"Nonlinear" covariance matrix and portfolio theory for non-Gaussian multivariate distributions

This paper offers a precise analytical characterization of the distribution of returns for a portfolio constituted of assets whose returns are described by an arbitrary joint multivariate distribution. In this goal, we introduce a non-linear transformation that maps the returns onto gaussian variables whose covariance matrix provides a new measure of dependence between the non-normal returns, generalizing the covariance matrix into a non-linear fractional covariance matrix. This nonlinear covariance matrix is chiseled to the specific fat tail structure of the underlying marginal distributions, thus ensuring stability and good-conditionning. The portfolio distribution is obtained as the solution of a mapping to a so-called phi-q field theory in particle physics, of which we offer an extensive treatment using Feynman diagrammatic techniques and large deviation theory, that we illustrate in details for multivariate Weibull distributions. The main result of our theory is that minimizing the portfolio variance (i.e. the relatively ``small'' risks) may often increase the large risks, as measured by higher normalized cumulants. Extensive empirical tests are presented on the foreign exchange market that validate satisfactorily the theory. For ``fat tail'' distributions, we show that an adequete prediction of the risks of a portfolio relies much more on the correct description of the tail structure rather than on their correlations.Comment: Latex, 76 page

Pion and Kaon Condensation at Finite Temperature and Density

In this paper, we study O(2N)-symmetric $\phi^4$-theory at finite temperature and density using the 2PI-1/N expansion. As specific examples, we consider pion condensation at finite isospin chemical potential and kaon condensation at finite chemical potential for hyper charge and isospin charge. We calculate the phase diagrams and the quasiparticle masses for pions and kaons in the large-N limit. It is shown that the effective potential and the gap equation can be renormalized by using local counterterms for the coupling constant and mass parameter, which are independent of temperature and chemical potentials.Comment: 10 pages. 7 Figures. v2: Better plots and figs. Added significant number of refs v3: Accepted for publication in PRD. Added a figure and improved part on renormalization as well as presentatio

Effective Theory of Wilson Lines and Deconfinement

To study the deconfining phase transition at nonzero temperature, I outline the perturbative construction of an effective theory for straight, thermal Wilson lines. Certain large, time dependent gauge transformations play a central role. They imply the existence of interfaces, which can be used to determine the form of the effective theory as a gauged, nonlinear sigma model of adjoint matrices. Especially near the transition, the Wilson line may undergo a Higgs effect. As an adjoint field, this can generate eigenvalue repulsion in the effective theory.Comment: 6 pages, LaTeX. Final, published version. Refs. 7, 39, and 40 added. In Ref. 37, there is an expanded discussion of a "fuzzy" bag mode

Hot-water aquifer storage: A field test

The basic water injection cycle used in a large-scale field study of heat storage in a confined aquifer near Mobile, Alabama is described. Water was pumped from an upper semi-confined aquifer, passed through a boiler where it was heated to a temperature of about 55 C, and injected into a medium sand confined aquifer. The injection well has a 6-inch (15-cm) partially-penetrating steel screen. The top of the storage formation is about 40 meters below the surface and the formation thickness is about 21 meters. In the first cycle, after a storage period of 51 days, the injection well was pumped until the temperature of the recovered water dropped to 33 c. At that point 55,300 cubic meters of water had been withdrawn and 66 percent of the injected energy had been recovered. The recovery period for the second cycle continued until the water temperature was 27.5 C and 100,100 cubic meters of water was recovered. At the end of the cycle about 90 percent of the energy injected during the cycle had been recovered

Naturally-phasematched second harmonic generation in a whispering gallery mode resonator

We demonstrate for the first time natural phase matching for optical frequency doubling in a high-Q whispering gallery mode resonator made of Lithium Niobate. A conversion efficiency of 9% is achieved at 30 micro Watt in-coupled continuous wave pump power. The observed saturation pump power of 3.2 mW is almost two orders of magnitude lower than the state-of-the-art. This suggests an application of our frequency doubler as a source of non-classical light requiring only a low-power pump, which easily can be quantum noise limited. Our theoretical analysis of the three-wave mixing in a whispering gallery mode resonator provides the relative conversion efficiencies for frequency doubling in various modes

