Upper and lower bounds for tunneling splittings in a symmetric double-well potential. Issue 57 (18th September 2020) - Ronto, Miklos; Pollak, Eli
Abstract : Ground state tunneling gaps: solid circles are mean of eigenvalues and lower bound gaps. Abstract : The accurate determination of tunneling splittings in chemistry and physics is an ongoing challenge. However, the widely used variational methods only provide upper bounds for the energy levels, and thus do not give bounds on the gap between them. Here, we show how the self-consistent lower bound theory developed previously can be applied to provide upper and lower bounds for tunneling splitting between symmetric and antisymmetric doublets in a symmetric double-well potential. The tight bounds are due to the very high accuracy of the lower bounds obtained for the energy levels, using the self-consistent lower bound theory. The accuracy of the lower bounds is comparable to that of the Ritz upper bounds. This is the first time that any theory gave upper and lower bounds to tunneling splittings.