Quasi-classical versus non-classical spectral asymptotics for magnetic Schroedinger operators with decreasing electric potentials

We consider the Schroedinger operator H on L^2(R^2) or L^2(R^3) with constant magnetic field and electric potential V which typically decays at infinity exponentially fast or has a compact support. We investigate the asymptotic behaviour of the discrete spectrum of H near the boundary points of its essential spectrum. If the decay of V is Gaussian or faster, this behaviour is non-classical in the sense that it is not described by the quasi-classical formulas known for the case where V admits a power-like decay.Comment: Corrected versio

Lifshitz Tails in Constant Magnetic Fields

We consider the 2D Landau Hamiltonian $H$ perturbed by a random alloy-type potential, and investigate the Lifshitz tails, i.e. the asymptotic behavior of the corresponding integrated density of states (IDS) near the edges in the spectrum of $H$. If a given edge coincides with a Landau level, we obtain different asymptotic formulae for power-like, exponential sub-Gaussian, and super-Gaussian decay of the one-site potential. If the edge is away from the Landau levels, we impose a rational-flux assumption on the magnetic field, consider compactly supported one-site potentials, and formulate a theorem which is analogous to a result obtained in the case of a vanishing magnetic field

On the discrete spectrum of spin-orbit Hamiltonians with singular interactions

We give a variational proof of the existence of infinitely many bound states below the continuous spectrum for spin-orbit Hamiltonians (including the Rashba and Dresselhaus cases) perturbed by measure potentials thus extending the results of J.Bruening, V.Geyler, K.Pankrashkin: J. Phys. A 40 (2007) F113--F117.Comment: 10 pages; to appear in Russian Journal of Mathematical Physics (memorial volume in honor of Vladimir Geyler). Results improved in this versio

Resonances Width in Crossed Electric and Magnetic Fields

We study the spectral properties of a charged particle confined to a two-dimensional plane and submitted to homogeneous magnetic and electric fields and an impurity potential. We use the method of complex translations to prove that the life-times of resonances induced by the presence of electric field are at least Gaussian long as the electric field tends to zero.Comment: 3 figure

Novel techniques for alpha/beta pulse shape discrimination in Borexino

Borexino could efficiently distinguish between alpha and beta radiation in its liquid scintillator by the characteristic time profile of their scintillation pulse. This alpha/beta discrimination, first demonstrated at the tonne scale in the Counting Test Facility prototype, was used throughout the lifetime of the experiment between 2007 and 2021. With this method, alpha events are identified and subtracted from the beta-like solar neutrino events. This is particularly important in liquid scintillator as alpha scintillation is quenched many-fold. In Borexino, the prominent Po-210 decay peak was a background in the energy range of electrons scattered from Be-7 solar neutrinos. Optimal alpha-beta discrimination was achieved with a "multi-layer perceptron neural network", which its higher ability to leverage the timing information of the scintillation photons detected by the photomultiplier tubes. An event-by-event, high efficiency, stable, and uniform pulse shape discrimination was essential in characterising the spatial distribution of background in the detector. This benefited most Borexino measurements, including solar neutrinos in the \pp chain and the first direct observation of the CNO cycle in the Sun. This paper presents the key milestones in alpha/beta discrimination in Borexino as a term of comparison for current and future large liquid scintillator detectorsComment: 13 pages, 14 figure