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Spectral statistics for random Schrödinger operators in the localized regime

François Germinet, Frédéric Klopp (2014)

Journal of the European Mathematical Society

We study various statistics related to the eigenvalues and eigenfunctions of random Hamiltonians in the localized regime. Consider a random Hamiltonian at an energy $E$ in the localized phase. Assume the density of states function is not too flat near $E$ . Restrict it to some large cube $Λ$ . Consider now $I_{Λ}$ , a small energy interval centered at $E$ that asymptotically contains infintely many eigenvalues when the volume of the cube $Λ$ grows to infinity. We prove that, with probability one in the large volume...

Spectral theory for a mathematical model of the weak interaction. I: The decay of the intermediate vector bosons $W^{\pm}$ .

Barbaroux, J.-M., Guillot, J.-C. (2009)

Advances in Mathematical Physics

Spectral theory of corrugated surfaces

Vojkan Jakšić (2001)

Journées équations aux dérivées partielles

We discuss spectral and scattering theory of the discrete laplacian limited to a half-space. The interesting properties of such operators stem from the imposed boundary condition and are related to certain phenomena in surface physics.

Spectre de l'équation de Schrödinger, application à la stabilité de la matière

Pierre Cartier (1976/1977)

Séminaire Bourbaki

Spectre de l'opérateur de Schrödinger magnétique avec symétrie d'ordre six

Philippe Kerdelhué (1992)

Mémoires de la Société Mathématique de France

Stability and semiclassics in self-generated fields

László Erdős, Soren Fournais, Jan Philip Solovej (2013)

Journal of the European Mathematical Society

We consider non-interacting particles subject to a fixed external potential $V$ and a self-generated magnetic field $B$ . The total energy includes the field energy $β \int B^{2}$ and we minimize over all particle states and magnetic fields. In the case of spin-1/2 particles this minimization leads to the coupled Maxwell-Pauli system. The parameter $β$ tunes the coupling strength between the field and the particles and it effectively determines the strength of the field. We investigate the stability and the semiclassical...

Stability of matter in classical and quantized fields.

Graf, Gian Michele (1998)

Documenta Mathematica

Stationary Schrödinger equations governing electronic states of quantum dots in the presence of spin-orbit splitting

Marta M. Betcke, Heinrich Voss (2007)

Applications of Mathematics

In this work we derive a pair of nonlinear eigenvalue problems corresponding to the one-band effective Hamiltonian accounting for the spin-orbit interaction governing the electronic states of a quantum dot. We show that the pair of nonlinear problems allows for the minmax characterization of its eigenvalues under certain conditions which are satisfied for our example of a cylindrical quantum dot and the common InAs/GaAs heterojunction. Exploiting the minmax property we devise an efficient iterative...

Strong resonant tunneling, level repulsion and spectral type for one-dimensional adiabatic quasi-periodic Schrödinger operators

Alexander Fedotov, Frédéric Klopp (2005)

Annales scientifiques de l'École Normale Supérieure

Sur l'approximation de Born-Oppenheimer des opérateurs d'onde

A. Martinez (1994/1995)

Séminaire Équations aux dérivées partielles (Polytechnique)

Displaying 21 – 30 of 30

Currently displaying 21 – 30 of 30