Quantum Decay of One-Dimensional Supercurrent: Role of Electromagnetic Field

The quantum decay of a one-dimensional small supercurrent is a charge non-neutral process which involves an electromagnetic field. I take proper account of magnetic and electric screening, respectively, and find that the electromagnetic field contributes an exponentially small multipling factor $e^{-A/\alpha }\sim e^{-100\mathrm{}}$ to the quantum decay rate with α the fine structure constant and $A$ a numerical constant of order unity. This means that a circulating supercurrent lives forever. Possible relevance with several recent experiments is discussed.