Knight Shift and Leading Superconducting Instability From Spin Fluctuations in Sr2RuO4

Recent nuclear magnetic resonance studies [A. Pustogow {\it et al.}, arXiv:1904.00047] have challenged the prevalent chiral triplet pairing scenario proposed for Sr$_2$RuO$_4$. To provide guidance from microscopic theory as to which other pair states might be compatible with the new data, we perform a detailed theoretical study of spin-fluctuation mediated pairing for this compound. We map out the phase diagram as a function of spin-orbit coupling, interaction parameters, and band-structure properties over physically reasonable ranges, comparing when possible with photoemission and inelastic neutron scattering data information. We find that even-parity pseudospin singlet solutions dominate large regions of the phase diagram, but in certain regimes spin-orbit coupling favors a near-nodal odd-parity triplet superconducting state, which is either helical or chiral depending on the proximity of the $\gamma$ band to the van Hove points. A surprising near-degeneracy of the nodal $s^\prime$- and $d_{x^2-y^2}$-wave solutions leads to the possibility of a near-nodal time-reversal symmetry broken $s^\prime+id_{x^2-y^2}$ pair state. Predictions for the temperature dependence of the Knight shift for fields in and out of plane are presented for all states.Comment: 5 pages (3 figures) + supplementary informatio

Astrometry with MCAO: HST-GeMS proper motions in the globular cluster NGC 6681

Aims: for the first time the astrometric capabilities of the Multi-Conjugate Adaptive Optics (MCAO) facility GeMS with the GSAOI camera on Gemini-South are tested to quantify the accuracy in determining stellar proper motions in the Galactic globular cluster NGC 6681. Methods: proper motions from HST/ACS for a sample of its stars are already available, and this allows us to construct a distortion-free reference at the epoch of GeMS observations that is used to measure and correct the temporally changing distortions for each GeMS exposure. In this way, we are able to compare the corrected GeMS images with a first-epoch of HST/ACS images to recover the relative proper motion of the Sagittarius dwarf spheroidal galaxy with respect to NGC 6681. Results: we find this to be (\mu_{\alpha}cos\delta, \mu_{\delta}) = (4.09,-3.41) mas/yr, which matches previous HST/ACS measurements with a very good accuracy of 0.03 mas/yr and with a comparable precision (r.m.s of 0.43 mas/yr). Conclusions: this study successfully demonstrates that high-quality proper motions can be measured for quite large fields of view (85 arcsec X 85 arcsec) with MCAO-assisted, ground-based cameras and provides a first, successful test of the performances of GeMS on multi-epoch data.Comment: 5 pages, 4 figures. Accepted for publication by A&A Letter

Predicting Failure using Conditioning on Damage History: Demonstration on Percolation and Hierarchical Fiber Bundles

We formulate the problem of probabilistic predictions of global failure in the simplest possible model based on site percolation and on one of the simplest model of time-dependent rupture, a hierarchical fiber bundle model. We show that conditioning the predictions on the knowledge of the current degree of damage (occupancy density $p$ or number and size of cracks) and on some information on the largest cluster improves significantly the prediction accuracy, in particular by allowing to identify those realizations which have anomalously low or large clusters (cracks). We quantify the prediction gains using two measures, the relative specific information gain (which is the variation of entropy obtained by adding new information) and the root-mean-square of the prediction errors over a large ensemble of realizations. The bulk of our simulations have been obtained with the two-dimensional site percolation model on a lattice of size $L \times L=20 \times 20$ and hold true for other lattice sizes. For the hierarchical fiber bundle model, conditioning the measures of damage on the information of the location and size of the largest crack extends significantly the critical region and the prediction skills. These examples illustrate how on-going damage can be used as a revelation of both the realization-dependent pre-existing heterogeneity and the damage scenario undertaken by each specific sample.Comment: 7 pages + 11 figure