Physica A 154 (1989) 289-306 North-Holland, Amsterdam QUANTUM TUNNELLING IN A DOUBLE SINE-GORDON SYSTEM NEAR THE INSTABILITY K. FURUYA” and A.O. CALDEIRA* Institute de Fisica “Gleb Wataghin”, Universidade Estadual de Campinas, 13081, Campinas, SP, Brazil Received 3 February 1988 Revised manuscript received 24 June 1988 A double sine-Gordon Hamiltonian is studied as a function of a parameter that changes the nature of the minima of the potential. The behaviour of the system in one of the several metastable vacua is particularly analyzed when this state is about to become unstable. The analysis is carried out in 1, 2 or 3 spatial dimensions within the WKB approximation. It is shown that as far as quantum tunnelling is concerned it is reasonable to approximate the double-sine potential by a simpler form only in 1, or 2 spatial dimensions. It is also shown that the dependence of the tunnelling rate on the free parameter is extremely simple in these low-dimensional cases. The importance of vacuum fluctuations in the low barrier regime is investigated by means of standard effective potential calculations. The latter suggests that zero point energy fluctuations drive the system unstable before the classical instability value of the free parameter is reached. Consequently one is not allowed to compute decay rates arbitrarily close to the instability of this false vacuum. 1. Introduction In this paper we shall be interested in studying the behaviour of a field theory described by the equation of motion 1 d2cp 22 -V2q+gsin2q+cusincp=0, (1.1) which is known in the literature as the “double sine-Gordon” equation. Our motivation to study this specific problem has actually come from a condensed matter model which we have been investigating recently [l]. The model describes a two-dimensional array of Heisenberg spins governed by the * Supported in part by Conselho National de Desenvolvimento Cientifico e Tecnol6gico (CNPq). 0378-4371/89/$03.50 0 Elsevier Science Publishers B.V. (North-Holland Physics Publishing Division)