Tunneling in a uniform one-dimensional superfluid: emergence of a complex instanton

Details Tunneling in a uniform one-dimensional superfluid: emergence of a complex instanton Tunneling in a uniform one-dimensional superfluid: emergence of a complex instanton

2004-08-24

arxiv.org/abs/cond-mat/0408500v2

Phys. Rev. A 71, 013602 (2005)

Physics

Condensed Matter

Other Condensed Matter

15 pages, 3 figures; to be published in Phys. Rev. A

Scientific paper

10.1103/PhysRevA.71.013602

In a uniform ring-shaped one-dimensional superfluid, quantum fluctuations that unwind the order parameter need to transfer momentum to quasiparticles (phonons). We present a detailed calculation of the leading exponential factor governing the rate of such phonon-assisted tunneling in a weakly-coupled Bose gas at a low temperature $T$. We also estimate the preexponent. We find that for small superfluid velocities the $T$-dependence of the rate is given mainly by $\exp(-c_s P/ 2T)$, where $P$ is the momentum transfer, and $c_s$ is the phonon speed. At low $T$, this represents a strong suppression of the rate, compared to the non-uniform case. As a part of our calculation, we identify a complex instanton, whose analytical continuation to suitable real-time segments is real and describes formation and decay of coherent quasiparticle states with nonzero total momenta.

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