Information theory of quantum systems with some hydrogenic applications

The information-theoretic representation of quantum systems, which complements the familiar energy description of the density-functional and wave-function-based theories, is here discussed. According to it, the internal disorder of the quantum-mechanical non-relativistic systems can be quantified by various single (Fisher information, Shannon entropy) and composite (e.g. Cramer-Rao, LMC shape and Fisher-Shannon complexity) functionals of the Schr\"odinger probability density. First, we examine these concepts and its application to quantum systems with central potentials. Then, we calculate these measures for hydrogenic systems, emphasizing their predictive power for various physical phenomena. Finally, some recent open problems are pointed out.Comment: 9 pages, 3 figure

Relativistic Klein-Gordon charge effects by information-theoretic measures

The charge spreading of ground and excited states of Klein-Gordon particles moving in a Coulomb potential is quantitatively analyzed by means of the ordinary moments and the Heisenberg measure as well as by use of the most relevant information-theoretic measures of global (Shannon entropic power) and local (Fisher's information) types. The dependence of these complementary quantities on the nuclear charge Z and the quantum numbers characterizing the physical states is carefully discussed. The comparison of the relativistic Klein-Gordon and non-relativistic Schrodinger values is made. The non-relativistic limits at large principal quantum number n and for small values of Z are also reached.Comment: Accepted in New Journal of Physic

Three strongly correlated charged bosons in a one-dimensional harmonic trap: natural orbital occupancies

We study a one-dimensional system composed of three charged bosons confined in an external harmonic potential. More precisely, we investigate the ground-state correlation properties of the system, paying particular attention to the strong-interaction limit. We explain for the first time the nature of the degeneracies appearing in this limit in the spectrum of the reduced density matrix. An explicit representation of the asymptotic natural orbitals and their occupancies is given in terms of some integral equations.Comment: 6 pages, 4 figures, To appear in European Physical Journal

CP Violation and Family Mixing in the Effective Electroweak Lagrangian

We construct the most general effective Lagrangian of the matter sector of the Standard Model, including mixing and CP violating terms. The Lagrangian contains the effective operators that give the leading contribution in theories where the physics beyond the Standard Model shows at a scale $\Lambda >>M_{W}$. We perform the diagonalization and passage to the physical basis in full generality. We determine the contribution to the different observables and discuss the possible new sources of CP violation, the idea being to be able to gain some knowledge about new physics beyond the Standard Model from general considerations, without having to compute model by model. The values of the coefficients of the effective Lagrangian in some theories, including the Standard Model, are presented and we try to draw some general conclusions about the general pattern exhibited by physics beyond the Standard Model in what concerns CP violation. In the process we have had to deal with two theoretical problems which are very interesting in their own: the renormalization of the CKM matrix elements and the wave function renormalization in the on-shell scheme when mixing is present.Comment: A misplaced sentence was correcte

Superconductivity induced by inter-band nesting in the three-dimensional honeycomb lattice

In order to study whether the inter-band nesting can favor superconductivity arising from electron-electron repulsion in a three-dimensional system, we have looked at the repulsive Hubbard model on a stack of honeycomb (i.e., non-Bravais) lattices with the FLEX method, partly motivated by the superconductivity observed in MgB2. By systematically changing the shape of Fermi surface with varied band filling n and the third-direction hopping, we have found that the pair scattering across the two-bands is indeed found to give rise to gap functions that change sign across the bands and behave as an s- or d-wave within each band. This implies (a) the electron repulsion can assist gapful pairing when a phonon-mechanism pairing exists, and (b) the electron repulsion alone, when strong enough, can give rise to a d-wave-like pairing, which should be, for a group-theoretic reason, a time-reversal broken d+id with point nodes in the gap

The unexplored role of sedentary time and physical activity in glucose and lipid metabolism-related placental mRNAs in pregnant women who are obese: the DALI lifestyle randomised controlled trial

Objective: We aimed to explore: (i) the association of sedentary time (ST) and physical activity (PA) during pregnancy with the placental expression of genes related to glucose and lipid metabolism in pregnant women who are obese; (ii) maternal metabolic factors mediating changes in these placental transcripts; and (iii) cord blood markers related to the mRNAs mediating neonatal adiposity. Design: Multicentre randomised controlled trial. Setting: Hospitals in nine European countries. Population: A cohort of 112 pregnant women with placental tissue. Methods: Both ST and moderate-to-vigorous PA (MVPA) levels were measured objectively using accelerometry at three time periods during pregnancy. Main outcome measures: Placental mRNAs (FATP2, FATP3, FABP4, GLUT1 and PPAR-γ) were measured with NanoString technology. Maternal and fetal metabolic markers and neonatal adiposity were assessed. Results: Longer periods of ST, especially in early to middle pregnancy, was associated with lower placental FATP2 and FATP3 expression (P \u3c 0.05), whereas MVPA at baseline was inversely associated with GLUT1 mRNA (P = 0.02). Although placental FATP2 and FATP3 expression were regulated by the insulin–glucose axis (P \u3c 0.05), no maternal metabolic marker mediated the association of ST/MVPA with placental mRNAs (P \u3e 0.05). Additionally, placental FATP2 expression was inversely associated with cord blood triglycerides and free fatty acids (FFAs; P \u3c 0.01). No cord blood marker mediated neonatal adiposity except for cord blood leptin, which mediated the effects of PPAR-γ on neonatal sum of skinfolds (P \u3c 0.05). Conclusions: In early to middle pregnancy, ST is associated with the expression of placental genes linked to lipid transport. PA is hardly related to transporter mRNAs. Strategies aimed at reducing sedentary behaviour during pregnancy could modulate placental gene expression, which may help to prevent unfavourable fetal and maternal pregnancy outcomes. Tweetable abstract: Reducing sedentary behaviour in pregnancy might modulate placental expression of genes related to lipid metabolism in women who are obese

