Lifschitz tail in a magnetic field: coexistence of classical and quantum behavior in the borderline case

We establish the exact low-energy asymptotics of the integrated density of states (Lifschitz tail) in a homogeneous magnetic field and Poissonian impu rities with a repulsive single-site potential of Gaussian decay. It has bee n known that the Gaussian potential tail discriminates between the so-calle d "classical" and "quantum" regimes, and precise asymptotics are known in t hese cases. For the borderline case, the coexistence of the classical and q uantum regimes was conjectured. Here we settle this last remaining open cas e to complete the full picture of the magnetic Lifschitz tails.