1,361 research outputs found
Positive Measure Spectrum for Schroedinger Operators with Periodic Magnetic Fields
We study Schroedinger operators with periodic magnetic field in Euclidean
2-space, in the case of irrational magnetic flux. Positive measure Cantor
spectrum is generically expected in the presence of an electric potential. We
show that, even without electric potential, the spectrum has positive measure
if the magnetic field is a perturbation of a constant one.Comment: 17 page
Spontaneous Edge Currents for the Dirac Equation in Two Space Dimensions
Spontaneous edge currents are known to occur in systems of two space dimensions in a strong magnetic field. The latter creates chirality and determines the direction of the currents. Here we show that an analogous effect occurs in a field-free situation when time reversal symmetry is broken by the mass term of the Dirac equation in two space dimensions. On a half plane, one sees explicitly that the strength of the edge current is proportional to the difference between the chemical potentials at the edge and in the bulk, so that the effect is analogous to the Hall effect, but with an internal potential. The edge conductivity differs from the bulk (Hall) conductivity on the whole plane. This results from the dependence of the edge conductivity on the choice of a selfadjoint extension of the Dirac Hamiltonian. The invariance of the edge conductivity with respect to small perturbations is studied in this example by topological techniques
Bloch Theory and Quantization of Magnetic Systems
Quantizing the motion of particles on a Riemannian manifold in the presence
of a magnetic field poses the problems of existence and uniqueness of
quantizations. Both of them are settled since the early days of geometric
quantization but there is still some structural insight to gain from spectral
theory. Following the work of Asch, Over & Seiler (1994) for the 2-torus we
describe the relation between quantization on the manifold and Bloch theory on
its covering space for more general compact manifolds.Comment: 20 page
-approximation of the integrated density of states for Schr\"odinger operators with finite local complexity
We study spectral properties of Schr\"odinger operators on \RR^d. The
electromagnetic potential is assumed to be determined locally by a colouring of
the lattice points in \ZZ^d, with the property that frequencies of finite
patterns are well defined. We prove that the integrated density of states
(spectral distribution function) is approximated by its finite volume
analogues, i.e.the normalised eigenvalue counting functions. The convergence
holds in the space where is any finite energy interval and is arbitrary.Comment: 15 pages; v2 has minor fixe
Inferential evaluations of sustainability attributes: Exploring how consumers imply product information
Consumers are often confronted with incomplete product information. In such instances, they can eliminate the product from further consideration due to higher associated uncertainty or ask for more information. Alternatively, they can apply subjective theories about covariation to infer the value of missing attributes. This paper investigates the latter option in the context of sustainability and provides an in-depth exploration of consumers' inference formations. Drawing from rich qualitative data, it offers a conceptualization of the underlying relationships consumers use to infer product sustainability based on other product attributes. The study further assesses whether these findings can be captured in a quantifiable way. To this end, inferred sustainability is conceptualized as a formative second-order construct, thereby depicting the influence of inference-triggering product attributes. (authors' abstract
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