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

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

2000-03-22

arxiv.org/abs/math-ph/0003023v1

Physics

Mathematical Physics

Scientific paper

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

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