Gravity with extra dimensions and dark matter interpretation: A straightforward approach

Any connection between dark matter and extra dimensions can be cognizably evinced from the associated effective energy-momentum tensor. In order to investigate and test such relationship, a higher dimensional spacetime endowed with a factorizable general metric is regarded to derive a general expression for the stress tensor -- from the Einstein-Hilbert action -- and to elicit the effective gravitational potential. A particular construction for the case of six dimensions is provided, and it is forthwith revealed that the missing mass phenomenon may be explained, irrespective of the dark matter existence. Moreover, the existence of extra dimensions in the universe accrues the possibility of a straightforward mechanism for such explanation. A configuration which density profile coincides with the Newtonian potential for spiral galaxies is constructed, from a 4-dimensional isotropic metric plus extra-dimensional components. A Miyamoto-Nagai \emph{ansatz} is used to solve Einstein equations. The stable rotation curves associated to such system are computed, in full compliance to the observational data, without fitting techniques. The density profiles are reconstructed and compared to that ones obtained from the Newtonian potential.Comment: 13 pages, 6 figure

A Straightforward approach to multifunctional graphene

Graphene has been covalently functionalized through a one‐pot reductive pathway using graphite intercalation compounds (GICs), in particular KC8, with three different orthogonally protected derivatives of 4‐aminobenzylamine. This novel multifunctional platform exhibits excellent bulk functionalization homogeneity (Hbulk) and degree of addition while preserving the chemical functionalities of the organic addends through different protecting groups, namely: tert‐butyloxycarbonyl (Boc), benzyloxycarbonyl (Cbz) and phthalimide (Pht). We have employed (temperature‐dependent) statistical Raman spectroscopy (SRS), X‐ray photoelectron spectroscopy (XPS), magic angle spinning solid state 13C NMR (MAS‐NMR), and a characterization tool consisting of thermogravimetric analysis coupled with gas chromatography and mass spectrometry (TG‐GC‐MS) to unambiguously demonstrate the covalent binding and the chemical nature of the different molecular linkers. This work paves the way for the development of smart graphene‐based materials of great interest in biomedicine or electronics, to name a few, and will serve as a guide in the design of new 2D multifunctional materials

Spin-spin correlators in Majorana representation

In the Majorana representation of a spin 1/2 we find an identity which relates spin-spin correlators to one-particle fermionic correlators. This should be contrasted with the straightforward approach in which two-particle (four-fermion) correlators need to be calculated. We discuss applications to the analysis of the dynamics of a spin coupled to a dissipative environment and of a quantum detector performing a continuous measurement of a qubit's state