Evidence for correlation effects: −√T behaviour in the low temperature electrical resistance of disordered metals

It is found that the electrical resistance for several metal-metalloid amorphous alloys decreases with increasing temperature as ?√T from about 20 mK to several K. The form and magnitude of this temperature dependence is in agreement with recent predictions from interaction theories.     

Cavity‐photon contribution to the effective interaction of electrons in parallel quantum dots

A single cavity photon mode is expected to modify the Coulomb interaction of an electron system in the cavity. Here we investigate this phenomena in a parallel double quantum dot system. We explore properties of the closed system and the system after it has been opened up for electron transport. We show how results for both cases support the idea that the effective electron‐electron interaction becomes more repulsive in the presence of a cavity photon field. This can be understood in terms of the cavity photons dressing the polarization terms in the effective mutual electron interaction leading to nontrivial delocalization or polarization of the charge in the double parallel dot potential. In addition, we find that the effective repulsion of the electrons can be reduced by quadrupolar collective oscillations excited by an external classical dipole electric field.     

How anesthetics, neurotransmitters, and antibiotics influence the relaxation processes in lipid membranes

We used pressure perturbation calorimetry to investigate the relaxation time scale after a jump into the melting transition regime of artificial lipid membranes. This time is equivalent to the characteristic rate of domain growth. The studies were performed on single-component large unilamellar and multilamellar vesicle systems with and without the addition of small molecules such as general anesthetics, neurotransmitters, and antibiotics. These drugs interact with membranes and affect melting points and profiles. In all systems, we found that heat capacity and relaxation times are linearly related to each other in a simple manner, and we outline the theoretical origin of this finding. Thus, the influence of a drug on the time scale of domain formation processes can be understood on the basis of their influence on the heat capacity profile. This allows estimations of the characteristic relaxation time scales in biological membranes.     

Harmonic morphisms from homogeneous Hadamard manifolds

We present a new method for manufacturing complex-valued harmonic morphisms from a wide class of Riemannian Lie groups. This yields new solutions from an important family of homogeneous Hadamard manifolds. We also give a new method for constructing left-invariant foliations on a large class of Lie groups producing harmonic morphisms.     

Cavity‐Photon‐Induced High‐Order Transitions between Ground States of Quantum Dots

It is shown that quantum electromagnetic transitions to high orders are essential to describe the time‐dependent path of a nanoscale electron system in a Coulomb blockade regime when coupled to external leads and placed in a 3D rectangular photon cavity. The electronic system consists of two quantum dots embedded asymmetrically in a short quantum wire. The two lowest in energy spin degenerate electron states are mostly localized in each dot with only a tiny probability in the other dot. In the presence of the leads, a slow high‐order transition between the ground states of the two quantum dots is identified. The Fourier power spectrum for photon–photon correlations in the steady state shows a Fano type of resonance for the frequency of the slow transition. Full account is taken of the geometry of the multilevel electronic system, and the electron–electron Coulomb interactions together with the para‐ and diamagnetic electron–photon interactions are treated with step‐wise exact numerical diagonalization and truncation of appropriate many‐body Fock spaces. The matrix elements for all interactions are computed analytically or numerically exactly.     

Regimes of radiative and nonradiative transitions in transport through an electronic system in a photon cavity reaching a steady state

We analyze how a multilevel many‐electron system in a photon cavity approaches the steady state when coupled to external leads. When a plunger gate is used to lower cavity photon dressed one‐ and two‐electron states below the bias window defined by the external leads, we can identify one regime with nonradiative transitions dominating the electron transport, and another regime with radiative transitions. Both transitions trap the electrons in the states below the bias bringing the system into a steady state. The order of the two regimes and their relative strength depends on the location of the bias window in the energy spectrum of the system and the initial conditions.

     

On R-trees with low query complexity

The R-tree is a well-known bounding-volume hierarchy that is suitable for storing geometric data on secondary memory. Unfortunately, no good analysis of its query time exists. We describe a new algorithm to construct an R-tree for a set of planar objects that has provably good query complexity for point location queries and range queries with ranges of small width. For certain important special cases, our bounds are optimal. We also show how to update the structure dynamically, and we generalize our results to higher-dimensional spaces.     

Harmonic morphisms from complex projective spaces

In this paper we study harmonic morphisms :U P ^m N ² from open subsets of complex projective spaces to Riemann surfaces. We construct many new examples of such maps which are not holomorphic with respect to the standard Kähler structure on P ^m.The research leading to this paper was supported by the Icelandic Science Fund and the Danish National Science Fund.