Bridging the ARCH model for finance and nonextensive entropy

Engle's ARCH algorithm is a generator of stochastic time series for financial returns (and similar quantities) characterized by a time-dependent variance. It involves a memory parameter $b$ ($b=0$ corresponds to {\it no memory}), and the noise is currently chosen to be Gaussian. We assume here a generalized noise, namely $q_n$-Gaussian, characterized by an index $q_{n} \in {\cal R}$ ($q_{n}=1$ recovers the Gaussian case, and $q_n>1$ corresponds to tailed distributions). We then match the second and fourth momenta of the ARCH return distribution with those associated with the $q$-Gaussian distribution obtained through optimization of the entropy S_{q}=\frac{% 1-\sum_{i} {p_i}^q}{q-1}, basis of nonextensive statistical mechanics. The outcome is an {\it analytic} distribution for the returns, where an unique $q\ge q_n$ corresponds to each pair $(b,q_n)$ ($q=q_n$ if $b=0$). This distribution is compared with numerical results and appears to be remarkably precise. This system constitutes a simple, low-dimensional, dynamical mechanism which accommodates well within the current nonextensive framework.Comment: 4 pages, 5 figures.Figure 4 fixe

Gasoline quality sensor based on tilted fiber Bragg gratings

FAPESP - FUNDAÇÃO DE AMPARO À PESQUISA DO ESTADO DE SÃO PAULOCNPQ - CONSELHO NACIONAL DE DESENVOLVIMENTO CIENTÍFICO E TECNOLÓGICOWe report on the study of an intensity-based optical fiber sensor for gasoline quality monitoring. The sensor setup employs two Bragg gratings with different spectral responses to interrogate the optical response of a tilted Bragg grating. The sensor operation is based on the tilted Bragg grating sensitivity to external refractive index changes, which are translated as power variations by the interrogation scheme. Gasoline-ethanol solutions with concentrations ranging from 0% to 60% ethanol were used to demonstrate the sensor performance. The results allowed to estimate that the sensor is able, within its resolution limit, to detect ethanol concentration variations of 1.5% in gasoline-ethanol solutions and discriminate temperature variations of 0.5 degrees C. The all-optical sensor setup is compact and robust, making it a competitive alternative for the realization of fuel quality analyses in practical applications.6218FAPESP - FUNDAÇÃO DE AMPARO À PESQUISA DO ESTADO DE SÃO PAULOCNPQ - CONSELHO NACIONAL DE DESENVOLVIMENTO CIENTÍFICO E TECNOLÓGICOFAPESP - FUNDAÇÃO DE AMPARO À PESQUISA DO ESTADO DE SÃO PAULOCNPQ - CONSELHO NACIONAL DE DESENVOLVIMENTO CIENTÍFICO E TECNOLÓGICO2014/50632-6Sem informaçã

Electrical manipulation of spin states in a single electrostatically gated transition-metal complex

We demonstrate an electrically controlled high-spin (S=5/2) to low-spin (S=1/2) transition in a three-terminal device incorporating a single Mn2+ ion coordinated by two terpyridine ligands. By adjusting the gate-voltage we reduce the terpyridine moiety and thereby strengthen the ligand-field on the Mn-atom. Adding a single electron thus stabilizes the low-spin configuration and the corresponding sequential tunnelling current is suppressed by spin-blockade. From low-temperature inelastic cotunneling spectroscopy, we infer the magnetic excitation spectrum of the molecule and uncover also a strongly gate-dependent singlet-triplet splitting on the low-spin side. The measured bias-spectroscopy is shown to be consistent with an exact diagonalization of the Mn-complex, and an interpretation of the data is given in terms of a simplified effective model.Comment: Will appear soon in Nanoletter

Scanning tunneling spectroscopy of layers of superconducting 2H-TaSe2_\textbf{2}: Evidence for a zero bias anomaly in single layers

