Browsing by Author "Cornean, Horia"

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    ON THE TWO-DIMENSIONAL QUANTUM CONFINED STARK EFFECT IN STRONG ELECTRIC FIELDS
    (2022) Cornean, Horia; Krejcirik, David; Pedersen, Thomas G.; Raymond, Nicolas; Stockmeyer, Edgardo
    We consider a Stark Hamiltonian on a two-dimensional bounded domain with Dirichlet boundary conditions. In the strong electric field limit we derive, under certain local convexity conditions, a three-term asymptotic expansion of the low-lying eigenvalues. This shows that the excitation frequencies are proportional to the square root of the boundary curvature at a certain point determined by the direction of the electric field.
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    Resolvent Convergence to Dirac Operators on Planar Domains
    (2019) Barbaroux, Jean-Marie; Cornean, Horia; Le Treust, Loic; Stockmeyer, Edgardo
    Consider a Dirac operator defined on the whole plane with a mass term of size m supported outside a domain . We give a simple proof for the norm resolvent convergence, as m goes to infinity, of this operator to a Dirac operator defined on with infinite-mass boundary conditions. The result is valid for bounded and unbounded domains and gives estimates on the speed of convergence. Moreover, the method easily extends when adding external matrix-valued potentials.
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    Spectral Gaps in Graphene Antidot Lattices
    (2017) Barbaroux, Jean-Marie; Cornean, Horia; Stockmeyer, Edgardo