Black hole solutions to the F4F_4-model and their orbits (I)

In this paper we continue the program of the classification of nilpotent orbits using the approach developed in arXiv:1107.5986, within the study of black hole solutions in D=4 supergravities. Our goal in this work is to classify static, single center black hole solutions to a specific N=2 four dimensional "magic" model, with special K\"ahler scalar manifold ${\rm Sp}(6,\mathbb{R})/{\rm U}(3)$, as orbits of geodesics on the pseudo-quaternionic manifold ${\rm F}_{4(4)}/[{\rm SL}(2,\mathbb{R})\times {\rm Sp}(6,\mathbb{R})]$ with respect to the action of the isometry group ${\rm F}_{4(4)}$. Our analysis amounts to the classification of the orbits of the geodesic "velocity" vector with respect to the isotropy group $H^*={\rm SL}(2,\mathbb{R})\times {\rm Sp}(6,\mathbb{R})$, which include a thorough classification of the \emph{nilpotent orbits} associated with extremal solutions and reveals a richer structure than the one predicted by the $\beta-\gamma$ labels alone, based on the Kostant Sekiguchi approach. We provide a general proof of the conjecture made in arXiv:0908.1742 which states that regular single center solutions belong to orbits with coinciding $\beta-\gamma$ labels. We also prove that the reverse is not true by finding distinct orbits with the same $\beta-\gamma$ labels, which are distinguished by suitably devised tensor classifiers. Only one of these is generated by regular solutions. Since regular static solutions only occur with nilpotent degree not exceeding 3, we only discuss representatives of these orbits in terms of black hole solutions. We prove that these representatives can be found in the form of a purely dilatonic four-charge solution (the generating solution in D=3) and this allows us to identify the orbit corresponding to the regular four-dimensional metrics.Comment: 81 pages, 24 tables, new section 4.4 about the fake superpotential added, typos corrected, references added, accepted in Nuclear Physics B.

Inference and learning in sparse systems with multiple states

We discuss how inference can be performed when data are sampled from the non-ergodic phase of systems with multiple attractors. We take as model system the finite connectivity Hopfield model in the memory phase and suggest a cavity method approach to reconstruct the couplings when the data are separately sampled from few attractor states. We also show how the inference results can be converted into a learning protocol for neural networks in which patterns are presented through weak external fields. The protocol is simple and fully local, and is able to store patterns with a finite overlap with the input patterns without ever reaching a spin glass phase where all memories are lost.Comment: 15 pages, 10 figures, to be published in Phys. Rev.

Spatio-temporal stochastic resonance induces patterns in wetland vegetation dynamics

Water availability is a major environmental driver affecting riparian and wetland vegetation. The interaction between water table fluctuations and vegetation in a stochastic environment contributes to the complexity of the dynamics of these ecosystems. We investigate the possible emergence of spatial patterns induced by spatio-temporal stochastic resonance in a simple model of groundwater-dependent ecosystems. These spatio-temporal dynamics are driven by the combined effect of three components: (i) an additive white Gaussian noise, accounting for external random disturbances such as fires or fluctuations in rain water availability, (ii) a weak periodic modulation in time, describing hydrological drivers such as seasonal fluctuations of water table depth, and (iii) a spatial coupling term, which takes into account the ability of vegetation to spread and colonize other parts of the landscape. A suitable cooperation between these three terms is able to give rise to ordered structures which show spatial and temporal coherence, and are statistically steady in time.Comment: 9 pages, 7 figure

Microscopic theory of quantum-transport phenomena in mesoscopic systems: A Monte Carlo approach

A theoretical investigation of quantum-transport phenomena in mesoscopic systems is presented. In particular, a generalization to ``open systems'' of the well-known semiconductor Bloch equations is proposed. The presence of spatial boundary conditions manifest itself through self-energy corrections and additional source terms in the kinetic equations, whose form is suitable for a solution via a generalized Monte Carlo simulation. The proposed approach is applied to the study of quantum-transport phenomena in double-barrier structures as well as in superlattices, showing a strong interplay between phase coherence and relaxation.Comment: to appear in Phys. Rev. Let

Field-induced Coulomb coupling in semiconductor macroatoms: application to "single-electron" quantum devices

A novel approach for the control of exciton-exciton Coulomb coupling in semiconductor macroatoms/molecules is proposed. We show that by applying properly tailored external fields, we can induce ---or significantly reinforce--- excitonic dipoles, which in turn allows to control and magnify intra- as well as inter-dot few-exciton effects. Such dipole-dipole interaction mechanism will be accounted for within a simple analytical model, which is found to be in good agreement with fully three-dimensional calculations. The proposed approach may play an important role for the design and realization of fully-optical quantum gates as well as ultrafast optical switches

