Short-timescale Fluctuations in the Difference Light Curves of QSO 0957+561A,B: Microlensing or Noise?

From optical R band data of the double quasar QSO 0957+561A,B, we made two new difference light curves (about 330 days of overlap between the time-shifted light curve for the A image and the magnitude-shifted light curve for the B image). We observed noisy behaviours around the zero line and no short-timescale events (with a duration of months), where the term event refers to a prominent feature that may be due to microlensing or another source of variability. Only one event lasting two weeks and rising - 33 mmag was found. Measured constraints on the possible microlensing variability can be used to obtain information on the granularity of the dark matter in the main lensing galaxy and the size of the source. In addition, one can also test the ability of the observational noise to cause the rms averages and the local features of the difference signals. We focused on this last issue. The combined photometries were related to a process consisting of an intrinsic signal plus a Gaussian observational noise. The intrinsic signal has been assumed to be either a smooth function (polynomial) or a smooth function plus a stationary noise process or a correlated stationary process. Using these three pictures without microlensing, we derived some models totally consistent with the observations. We finally discussed the sensitivity of our telescope (at Teide Observatory) to several classes of microlensing variability.Comment: MNRAS, in press (LaTeX, 14 pages, 22 eps figures

Orbital and spin relaxation in single and coupled quantum dots

Phonon-induced orbital and spin relaxation rates of single electron states in lateral single and double quantum dots are obtained numerically for realistic materials parameters. The rates are calculated as a function of magnetic field and interdot coupling, at various field and quantum dot orientations. It is found that orbital relaxation is due to deformation potential phonons at low magnetic fields, while piezoelectric phonons dominate the relaxation at high fields. Spin relaxation, which is dominated by piezoelectric phonons, in single quantum dots is highly anisotropic due to the interplay of the Bychkov-Rashba and Dresselhaus spin-orbit couplings. Orbital relaxation in double dots varies strongly with the interdot coupling due to the cyclotron effects on the tunneling energy. Spin relaxation in double dots has an additional anisotropy due to anisotropic spin hot spots which otherwise cause giant enhancement of the rate at useful magnetic fields and interdot couplings. Conditions for the absence of the spin hot spots in in-plane magnetic fields (easy passages) and perpendicular magnetic fields (weak passages) are formulated analytically for different growth directions of the underlying heterostructure. It is shown that easy passages disappear (spin hot spots reappear) if the double dot system loses symmetry by an xy-like perturbation.Comment: 13 pages, 9 figure

The measurement of the value of a language

We address the problem of assessing the value of a language. We consider a stylized model of multilingual societies in which we introduce axioms formalizing the principles of impartiality, monotonicity, invariance and consistency. We show that the combination of these axioms characterizes a family of communicative benefit functions which assign a value to each language in the society. The functions within the family involve a two-step procedure. First, they identify the groups of agents that can communicate in each language. Second, each group is assigned an aggregate (size-dependent) value, which is evenly divided among the languages in which the group can communicate. Our novel approach could be useful in a wide range of empirical applications and policy decisions.The first author acknowledges the financial support from the Spanish Government through grant PGC2018-093542-B-I00 funded by MCIN/AEI/10.13039/501100011033 and by 'ERDF A way of making Europe'. The second author acknowledges the Spanish Government through grant PID2020-115011GB-I00, funded by MCIN/AEI/10.13039/501100011033. Funding for publishing: Universidad Pablo de Olavide/CBUA

Virtual Processes and Superradiance in Spin-Boson Models

We consider spin-boson models composed by a single bosonic mode and an ensemble of $N$ identical two-level atoms. The situation where the coupling between the bosonic mode and the atoms generates real and virtual processes is studied, where the whole system is in thermal equilibrium with a reservoir at temperature $\beta^{-1}$. Phase transitions from ordinary fluorescence to superradiant phase in three different models is investigated. First a model where the coupling between the bosonic mode and the $j-th$ atom is via the pseudo-spin operator $\sigma^{,z}_{(j)}$ is studied. Second, we investigate the generalized Dicke model, introducing different coupling constants between the single mode bosonic field and the environment, $g_{1}$ and $g_{2}$ for rotating and counter-rotating terms, respectively. Finally it is considered a modified version of the generalized Dicke model with intensity-dependent coupling in the rotating terms. In the first model the zero mode contributes to render the canonical entropy a negative quantity for low temperatures. The last two models presents phase transitions, even when only Hamiltonian terms which generates virtual processes are considered

Determination of the properties of the central engine in microlensed QSOs

We study a recently observed gravitational microlensing peak in the V-band light curve of Q2237+0305A using a relatively simple, but highly consistent with the data (the best-fit reduced \chi^2 is very close to 1), physical model. The source quasar is assumed to be a Newtonian geometrically-thin and optically-thick accretion disk. The disk has an arbitrary orientation, and both blackbody and greybody emission spectra are considered. When the electron-photon scattering plays a role, the greybody spectrum will be a simplified version of the exact one. In our model the microlensing variability result from the source crossing a caustic straight line. The main goal is to estimate the black hole mass and the mass accretion rate in QSO 2237+0305 as well as to discuss the power and the weakness of the technique, some possible improvements, and the future prospects from multifrequency monitoring of new microlensing peaks. We also put into perspective the new methodology and the results on the central engine in QSO 2237+0305. From the fitted microlensing parameters and reasonable dynamical/cosmological constraints, it is concluded that QSO 2237+0305 harbours a central massive black hole: 10^7 M_Sun < M < 6 10^8 M_Sun. While the information about the central dark mass is very interesting, the mass accretion rate is not so well constrained. The typical values of the disk luminosity/Eddington luminosity ratio are in the (1-20)*\epsilon range, where \epsilon \leq 1 is the emissivity relative to a blackbody and the highest L/L_{Edd} ratio corresponds to the largest deflector motion. Therefore, in order to verify L/L_{Edd} \leq 1, a relatively small projected peculiar motion of the lens galaxy and a greybody emission seem to be favored.Comment: Astron. Astrophys., in press (LaTeX, 18 pages, 4 eps figures