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 impurities with a repulsive single-site potential of Gaussian decay. It has been known that the Gaussian potential tail discriminates between the so-calle...
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| Veröffentlicht in: | Probability theory and related fields 2001-10, Vol.121 (2), p.219-236 |
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| creator | ERDOS, Laszlo |
| description | 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. |
| doi_str_mv | 10.1007/PL00008803 |
| format | Article |
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| subjects | Asymptotic properties Exact sciences and technology Fluctuation phenomena, random processes, noise, and brownian motion Magnetic fields Mathematics Physics Probability Probability and statistics Probability theory and stochastic processes Sciences and techniques of general use Special processes (renewal theory, markov renewal processes, semi-markov processes, statistical mechanics type models, applications) Statistical physics, thermodynamics, and nonlinear dynamical systems |
| title | Lifschitz tail in a magnetic field : coexistence of classical and quantum behavior in the borderline case |
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