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We consider metric perturbations of the Landau Hamiltonian. We investigate the asymptotic behaviour of the discrete spectrum of the perturbed operator near the Landau levels, for perturbations with power-like decay, exponential decay or compact support.
We consider the Landau Hamiltonian perturbed by a long-range electric potential $V$. The spectrum of the perturbed operator consists of eigenvalue clusters which accumulate to the Landau levels. First, we obtain an estimate of the rate of the shrinki
We consider the twisted waveguide $Omega_theta$, i.e. the domain obtained by the rotation of the bounded cross section $omega subset {mathbb R}^{2}$ of the straight tube $Omega : = omega times {mathbb R}$ at angle $theta$ which depends on the variabl
We consider the Schrodinger operator with constant magnetic field defined on the half-plane with a Dirichlet boundary condition, $H_0$, and a decaying electric perturbation $V$. We analyze the spectral density near the Landau levels, which are thresh
Let $A$ be a self-adjoint operator on a Hilbert space $fH$. Assume that the spectrum of $A$ consists of two disjoint components $sigma_0$ and $sigma_1$. Let $V$ be a bounded operator on $fH$, off-diagonal and $J$-self-adjoint with respect to the orth
We consider the 3D Schrodinger operator $H_0$ with constant magnetic field $B$ of scalar intensity $b>0$, and its perturbations $H_+$ (resp., $H_-$) obtained by imposing Dirichlet (resp., Neumann) conditions on the boundary of the bounded domain $Ome