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We consider Schrödinger operators on a class of periodic quantum graphs with randomly distributed Kirchhoff coupling constants at all vertices. We obtain necessary conditions for localization on… (More)

We study Lifshitz tails for random Schrodinger operators where the random potential is alloy type in the sense that the single site potentials are independent, identically distributed, but they may… (More)

- Fr'ed'eric Klopp
- 2009

Consider Γ, a non-degenerate lattice in $${{\mathbb R}^2}$$ and a constant magnetic field B with a flux though a cell of Γ that is a rational multiple of 2π. We prove that for a generic Γ-periodic… (More)

We consider the difference Schr{\''o}dinger equation $\psi(z+h)+\psi(z-h)+ v(z)\psi(z)=0$ where $z$ is a complex variable and $h$ is a small positive parameter. If $v$ is an analytic function, then,… (More)

We study the cut-off resolvent of semiclassical Schr{\"o}dinger operators on $\mathbb{R}^d$ with bounded compactly supported potentials $V$. We prove that for real energies $\lambda^2$ in a compact… (More)

We consider the difference Schr{\"o}dinger equation $\psi$(z + h) + $\psi$(z -- h) + v(z)$\psi$(z) = 0 where z is a complex variable, h > 0 is a parameter, and v is an analytic function. As h… (More)