Some rigorous results on the Pauli-Fierz model of classical electrodynamics
Some weighted norm inequalities concerning the Schrödinger operators.
Space of local fields in integrable field theory and deformed abelian differentials.
Spacelike singularities and hidden symmetries of gravity.
Spaces of observables
Space-time decompositions via differential forms
The author presents a simple method (by using the standard theory of connections on principle bundles) of -decomposition of the physical equations written in terms of differential forms on a 4-dimensional spacetime of general relativity, with respect to a general observer. Finally, the author suggests possible applications of such a decomposition to the Maxwell theory.
Sparse grids for the Schrödinger equation
We present a sparse grid/hyperbolic cross discretization for many-particle problems. It involves the tensor product of a one-particle multilevel basis. Subsequent truncation of the associated series expansion then results in a sparse grid discretization. Here, depending on the norms involved, different variants of sparse grid techniques for many-particle spaces can be derived that, in the best case, result in complexities and error estimates which are independent of the number of particles. Furthermore...
Spatial patterns for the three species Gross-Pitaevskii system in the plane.
Spectra of elements in the group ring of SU(2)
We present a new method for establishing the ‘‘gap” property for finitely generated subgroups of , providing an elementary solution of Ruziewicz problem on as well as giving many new examples of finitely generated subgroups of with an explicit gap. The distribution of the eigenvalues of the elements of the group ring in the -th irreducible representation of is also studied. Numerical experiments indicate that for a generic (in measure) element of , the “unfolded” consecutive spacings...
Spectra of observables in the -oscillator and -analogue of the Fourier transform.
Spectral analysis in a thin domain with periodically oscillating characteristics
The paper deals with a Dirichlet spectral problem for an elliptic operator with ε-periodic coefficients in a 3D bounded domain of small thickness δ. We study the asymptotic behavior of the spectrum as ε and δ tend to zero. This asymptotic behavior depends crucially on whether ε and δ are of the same order (δ ≈ ε), or ε is much less than δ(δ = ετ, τ < 1), or ε is much greater than δ(δ = ετ, τ > 1). We consider all three cases.
Spectral analysis in a thin domain with periodically oscillating characteristics
The paper deals with a Dirichlet spectral problem for an elliptic operator with ε-periodic coefficients in a 3D bounded domain of small thickness δ. We study the asymptotic behavior of the spectrum as ε and δ tend to zero. This asymptotic behavior depends crucially on whether ε and δ are of the same order (δ ≈ ε), or ε is much less than δ(δ = ετ, τ < 1), or ε is much greater than δ(δ = ετ, τ > 1). ...
Spectral analysis of relativistic atoms -- Dirac operators with singular potentials.
Spectral analysis of relativistic atoms -- interaction with the quantized radiation field.
Spectral analysis of unbounded Jacobi operators with oscillating entries
We describe the spectra of Jacobi operators J with some irregular entries. We divide ℝ into three “spectral regions” for J and using the subordinacy method and asymptotic methods based on some particular discrete versions of Levinson’s theorem we prove the absolute continuity in the first region and the pure pointness in the second. In the third region no information is given by the above methods, and we call it the “uncertainty region”. As an illustration, we introduce and analyse the OP family...
Spectral and scattering theory for symbolic potentials of order zero
Spectral asymptotics for Schrödinger operators with a degenerate potential
Spectral bisection algorithm for solving Schrödinger equation using upper and lower solutions.
Spectral distances: results for Moyal plane and noncommutative torus.
Spectral projection, residue of the scattering amplitude and Schrödinger group expansion for barrier-top resonances
We study the spectral projection associated to a barrier-top resonance for the semiclassical Schrödinger operator. First, we prove a resolvent estimate for complex energies close to such a resonance. Using that estimate and an explicit representation of the resonant states, we show that the spectral projection has a semiclassical expansion in integer powers of , and compute its leading term. We use this result to compute the residue of the scattering amplitude at such a resonance. Eventually, we...