Additivity and non-additivity of multipartite entanglement measures

We study the additivity property of three multipartite entanglement measures, i.e. the geometric measure of entanglement (GM), the relative entropy of entanglement and the logarithmic global robustness. First, we show the additivity of GM of multipartite states with real and non-negative entries in the computational basis. Many states of experimental and theoretical interests have this property, e.g. Bell diagonal states, maximally correlated generalized Bell diagonal states, generalized Dicke states, the Smolin state, and the generalization of D\"{u}r's multipartite bound entangled states. We also prove the additivity of other two measures for some of these examples. Second, we show the non-additivity of GM of all antisymmetric states of three or more parties, and provide a unified explanation of the non-additivity of the three measures of the antisymmetric projector states. In particular, we derive analytical formulae of the three measures of one copy and two copies of the antisymmetric projector states respectively. Third, we show, with a statistical approach, that almost all multipartite pure states with sufficiently large number of parties are nearly maximally entangled with respect to GM and relative entropy of entanglement. However, their GM is not strong additive; what's more surprising, for generic pure states with real entries in the computational basis, GM of one copy and two copies, respectively, are almost equal. Hence, more states may be suitable for universal quantum computation, if measurements can be performed on two copies of the resource states. We also show that almost all multipartite pure states cannot be produced reversibly with the combination multipartite GHZ states under asymptotic LOCC, unless relative entropy of entanglement is non-additive for generic multipartite pure states.Comment: 45 pages, 4 figures. Proposition 23 and Theorem 24 are revised by correcting a minor error from Eq. (A.2), (A.3) and (A.4) in the published version. The abstract, introduction, and summary are also revised. All other conclusions are unchange

Parabolic stable surfaces with constant mean curvature

We prove that if u is a bounded smooth function in the kernel of a nonnegative Schrodinger operator $-L=-(\Delta +q)$ on a parabolic Riemannian manifold M, then u is either identically zero or it has no zeros on M, and the linear space of such functions is 1-dimensional. We obtain consequences for orientable, complete stable surfaces with constant mean curvature $H\in\mathbb{R}$ in homogeneous spaces $\mathbb{E}(\kappa,\tau)$ with four dimensional isometry group. For instance, if M is an orientable, parabolic, complete immersed surface with constant mean curvature H in $\mathbb{H}^2\times\mathbb{R}$, then $|H|\leq 1/2$ and if equality holds, then M is either an entire graph or a vertical horocylinder.Comment: 15 pages, 1 figure. Minor changes have been incorporated (exchange finite capacity by parabolicity, and simplify the proof of Theorem 1)

Completeness in hybrid type theory

We show that basic hybridization (adding nominals and @ operators) makes it possible to give straightforward Henkin-style completeness proofs even when the modal logic being hybridized is higher-order. The key ideas are to add nominals as expressions of type t, and to extend to arbitrary types the way we interpret @i in propositional and first-order hybrid logic. This means: interpret @iαa, where αa is an expression of any type a, as an expression of type a that rigidly returns the value that αa receives at the i-world. The axiomatization and completeness proofs are generalizations of those found in propositional and first-order hybrid logic, and (as is usual in hybrid logic) we automatically obtain a wide range of completeness results for stronger logics and languages. Our approach is deliberately low-tech. We don’t, for example, make use of Montague’s intensional type s, or Fitting-style intensional models; we build, as simply as we can, hybrid logic over Henkin’s logic.submittedVersionFil: Areces, Carlos Eduardo. Universidad Nacional de Córdoba. Facultad de Matemática, Astronomía y Física; Argentina.Fil: Blackburn, Patrick. University of Roskilde. Centre for Culture and Identity. Department of Philosophy and Science Studies; Dinamarca.Fil: Huertas, Antonia. Universitat Oberta de Catalunya; España.Fil: Manzano, María. Universidad de Salamanca; España.Ciencias de la Computació

Ground-state correlation properties of charged bosons trapped in strongly anisotropic harmonic potentials

We study systems of a few charged bosons contained within a strongly anisotropic harmonic trap. A detailed examination of the ground-state correlation properties of two-, three-, and four-particle systems is carried out within the framework of the single-mode approximation of the transverse components. The linear correlation entropy of the quasi-1D systems is discussed in dependence on the confinement anisotropy and compared with a strictly 1D limit. Only at weak interaction the correlation properties depend strongly on the anisotropy parameter.Comment: 5 pages, 6 figure