The geometry of the double gyroid wire network: quantum and classical

Quantum wire networks have recently become of great interest. Here we deal with a novel nano material structure of a Double Gyroid wire network. We use methods of commutative and non-commutative geometry to describe this wire network. Its non--commutative geometry is closely related to non-commutative 3-tori as we discuss in detail.Comment: pdflatex 9 Figures. Minor changes, some typos and formulation

Re-gauging groupoid, symmetries and degeneracies for graph Hamiltonians and applications to the Gyroid wire network

We study a class of graph Hamiltonians given by a type of quiver representation to which we can associate (non)-commutative geometries. By selecting gauging data, these geometries are realized by matrices through an explicit construction or a Kan extension. We describe the changes in gauge via the action of a re-gauging groupoid. It acts via matrices that give rise to a noncommutative 2-cocycle and hence to a groupoid extension (gerbe). We furthermore show that automorphisms of the underlying graph of the quiver can be lifted to extended symmetry groups of re-gaugings. In the commutative case, we deduce that the extended symmetries act via a projective representation. This yields isotypical decompositions and super-selection rules. We apply these results to the primitive cubic, diamond, gyroid and honeycomb wire networks using representation theory for projective groups and show that all the degeneracies in the spectra are consequences of these enhanced symmetries. This includes the Dirac points of the G(yroid) and the honeycomb systems

Local models and global constraints for degeneracies and band crossings

We study topological properties of families of Hamiltonians which may contain degenerate energy levels aka. band crossings. The primary tool are Chern classes, Berry phases and slicing by surfaces. To analyse the degenerate locus, we study local models. These give information about the Chern classes and Berry phases. We then give global constraints for the topological invariants. This is an hitherto relatively unexplored subject. The global constraints are more strict when incorporating symmetries such as time reversal symmetries. The results can also be used in the study of deformations. We furthermore use these constraints to analyse examples which include the Gyroid geometry, which exhibits Weyl points and triple crossings and the honeycomb geometry with its two Dirac points

The possible importance of synchrotron/inverse Compton losses to explain fast mm-wave and hard X-ray emission of a solar event

The solar burst of 21 May 1984, presented a number of unique features. The time profile consisted of seven major structures (seconds), with a turnover frequency of greater than or approximately 90 GHz, well correlated in time to hard X-ray emission. Each structure consisted of multiple fast pulses (0.1 seconds), which were analyzed in detail. A proportionality between the repetition rate of the pulses and the burst fluxes at 90 GHz and greater than or approximately 100 keV hard X-rays, and an inverse proportionality between repetition rates and hard X-ray power law indices were found. A synchrotron/inverse Compton model was applied to explain the emission of the fast burst structures, which appear to be possible for the first three or four structures

The possible importance of synchrotron/inverse Compton losses to explain fast MM-wave and hard X-ray emission of a solar event

The solar burst of 21 May 1984 presented a number of unique features. The time profile consisted of seven major structures (seconds), with a turnover frequency or approx. 90 GHz, well correlated in time to hard X-ray emission. Each structure consisted of multiple fast pulses (.1 seconds), which were analyzed in detail. A proportionality between the repetition rate of the pulses and the burst fluxes at 90 GHz and or approx. 100 keV hard X-rays, and an inverse proportionality between repetition rates and hard X-rays power law indices have been found. A synchrotron/inverse Compton model has been applied to explain the emission of the fast burst structures, which appear to be possible for the first three or four structures

A new class of solar burst with MM-wave emission but only at the highest frequency (90 GHz)

High sensitivity and high time resolution solar observations at 90 GHz (lambda = 3.3 mm) have identified a unique impulsive burst on May 21, 1984 with emission that was more intense at this frequency than at lower frequencies. The first major time structure of the burst was over 10 times more intense at 90 GHz than at 30 GHz, 7 GHz, or 2.8 GHz.Only 6 seconds later, the 30 GHz impulsive structures started to be observed but still with lower intensity than at 90 GHz. Hard X-ray time structures at energies above 25 keV were almost identical to the 90 GHZ structures (to better than one second). All 90 GHz major time structures consisted of trains of multiple subsecond pulses with rise times as short as 0.03 sec and amplitudes large compared to the mean flux. When detectable, the 30 GHz subsecond pulses had smaller relative amplitude and were in phase with the corresponding 90 GHz pulses

Multiple energetic injections in a strong spike-like solar burst

An intense and fast spike-like solar burst was built up of short time scale structures superimposed on an underlying gradual emission, the time evolution of which shows remarkable proportionality between hard X-ray and microwave fluxes. The finer time structure were best defined at mm-microwaves. At the peak of the event, the finer structures repeat every 30x60ms. The more slowly varying component with a time scale of about 1 second was identified in microwave hard X-rays throughout the burst duration. It is suggested that X-ray fluxes might also be proportional to the repetition rate of basic units of energy injection (quasi-quantized). The relevant parameters of one primary energy release site are estimated both in the case where hard X-rays are produced primarily by thick-target bremsstrahlung, and when they are purely thermal. The relation of this figure to global energy considerations is discussed