Low-Dimensional Magnetic Systems

Low Dimensional Hamiltonian Systems

The theory of differential forms began with a discovery of Poincaré who found conservation laws of a new type for Hamiltonian systems—The Integral Invariants. Even in the absence of non-trivial integrals of motion, there exist invariant differential forms: a symplectic two-form, or a contact one-form for geodesic flows. Some invariant forms can be naturally considered as “forms on the quotient....

Magnetic Interactions in Low-Dimensional Iron Nanostructures

Spin and angle resolved photoemission on non-magnetic low-dimensional systems.

The electronic structure of non-magnetic low-dimensional materials can acquire a spin structure due to the breaking of the inversion symmetry at the surface or interface. This so-called Rashba effect is a prime candidate for the manipulation of the electron spin without using any magnetic fields. This is crucial for the emerging field of spintronics, where the spin of the electron instead of it...

Hot electrons in low-dimensional phonon systems

A simple bulk model of electron-phonon coupling in metals has been partially successful in explaining experiments on metal films that actually involve surfaceor other low-dimensional phonons. However, by an exact application of this standard model to a semi-infinite substrate with a free surface, making use of the actual vibrational modes of the substrate, we show that such agreement is fortuit...

Nonparametric forecasting of low-dimensional dynamical systems.

This paper presents a nonparametric modeling approach for forecasting stochastic dynamical systems on low-dimensional manifolds. The key idea is to represent the discrete shift maps on a smooth basis which can be obtained by the diffusion maps algorithm. In the limit of large data, this approach converges to a Galerkin projection of the semigroup solution to the underlying dynamics on a basis a...