We consider the quantum tunneling phenomenon in a well-behaved triple-well potential. As required by the semiclassical approximation we take into account the quadratic fluctuations over the instanton which represents as usual the localised finite-action solution of the euclidean equation of motion. The determinants of the quadratic differential operators at issue are evaluated by means of the Gelfang-Yaglom method. In doing so the explicit computation of the conventional ratio of determinants takes as reference the harmonic oscillator whose frequency is the average of the individual frequencies derived from the non-equivalent minima of the potential. Eventually the physical effects of the multi-instanton configurations are included in this approach. As a matter of fact we obtain information about the energies of the ground-state and the two first excited levels of the discrete spectrum at issue.
We study first-order spatial coherence for interacting polar bosons trapped in triple-well potentials. It is argued that besides the well-known coherence produced by couplings related to tunneling between the sites, there exists a nonlocal coherence predominantly determined by intersite interactions, which prevails between the outer sites of the triple well when their total filling is odd. We find that the nonlocal interaction-induced coherence originates from the superposition of degenerate many-body states in symmetric triple wells, and demonstrate its robustness against perturbations due to various tunneling mechanisms and thermal fluctuations.