Two-dimensional lattice-fluid model with water-like anomalies

We investigate a lattice-fluid model defined on a two-dimensional triangular lattice, with the aim of reproducing qualitatively some anomalous properties of water. Model molecules are of the "Mercedes Benz" type, i.e., they possess a D3 (equilateral triangle) symmetry, with three bonding arms. Bond formation depends both on orientation and local density. We work out phase diagrams, response functions, and stability limits for the liquid phase, making use of a generalized first order approximation on a triangle cluster, whose accuracy is verified, in some cases, by Monte Carlo simulations. The phase diagram displays one ordered (solid) phase which is less dense than the liquid one. At fixed pressure the liquid phase response functions show the typical anomalous behavior observed in liquid water, while, in the supercooled region, a reentrant spinodal is observed.Comment: 9 pages, 1 table, 7 figure

Cluster Variation Method in Statistical Physics and Probabilistic Graphical Models

The cluster variation method (CVM) is a hierarchy of approximate variational techniques for discrete (Ising--like) models in equilibrium statistical mechanics, improving on the mean--field approximation and the Bethe--Peierls approximation, which can be regarded as the lowest level of the CVM. In recent years it has been applied both in statistical physics and to inference and optimization problems formulated in terms of probabilistic graphical models. The foundations of the CVM are briefly reviewed, and the relations with similar techniques are discussed. The main properties of the method are considered, with emphasis on its exactness for particular models and on its asymptotic properties. The problem of the minimization of the variational free energy, which arises in the CVM, is also addressed, and recent results about both provably convergent and message-passing algorithms are discussed.Comment: 36 pages, 17 figure

Possible d+id scenario in La_{2-x}Sr_{x}CuO_4 by point-contact measurements

We analyze the results of point-contact measurements in La_{2-x}Sr_{x}CuO_{4} (LSCO) previously reported as a clear evidence of the separation between gap and pseudogap in this copper oxide. Here we show that, in addition to this, the conductance curves of our point-contact junctions -- showing clear Andreev reflection features -- can be interpreted as supporting a nodeless d_{x^2-y^2}+id_{xy}-wave symmetry of the gap in LSCO. The results of our analysis, in particular the doping dependence of the subdominant d_{xy} gap component, are discussed and compared to the predictions of different theoretical models.Comment: 6 pages, 4 eps figures, presented at SATT11 Conference (Vietri sul Mare, March 2002). To appear in Int. J. Mod. Phy

Some remarks on the coherent-state variational approach to nonlinear boson models

The mean-field pictures based on the standard time-dependent variational approach have widely been used in the study of nonlinear many-boson systems such as the Bose-Hubbard model. The mean-field schemes relevant to Gutzwiller-like trial states $|F>$, number-preserving states $|\xi >$ and Glauber-like trial states $|Z>$ are compared to evidence the specific properties of such schemes. After deriving the Hamiltonian picture relevant to $|Z>$ from that based on $|F>$, the latter is shown to exhibit a Poisson algebra equipped with a Weyl-Heisenberg subalgebra which preludes to the $|Z>$-based picture. Then states $|Z>$ are shown to be a superposition of $\cal N$-boson states $|\xi>$ and the similarities/differences of the $|Z>$-based and $|\xi>$-based pictures are discussed. Finally, after proving that the simple, symmetric state $|\xi>$ indeed corresponds to a SU(M) coherent state, a dual version of states $|Z>$ and $|\xi>$ in terms of momentum-mode operators is discussed together with some applications.Comment: 16 page

Capacity-achieving CPM schemes

The pragmatic approach to coded continuous-phase modulation (CPM) is proposed as a capacity-achieving low-complexity alternative to the serially-concatenated CPM (SC-CPM) coding scheme. In this paper, we first perform a selection of the best spectrally-efficient CPM modulations to be embedded into SC-CPM schemes. Then, we consider the pragmatic capacity (a.k.a. BICM capacity) of CPM modulations and optimize it through a careful design of the mapping between input bits and CPM waveforms. The so obtained schemes are cascaded with an outer serially-concatenated convolutional code to form a pragmatic coded-modulation system. The resulting schemes exhibit performance very close to the CPM capacity without requiring iterations between the outer decoder and the CPM demodulator. As a result, the receiver exhibits reduced complexity and increased flexibility due to the separation of the demodulation and decoding functions.Comment: Submitted to IEEE Transactions on Information Theor