A calculus of observables on a Dirac particle
A comprehensive proof of localization for continuous Anderson models with singular random potentials
We study continuous Anderson Hamiltonians with non-degenerate single site probability distribution of bounded support, without any regularity condition on the single site probability distribution. We prove the existence of a strong form of localization at the bottom of the spectrum, which includes Anderson localization (pure point spectrum with exponentially decaying eigenfunctions) with finite multiplicity of eigenvalues, dynamical localization (no spreading of wave packets under the time evolution),...
A continuous geometry as a mathematical model for quantum mechanics
A convergence theorem for Dirichlet forms with applications to boundary value problems with varying domains.
A discrete and finite approach to past physical reality.
A discrete Hardy-Laptev-Weidl-type inequality and associated Schrödinger-type operators.
A duality between Schrödinger operators on graphs and certain Jacobi matrices
A family of exactly solvable radial quantum systems on space of non-constant curvature with accidental degeneracy in the spectrum.
A field equation defined by a Hurwitz pair
A gauge theoretical approach to space-time structures
A generalization of Gordon's theorem and applications to quasiperiodic Schrödinger operators.
A generalized coherent state approach of the quantum dynamics for suitable time-dependent hamiltonians
A generating function for fatgraphs
A Lieb-Thirring bound for a magnetic Pauli Hamiltonian (II).
We establish a Lieb-Thirring type estimate for Pauli Hamiltonians with non-homogeneous magnetic fields. Besides of depending on the size of the field, the bound also takes into account the size of the field gradient. We then apply the inequality to prove stability of non-relativistic quantum mechanical matter coupled to the quantized ultraviolet-cutoff electromagnetic field for arbitrary values of the fine structure constant.
A method for weight multiplicity computation based on Berezin quantization.
A minimax principle for eigenvalues in spectral gaps: Dirac operators with Coulomb potentials.
A model of atomic radiation
A new method for obtaining solutions of the Dirac equation.
A note concerning the "Feynman integrability" of sets of trajectories
A numerically efficient approach to the modelling of double-Qdot channels
We consider the electronic properties of a system consisting of two quantum dots in physical proximity, which we will refer to as the double-Qdot. Double-Qdots are attractive in light of their potential application to spin-based quantum computing and other electronic applications, e.g. as specialized sensors. Our main goal is to derive the essential properties of the double-Qdot from a model that is rigorous yet numerically tractable, and largely circumvents the complexities of an ab initio simulation....