Browsing by Author "Lotoreichik, Vladimir"

Now showing 1 - 2 of 2
  • No Thumbnail Available
    Item
    A Variational Formulation for Dirac Operators in Bounded Domains. Applications to Spectral Geometric Inequalities
    (2021) Antunes, Pedro R. S.; Benguria, Rafael D.; Lotoreichik, Vladimir; Ourmieres-Bonafos, Thomas
    We investigate spectral features of the Dirac operator with infinite mass boundary conditions in a smooth bounded domain of R-2. Motivated by spectral geometric inequalities, we prove a non-linear variational formulation to characterize its principal eigenvalue. This characterization turns out to be very robust and allows for a simple proof of a Szego type inequality as well as a new reformulation of a Faber-Krahn type inequality for this operator. The paper is complemented with strong numerical evidences supporting the existence of a Faber-Krahn type inequality.
  • No Thumbnail Available
    Item
    The fate of Landau levels under δ-interactions
    (2022) Behrndt, Jussi; Holzmann, Markus; Lotoreichik, Vladimir; Raikov, Georgi
    We consider the self-adjoint Landau Hamiltonian H-0 in L-2(R-2) whose spectrum consists of infinitely degenerate eigenvalues Lambda(q), q is an element of Z(+), and the perturbed Landau Hamiltonian H-upsilon = H-0 + upsilon delta(Gamma), where Gamma subset of R-2 is a regular Jordan C-1,C-1-curve and upsilon is an element of L-p(Gamma; R), p > 1, has a constant sign. We investigate ker(H-upsilon - Lambda(q)), q is an element of Z(+), and show that generically