Analysis of nonperturbative fluctuations in a triple-well potential

Details Analysis of nonperturbative fluctuations in a triple-well potential Analysis of nonperturbative fluctuations in a triple-well potential

2001-03-03

arxiv.org/abs/quant-ph/0103010v1

Phys.Lett. A283 (2001) 285-290

Physics

Quantum Physics

12 pages, RevTex

Scientific paper

10.1016/S0375-9601(01)00265-1

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.

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