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Quantum tunnelling in a double sine-Gordon system near the instability

Author

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  • Furuya, K.
  • Caldeira, A.O.

Abstract

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.

Suggested Citation

  • Furuya, K. & Caldeira, A.O., 1989. "Quantum tunnelling in a double sine-Gordon system near the instability," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 154(2), pages 289-306.
    • Handle: RePEc:eee:phsmap:v:154:y:1989:i:2:p:289-306
    DOI: 10.1016/0378-4371(89)90014-9
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