Quantum phase slips with and without disorder

The rate of quantum phase slips (QPS) in one-dimensional superfluids and superconductors can be computed from first principles in two limiting cases. One [1] is the uniform (no-disorder) limit, appropriate for suitably prepared atomic gases. The other [2] is the limit when the core resistance of a QPS is effectively infinite, appropriate for a sufficiently long disordered superconducting wire. In the latter case, the calculation applies on the superconducting side of the superconductor-insulator transition, where the dilute instanton gas approximation can be used. It is essential to first compute the instanton rate for a given disorder configuration and then average over disorder, as opposed to working with instantons of a disorder-averaged effective theory. Curiously, in neither of the above cases the system is in the XY universality class: in the uniform limit, the QPS rate is suppressed exponentially at low temperatures, as a consequence of the momentum conservation, while the second case (a relatively long disordered wire) maps onto dissipative quantum mechanics, with the dissipative coefficient controlled by the plasmon impedance $Z$. The role of a finite core resistance can be understood within the picture of effective resistors, representing different dissipative effects, connected in parallel. \newline \newline [1] S. Khlebnikov, Phys. Rev. Lett. {\bf 93}, 090403 (2004); Phys. Rev. A {\bf 71}, 013602 (2005). \newline [2] S. Khlebnikov and L. P. Pryadko, Phys. Rev. Lett. {\bf 95}, 107007 (2005).