Stepwise introduction of model complexity in a generalized master equation approach to time-dependent transport

We demonstrate that with a stepwise introduction of complexity to a model of an electron system embedded in a photonic cavity and a carefully controlled stepwise truncation of the ensuing many-body space it is possible to describe the time-dependent transport of electrons through the system with a non-Markovian generalized quantum master equation. We show how this approach retains effects of an external magnetic field and the geometry of an anisotropic electronic system. The Coulomb interaction between the electrons and the full electromagnetic coupling between the electrons and the photons are treated in a non-perturbative way using "exact numerical diagonalization".Comment: RevTeX, 14 pages with included eps figures, replaced to mend scaling in figure axes for time "t" and current "J

Biharmonic functions on spheres and hyperbolic spaces

We construct new explicit proper r-harmonic functions on the standard n-dimensional sphere S^n and hyperbolic space H^n for any r\ge 1 and n\ge 2

Holomorphic harmonic morphisms from four-dimensional non-Einstein manifolds

We construct 4-dimensional Riemannian Lie groups carrying left-invariant conformal foliations with minimal leaves of codimension 2. We show that these foliations are holomorphic with respect to an (integrable) Hermitian structure which is not K\" ahler. We then prove that the Riemannian Lie groups constructed are {\it not} Einstein manifolds. This answers an important open question in the theory of complex-valued harmonic morphisms from Riemannian 4-manifolds.Comment: Keywords: harmonic morphisms, holomorphic, Einstein manifolds. arXiv admin note: substantial text overlap with arXiv:1310.5113, arXiv:1312.278

A note on Biharmonic functions on the Thurston geometries

We construct new explicit proper biharmonic functions on the $3$-dimensional Thurston geometries \Sol, \Nil, \SL2, H^2\times\rn and S^2\times\rn

Holomorphic harmonic morphisms from cosymplectic almost Hermitian manifolds

We study 4-dimensional Riemannian manifolds equipped with a minimal and conformal foliation $\mathcal F$ of codimension 2. We prove that the two adapted almost Hermitian structures $J_1$ and $J_2$ are both cosymplectic if and only if $\mathcal F$ is Riemannian and its horizontal distribution $\mathcal H$ is integrable.Comment: arXiv admin note: text overlap with arXiv:1310.5113, arXiv:1405.505

Harmonic morphisms from five-dimensional Lie groups

We consider 5-dimensional Lie groups with left-invariant Riemannian metrics. For such groups we give a partial classification of left-invariant conformal foliations with minimal leaves of codimension 2. These foliations produce local complex-valued harmonic morphisms

Harmonic morphisms from the classical compact semisimple Lie groups

In this paper we introduce a new method for manufacturing harmonic morphisms from semi-Riemannian manifolds. This is employed to yield a variety of new examples from the compact Lie groups SO(n), SU(n) and Sp(n) equipped with their standard Riemannian metrics. We develop a duality principle and show how this can be used to construct the first known examples of harmonic morphisms from the non-compact Lie groups SL(n,R), SU(2n), Sp(n,R), SO(2n), SO(p,q), SU(p,q) and Sp(p,q) equipped with their standard dual semi-Riemannian metrics.Comment: 14 pages; minor change

Calculation of flows and disaggregation of accumulated values

Some important economic flow variables, notably consumption and investment, have only been observed annually in Iceland. We have developed methods to estimate the flow by spline functions or Fourier series. Aggregated values over shorter intervals can be obtained by integration of the flows. A method to obtain quarterly values from annual observations by estimating a quarterly time series model from the observed values is also presented. The source code of Fortran programs and examples of input files are included. Access to the NAG subroutines is necessary to use the programs directly.

Collective modes and the far-infrared absorption of the two-dimensional electron gas in a periodic quantizing magnetic field

We investigate the far-infrared (FIR) absorption of a two-dimensional electron gas in a periodically modulated quantizing magnetic field. The magnetic field varies along only one spatial direction and the external time-dependent electric field is linearly polarized along that axis. The mutual Coulomb interaction of the electrons is treated self-consistently in the ground state and in the absorption calculation within the Hartree approximation. The effects of the magnetic material on top of the heterostructure as a grating coupler is included in the time-dependent incident FIR electric field. We show that similar to an electric modulation, the absorption can be directly correlated to the underlying electronic energy bands. In addition, the magnetic modulation leads to absorption spectra with a richer structure due to the quite different static response of the electron density to the modulation.Comment: 11 pages, 7 figures, to appear in Superlattices and Microstructure