Thermodynamics of conformal fields in topologically non-trivial space-time backgrounds

We analyze the finite temperature behaviour of massless conformally coupled scalar fields in homogeneous lens spaces $S^3/{\mathbb Z}_p$. High and low temperature expansions are explicitly computed and the behavior of thermodynamic quantities under thermal duality is scrutinized. The analysis of the entropy of the different lens spaces in the high-temperature limit points out the appearance of a topological nonextensive entropy, besides the standard Stefan-Boltzmann extensive term. The remaining terms are exponentially suppressed by the temperature. The topological entropy appears as a subleading correction to the free energy that can be obtained from the determinant of the lens space conformal Laplacian operator. In the low-temperature limit the leading term in the free energy is the Casimir energy and there is no trace of any power correction in any lens space. In fact, the remaining corrections are always exponentially suppressed by the inverse of the temperature. The duality between the results of both expansions is further analyzed in the paper.Comment: 21 pages, 2 figure

Charge density and conductivity of disordered Berry-Mondragon graphene nanoribbons

We consider gated graphene nanoribbons subject to Berry-Mondragon boundary conditions in the presence of weak impurities. Using field--theoretical methods, we calculate the density of charge carriers (and, thus, the quantum capacitance) as well as the optical and DC conductivities at zero temperature. We discuss in detail their dependence on the gate (chemical) potential, and reveal a non-linear behaviour induced by the quantization of the transversal momentum.Comment: 17 pages, version accepted for publication in EPJ

The quantum Hall effect in graphene samples and the relativistic Dirac effective action

We study the Euclidean effective action per unit area and the charge density for a Dirac field in a two--dimensional spatial region, in the presence of a uniform magnetic field perpendicular to the 2D--plane, at finite temperature and density. In the limit of zero temperature we reproduce, after performing an adequate Lorentz boost, the Hall conductivity measured for different kinds of graphene samples, depending upon the phase choice in the fermionic determinant.Comment: Conclusions extended. References added. 9 pages. 1 figur

Planar QED at finite temperature and density: Hall conductivity, Berry's phases and minimal conductivity of graphene

We study 1-loop effects for massless Dirac fields in two spatial dimensions, coupled to homogeneous electromagnetic backgrounds, both at zero and at finite temperature and density. In the case of a purely magnetic field, we analyze the relationship between the invariance of the theory under large gauge transformations, the appearance of Chern-Simons terms and of different Berry's phases. In the case of a purely electric background field, we show that the effective Lagrangian is independent of the chemical potential and of the temperature. More interesting: we show that the minimal conductivity, as predicted by the quantum field theory, is the right multiple of the conductivity quantum and is, thus, consistent with the value measured for graphene, with no extra factor of pi in the denominator.Comment: 27 pages, no figures. Minor misprints corrected. Final version, to appear in J. Phys. A: Math. Ge

Uncertainty in data integration systems: automatic generation of probabilistic relationships

This paper proposes a method for the automatic discovery of probabilistic relationships in the environment of data integration systems. Dynamic data integration systems extend the architecture of current data integration systems by modeling uncertainty at their core. Our method is based on probabilistic word sense disambiguation (PWSD), which allows to automatically lexically annotate (i.e. to perform annotation w.r.t. a thesaurus/lexical resource) the schemata of a given set of data sources to be integrated. From the annotated schemata and the relathionships defined in the thesaurus, we derived the probabilistic lexical relationships among schema elements. Lexical relationships are collected in the Probabilistic Common Thesaurus (PCT), as well as structural relationships

Analytic continuation of the Hurwitz Zeta Function with physical application

A new formula relating the analytic continuation of the Hurwitz zeta function to the Euler gamma function and a polylogarithmic function is presented. In particular, the values of the first derivative of the real part of the analytic continuation of the Hurwitz zeta function for even negative integers and the imaginary one for odd negative integers are explicitly given. The result can be of interest both on mathematical and physical side, because we are able to apply our new formulas in the context of the Spectral Zeta Function regularization, computing the exact pair production rate per space-time unit of massive Dirac particles interacting with a purely electric background field.Comment: Replaced version, minor changes. 9 pages, to be published in J. Math. Phy

LigAdvisor: A versatile and user-friendly web-platform for drug design

Although several tools facilitating in silico drug design are available, their results are usually difficult to integrate with publicly available information or require further processing to be fully exploited. The rational design of multi-target ligands (polypharmacology) and the repositioning of known drugs towards unmet therapeutic needs (drug repurposing) have raised increasing attention in drug discovery, although they usually require careful planning of tailored drug design strategies. Computational tools and data-driven approaches can help to reveal novel valuable opportunities in these contexts, as they enable to efficiently mine publicly available chemical, biological, clinical, and disease-related data. Based on these premises, we developed LigAdvisor, a data-driven webserver which integrates information reported in DrugBank, Protein Data Bank, UniProt, Clinical Trials and Therapeutic Target Database into an intuitive platform, to facilitate drug discovery tasks as drug repurposing, polypharmacology, target fishing and profiling. As designed, LigAdvisor enables easy integration of similarity estimation results with clinical data, thereby allowing a more efficient exploitation of information in different drug discovery contexts. Users can also develop customizable drug design tasks on their own molecules, by means of ligand- and target-based search modes, and download their results. LigAdvisor is publicly available at https://ligadvisor.unimore.it/

Topological entropy and renormalization group flow in 3-dimensional spherical spaces

We analyze the renormalization group (RG) flow of the temperature independent term of the entropy in the high temperature limit ß/a « 1 of a massive field theory in 3-dimensional spherical spaces, M 3, with constant curvature 6/a 2. For masses lower than 2p/ß , this term can be identified with the free energy of the same theory on M 3 considered as a 3-dimensional Euclidean space-time. The non-extensive part of this free energy, S hol, is generated by the holonomy of the spatial metric connection. We show that for homogeneous spherical spaces the holonomy entropy S hol decreases monotonically when the RG scale flows to the infrared. At the conformal fixed points the values of the holonomy entropy do coincide with the genuine topological entropies recently introduced. The monotonic behavior of the RG flow leads to an inequality between the topological entropies of the conformal field theories connected by such flow, i.e. S top UV¿>¿S top IR . From a 3-dimensional viewpoint the same term arises in the 3-dimensional Euclidean effective action and has the same monotonic behavior under the RG group flow. We conjecture that such monotonic behavior is generic, which would give rise to a 3-dimensional generalization of the c-theorem, along the lines of the 2-dimensional c-theorem and the 4-dimensional a-theorem. The conjecture is related to recent formulations of the F-theorem. In particular, the holonomy entropy on lens spaces is directly related to the topological Rényi entanglement entropy on disks of 2-dimensional flat spaces

Heat kernel coefficients for chiral bag boundary conditions

We study the asymptotic expansion of the smeared L2-trace of fexp(-tP^2) where P is an operator of Dirac type, f is an auxiliary smooth smearing function which is used to localize the problem, and chiral bag boundary conditions are imposed. Special case calculations, functorial methods and the theory of zeta and eta invariants are used to obtain the boundary part of the heat-kernel coefficients a1 and a2.Comment: Published in J. Phys. A38, 2259-2276 (2005). Record without file already exists on the SLAC recor

Strong ellipticity and spectral properties of chiral bag boundary conditions

We prove strong ellipticity of chiral bag boundary conditions on even dimensional manifolds. From a knowledge of the heat kernel in an infinite cylinder, some basic properties of the zeta function are analyzed on cylindrical product manifolds of arbitrary even dimension.Comment: 16 pages, LaTeX, References adde