We discuss fluctuations near the second order phase transition where the free energy has an additional non-Hermitian term. The spectrum of the fluctuations changes when the odd-parity potential amplitude exceeds the critical value corresponding to th
e PT-symmetry breakdown in the topological structure of the Hilbert space of the effective non-Hermitian Hamiltonian. We calculate the fluctuation contribution to the differential resistance of a superconducting weak link and find the manifestation of the PT-symmetry breaking in its temperature evolution. We successfully validate our theory by carrying out measurements of far from equilibrium transport in mesoscale-patterned superconducting wires.
We investigate experimentally the electric transport at the insulating side of the superconductor to insulator transition in thin TiN-films. At temperatures T > 50 mK we observe an Arrhenius-type conductance, with an activation energy depending logar
ithmically on the sample size. At high bias the current voltage (I-V) characteristics display a large current jump into an electron heating dominated regime. For the largest samples, and below 50 mK we observe a low-bias power law I ~ V^alpha characteristics with an exponent alpha > 1 rapidly growing with decreasing temperature, which is expected for a binding-unbinding crossover of the charge-Berezinskii-Kosterlitz-Thouless type.
