP) as the class of paths which dominate the path integral in the classically forbidden region. Considering a 1+1 dimensional field theory example we show that there are five natural conditions that any associated bound state in the classically allowed region should satisfy if resonant tunnelling is to occur, and we then proceed to show that it is impossible to satisfy all five conditions simultaneously. Using this as a guidebook, we then show how to evade our no go theorem by breaking one of those conditions. As a result we give the first explicit example of resonant tunnelling in QFT, albeit given a rather contrived set of initial conditions that only the most optimistic observer would deem relevant in addressing the cosmological constant problem.