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Visar resultat 1 - 5 av 6 avhandlingar som matchar ovanstående sökkriterier.

  1. 1. Spectral Inequalities and Their Applications in Quantum Mechanics

    Författare :Fabian Portmann; Ari Laptev; Robert Seiringer; KTH; []
    Nyckelord :NATURVETENSKAP; NATURAL SCIENCES; Spectral inequalities; quantum mechanics; Hardy inequalities; Sobolev inequalities; Lieb-Thirring inequalities; stability of matter; Bose gases; Bose-Einstein condensation; Mathematics; Matematik; Fysik; Physics;

    Sammanfattning : The work presented in this thesis revolves around spectral inequalities and their applications in quantum mechanics.In Paper A, the ground state energy of an atom confined to two dimensions is analyzed in the limit when the charge of the nucleus Z becomes very large. LÄS MER

  3. 2. Hardy-Lieb-Thirring inequalities for eigenvalues of Schrödinger operators

    Författare :Rupert L. Frank; Ari Laptev; Jan Philip Solovej; KTH; []
    Nyckelord :NATURVETENSKAP; NATURAL SCIENCES; MATHEMATICS; MATEMATIK;

    Sammanfattning : This thesis is devoted to quantitative questions about the discrete spectrum of Schrödinger-type operators. In Paper I we show that the Lieb-Thirring inequalities on moments of negative eigen¬values remain true, with possibly different constants, when the critical Hardy weight is subtracted from the Laplace operator. LÄS MER

  4. 3. Spectral estimates for the magnetic Schrödinger operator and the Heisenberg Laplacian

    Författare :Anders Hansson; Ari Laptev; B Malcolm Brown; KTH; []
    Nyckelord :NATURVETENSKAP; NATURAL SCIENCES; spectral theory; Schrödinger operator; magnetic field; Aharonov-Bohm; Lieb-Thirring; diamagnetic inequality; Heisenberg group; Heisenberg Laplacian; hypoelliptic; spektralteori; Schrödingeroperator; magnetfält; Aharonov-Bohm; Lieb-Thirring; diamagnetisk olikhet; Heisenberggrupp; Heisenberg-Laplace-operator; hypoelliptisk; MATHEMATICS; MATEMATIK;

    Sammanfattning : I denna avhandling, som omfattar fyra forskningsartiklar, betraktas två operatorer inom den matematiska fysiken. De båda tidigare artiklarna innehåller resultat för Schrödingeroperatorn med Aharonov-Bohm-magnetfält. LÄS MER

  5. 4. Asymptotic and universal spectral estimates with applications in many-body quantum mechanics and spectral shape optimization

    Författare :Simon Larson; Ari Laptev; Stefan Steinerberger; KTH; []
    Nyckelord :NATURVETENSKAP; NATURAL SCIENCES; Spectral theory; shape optimization; semiclassical asymptotics; spectral inequalities; quantum mechanics; Mathematics; Matematik;

    Sammanfattning : This thesis consists of eight papers primarily concerned with the quantitative study of the spectrum of certain differential operators. The majority of the results split into two categories. LÄS MER

  7. 5. Schrödinger Operators in Waveguides

    Författare :Tomas Ekholm; Timo Weidl; Ari Laptev; Pavel Exner; KTH; []
    Nyckelord :NATURVETENSKAP; NATURAL SCIENCES; Schrödinger Operators; Hardy Inequalities; Mathematical physics; Matematisk fysik;

    Sammanfattning : In this thesis, which consists of four papers, we study the discrete spectrum of Schrödinger operators in waveguides. In these domains the quadratic form of the Dirichlet Laplacian operator does not satisfy any Hardy inequality. LÄS MER