18 citations · 53 across the 9 of their papers we have counts for
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The almost periodic gauge transform -- An abstract scheme with applications to Dirac Operators
Jean Lagacé, Sergey Morozov, Leonid Parnovski +2
One of the main tools used to understand both qualitative and quantitative spectral behaviour of periodic and almost periodic Schrödinger operators is the method of gauge transform…
Lower bounds on the moduli of three-dimensional Coulomb-Dirac operators via fractional Laplacians with applications
Sergey Morozov, David Müller
For let be the distinguished self-adjoint realisation of the three-dimensional Coulomb-Dirac operator . For $ν\…
On the virtual levels of positively projected massless Coulomb-Dirac operators
Sergey Morozov, David Müller
Considering different self-adjoint realisations of positively projected massless Coulomb-Dirac operators we find out, under which conditions any negative perturbation, however smal…
Lieb-Thirring and Cwickel-Lieb-Rozenblum inequalities for perturbed graphene with a Coulomb impurity
Sergey Morozov, David Müller
We study the two dimensional massless Coulomb-Dirac operator restricted to its positive spectral subspace and prove estimates on the negative eigenvalues created by electromagnetic…
On the minimax principle for Coulomb-Dirac operators
Sergey Morozov, David Müller
Let q and v be symmetric sesquilinear forms such that v is a form perturbation of q. Then we can associate a unique self-adjoint operator B to q+ v. Assuming that B has a gap (a, b…
Complete asymptotic expansion of the integrated density of states of multidimensional almost-periodic pseudo-differential operators
Sergey Morozov, Leonid Parnovski, Roman Shterenberg
We obtain a complete asymptotic expansion of the integrated density of states of operators of the form H =(-Δ)^w +B in R^d. Here w >0, and B belongs to a wide class of almost-perio…
Lower bound on the density of states for periodic Schrödinger operators
Sergey Morozov, Leonid Parnovski, Irina Pchelintseva
We consider Schrödinger operators with smooth periodic potentials in Euclidean spaces of dimension bigger than 1 and prove a uniform lower bound on the density of states for large…
Exponential decay of eigenfunctions of Brown-Ravenhall operators
Sergey Morozov
We prove the exponential decay of eigenfunctions of reductions of Brown-Ravenhall operators to arbitrary irreducible representations of rotation-reflection and permutation symmetry…
Essential Spectrum of Multiparticle Brown-Ravenhall Operators in External Field
Sergey Morozov
The essential spectrum of multiparticle Brown-Ravenhall operators is characterized in terms of two--cluster decompositions for a wide class of external fields and interparticle int…
Stability of atoms in the Brown-Ravenhall model
Sergey Morozov, Semjon Vugalter
We consider the Brown--Ravenhall model of a relativistic atom with N electrons and a nucleus of charge Z and prove the existence of an infinite number of discrete eigenvalues for N…