We report a characterization of surfaces of the dichalcogenide TaSe$_2$ using scanning tunneling microscopy and spectroscopy (STM/S) at 150 mK. When the top layer has the 2H structure and the layer immediately below the 1T structure, we find a singular spatial dependence of the tunneling conductance below 1 K, changing from a zero bias peak on top of Se atoms to a gap in between Se atoms. The zero bias peak is additionally modulated by the commensurate $3a_0 \times 3a_0$ charge density wave of 2H-TaSe$_2$. Multilayers of 2H-TaSe$_2$ show a spatially homogeneous superconducting gap with a critical temperature also of 1 K. We discuss possible origins for the peculiar tunneling conductance in single layers.Comment: 10 pages, 10 figure

Strong polarization-induced reduction of addition energies in single-molecule nanojunctions

We address polarization-induced renormalization of molecular levels in solid-state based single-molecule transistors and focus on an organic conjugate molecule where a surprisingly large reduction of the addition energy has been observed. We have developed a scheme that combines a self-consistent solution of a quantum chemical calculation with a realistic description of the screening environment. Our results indeed show a large reduction, and we explain this to be a consequence of both (a) a reduction of the electrostatic molecular charging energy and (b) polarization induced level shifts of the HOMO and LUMO levels. Finally, we calculate the charge stability diagram and explain at a qualitative level general features observed experimentally.Comment: 9 pages, 5 figure

Strong enhancement of superconductivity at high pressures within the charge-density-wave states of 2H-TaS 2 and 2H-TaSe 2

We present measurements of the superconducting and charge density wave critical temperatures (Tc and TCDW) as a function of pressure in the transition metal dichalchogenides 2H-TaSe2 and 2H-TaS2. Resistance and susceptibility measurements show that Tc increases from temperatures below 1 K up to 8.5 K at 9.5 GPa in 2H-TaS2 and 8.2 K at 23 GPa in 2H-TaSe2. We observe a kink in the pressure dependence of TCDW at about 4 GPa that we attribute to the lock-in transition from incommensurate CDW to commensurate CDW. Above this pressure, the commensurate TCDW slowly decreases coexisting with superconductivity within our full pressure range.Comment: Published in Phys. Rev B 93, 184512 (2016

Demonstration experiments for solid state physics using a table top mechanical Stirling refrigerator

Liquid free cryogenic devices are acquiring importance in basic science and engineering. But they can also lead to improvements in teaching low temperature an solid state physics to graduate students and specialists. Most of the devices are relatively expensive, but small sized equipment is slowly becoming available. Here, we have designed several simple experiments which can be performed using a small Stirling refrigerator. We discuss the measurement of the critical current and temperature of a bulk YBa2Cu3O(7-d) (YBCO) sample, the observation of the levitation of a magnet over a YBCO disk when cooled below the critical temperature and the observation of a phase transition using ac calorimetry. The equipment can be easily handled by students, and also used to teach the principles of liquid free cooling

Some Open Points in Nonextensive Statistical Mechanics

We present and discuss a list of some interesting points that are currently open in nonextensive statistical mechanics. Their analytical, numerical, experimental or observational advancement would naturally be very welcome.Comment: 30 pages including 6 figures. Invited paper to appear in the International Journal of Bifurcation and Chao

Optical linear polarization in ultra cool dwarfs: A tool to probe dust in the ultra cool dwarf atmospheres

Aims.Recent studies have detected linear polarization in L dwarfs in the optical I band. Theoretical models have been developed to explain this polarization. These models predict higher polarization at shorter wavelengths. We discuss the polarization in the R and I band of 4 ultra cool dwarfs. Methods.We report linear polarization measurements of 4 ultra cool dwarfs in the R and I bands using the Intermediate dispersion Spectrograph and Imaging System (ISIS) mounted on the 4.2m William Herschel Telescope (WHT). Results.As predicted by theoretical models, we find a higher degree of polarization in the R band when compared to polarization in the I band for 3/4 of these ultra cool dwarfs. This suggests that dust scattering asymmetry is caused by oblateness >.We also show how these measurements fit the theoretical models. A case for variability of linear polarization is found, which suggests the presence of randomly distributed dust clouds. We also discuss one case for the presence of a cold debris disk.Comment: 7 pages, 2 figure