Deformed symmetries from quantum relational observables

Deformed Special Relativity (DSR) is a candidate phenomenological theory to describe the Quantum Gravitational (QG) semi-classical regime. A possible interpretation of DSR can be derived from the notion of deformed reference frame. Observables in (quantum) General Relativity can be constructed from (quantum) reference frame – a physical observable is then a relation between a system of interest and the reference frame. We present a toy model and study an example of such quantum relational observables. We show how the intrinsic quantum nature of the reference frame naturally leads to a deformation of the symmetries, comforting DSR to be a good candidate to describe the QG semi-classical regime

Spin-Photon Dynamics of Quantum Dots in Two-mode Cavities

A quantum dot interacting with two resonant cavity modes is described by a two-mode Jaynes-Cummings model. Depending on the quantum dot energy level scheme, the interaction of a singly doped quantum dot with a cavity photon generates entanglement of electron spin and cavity states or allows one to implement a SWAP gate for spin and photon states. An undoped quantum dot in the same structure generates pairs of polarization entangled photons from an initial photon product state. For realistic cavity loss rates, the fidelity of these operations is of order 80%.Comment: 6 pages, 4 figures; extended discussion of experimental implementatio

The circumstellar disk of FS Tau B - A self-consistent model based on observations in the mid-infrared with NACO -

Protoplanetary disks are a byproduct of the star formation process. In the dense mid-plane of these disks, planetesimals and planets are expected to form. The first step in planet formation is the growth of dust particles from submicrometer-sized grains to macroscopic mm-sized aggregates. The grain growth is accompanied by radial drift and vertical segregation of the particles within the disk. To understand this essential evolutionary step, spatially resolved multi-wavelength observations as well as photometric data are necessary which reflect the properties of both disk and dust. We present the first spatially resolved image obtained with NACO at the VLT in the L$_\text{p}$ band of the near edge-on protoplanetary disk FS Tau B. Based on this new image, a previously published Hubble image in H band and the spectral energy distribution from optical to millimeter wavelengths, we derive constraints on the spatial dust distribution and the progress of grain growth. For this purpose we perform a disk modeling using the radiative transfer code MC3D. Radial drift and vertical sedimentation of the dust are not considered. We find a best-fit model which features a disk extending from $2\,\text{AU}$ to several hundreds AU with a moderately decreasing surface density and $M_\text{disk}=2.8\,\times\,10^{-2}\,\text{M}_\odot$. The inclination amounts to $i=80^\circ$. Our findings indicate that substantial dust grain growth has taken place and that grains of a size equal to or larger than $1\,\text{mm}$ are present in the disk. In conclusion, the parameters describing the vertical density distribution are better constrained than those describing the radial disk structure.Comment: 10 pages, 9 figures, 2 table

Potentially crystalline lifts of certain prescribed types

We prove several results concerning the existence of potentially crystalline lifts with prescribed Hodge-Tate weights and inertial types of a given n-dimensional mod p representation of the absolute Galois group of K, where K/Q_p is a finite extension. Some of these results are proved by purely local methods, and are expected to be useful in the application of automorphy lifting theorems. The proofs of the other results are global, making use of automorphy lifting theorems.Comment: 22 pages; final version, to appear in Document

A comparison between obstructions to local-global principles over semiglobal fields

We consider local-global principles for rational points on varieties, in particular torsors, over one-variable function fields over complete discretely valued fields. There are several notions of such principles, arising either from the valuation theory of the function field, or from the geometry of a regular model of the function field. Our results compare the corresponding obstructions, proving in particular that a local-global principle with respect to valuations implies a local-global principle with respect to a sufficiently fine regular model.Comment: 10 pages; published versio