# Exact results for disordered systems/superfluids II: superfluid-to-Bose glass transition in 1D

Nikolai Prokof'ev, University of Massachusetts Amherst

04.05.2016 at 12:45

I will start by showing that the Giamarchi-Shultz criterion K=3/2 for the localization transition in 1D superfluids (where K is the Luttinger liquid parameter) has the same status as the Nelson- Kosterlitz formula for finite- temperature 2D superfluids---it is exact for finite disorder strength.

However, in strongly disordered 1d superfluids there exists an alternative universality class, scratched-XY. The new universality class is characterized by another universal relation K=1/>3/2 , where is the microscopic exponent characterizing the exponentially rare- exponentially weak power-low distribution of effective Josephson junctions. The RG equations for the scratched-XY behavior are asymptotically exact.

A 450, Theresienstr. 37