Spectral properties of the spin-boson hamiltonian
Spectral resolutions for -complete lattice effect algebras
Spectral Riesz-Cesàro means: How the square root function helps us to see around the world.
Spectral shift and multiplicity of the first eigenvalue of the magnetic Schrödinger operator in two dimensions
We show that the lowest eigenvalue of the magnetic Schrödinger operator on a line bundle over a compact Riemann surface is bounded by the -norm of the magnetic field . This implies a similar bound on the multiplicity of the ground state. An example shows that this degeneracy can indeed be comparable with even in case of the trivial bundle.
Spectral statistics.
Spectral statistics for random Schrödinger operators in the localized regime
We study various statistics related to the eigenvalues and eigenfunctions of random Hamiltonians in the localized regime. Consider a random Hamiltonian at an energy in the localized phase. Assume the density of states function is not too flat near . Restrict it to some large cube . Consider now , a small energy interval centered at that asymptotically contains infintely many eigenvalues when the volume of the cube 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 .
Spectral theory of corrugated surfaces
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.
Spectral theory of damped quantum chaotic systems
We investigate the spectral distribution of the damped wave equation on a compact Riemannian manifold, especially in the case of a metric of negative curvature, for which the geodesic flow is Anosov. The main application is to obtain conditions (in terms of the geodesic flow on and the damping function) for which the energy of the waves decays exponentially fast, at least for smooth enough initial data. We review various estimates for the high frequency spectrum in terms of dynamically defined...
Spectral theory of invariant operators, sharp inequalities, and representation theory
The paper represents the lectures given by the author at the 16th Winter School on Geometry and Physics, Srni, Czech Republic, January 13-20, 1996. He develops in an elegant manner the theory of conformal covariants and the theory of functional determinant which is canonically associated to an elliptic operator on a compact pseudo-Riemannian manifold. The presentation is excellently realized with a lot of details, examples and open problems.
Spectral Theory of the Dirac Operator.
Spectre de l'équation de Schrödinger, application à la stabilité de la matière
Spectre de l'opérateur de Schrödinger magnétique avec symétrie d'ordre six
Spectrum generating functions for oscillators in Wigner's quantization
The n-dimensional (isotropic and non-isotropic) harmonic oscillator is studied as a Wigner quantum system. In particular, we focus on the energy spectrum of such systems. We show how to solve the compatibility conditions in terms of 𝔬𝔰𝔭(1|2n) generators, and also recall the solution in terms of 𝔤𝔩(1|n) generators. A method is described for determining a spectrum generating function for an element of the Cartan subalgebra when working with a representation of any Lie (super)algebra. Here, the...
Spectrum of the laplacian in a narrow curved strip with combined Dirichlet and Neumann boundary conditions
We consider the laplacian in a domain squeezed between two parallel curves in the plane, subject to Dirichlet boundary conditions on one of the curves and Neumann boundary conditions on the other. We derive two-term asymptotics for eigenvalues in the limit when the distance between the curves tends to zero. The asymptotics are uniform and local in the sense that the coefficients depend only on the extremal points where the ratio of the curvature radii of the Neumann boundary to the Dirichlet one...
Spectrum of the Laplacian in a narrow curved strip with combined Dirichlet and Neumann boundary conditions
We consider the Laplacian in a domain squeezed between two parallel curves in the plane, subject to Dirichlet boundary conditions on one of the curves and Neumann boundary conditions on the other. We derive two-term asymptotics for eigenvalues in the limit when the distance between the curves tends to zero. The asymptotics are uniform and local in the sense that the coefficients depend only on the extremal points where the ratio of the curvature radii of the Neumann boundary to the Dirichlet one...
Spectrum of the Laplacian in narrow tubular neighbourhoods of hypersurfaces with combined Dirichlet and Neumann boundary conditions
We consider the Laplacian in a domain squeezed between two parallel hypersurfaces in Euclidean spaces of any dimension, subject to Dirichlet boundary conditions on one of the hypersurfaces and Neumann boundary conditions on the other. We derive two-term asymptotics for eigenvalues in the limit when the distance between the hypersurfaces tends to zero. The asymptotics are uniform and local in the sense that the coefficients depend only on the extremal points where the ratio of the area of the Neumann...
Spin chain connected to the quantum superalgebra .
Spinor equations in Weyl geometry
This paper deals with Dirac, twistor and Killing equations on Weyl manifolds with -spin structures. A conformal Schrödinger-Lichnerowicz formula is presented and used to derive integrability conditions for these equations. It is shown that the only non-closed Weyl manifolds of dimension greater than 3 that admit solutions of the real Killing equation are 4-dimensional and non-compact. Any Weyl manifold of dimension greater than 3, that admits a real Killing spinor has to be Einstein-Weyl.
Spinor types in infinite dimensions.