Progress in the mathematical theory of quantum disordered systems

We review recent progress in the mathematical theory of quantum disordered systems: the Anderson transition, including some joint work with Marchetti, the (quantum and classical) Edwards-Anderson (EA) spin-glass model and return to equilibrium for a class of spin-glass models, which includes the EA model initially in a very large transverse magnetic field. (C) 2012 American Institute of Physics. [http://dx.doi.org/10.1063/1.4770066]

Vectorial capacity, basic reproduction number, force of infection and all that: formal notation to complete and adjust their classical concepts and equations

A dimensional analysis of the classical equations related to the dynamics of vector-borne infections is presented. It is provided a formal notation to complete the expressions for the Ross' threshold theorem, the Macdonald's basic reproduction "rate" and sporozoite "rate", Garret-Jones' vectorial capacity and Dietz-Molineaux-Thomas' force of infection. The analysis was intended to provide a formal notation that complete the classical equations proposed by these authors.

Supersymmetric extension of the quantum spherical model

In this work, we present a supersymmetric extension of the quantum spherical model, both in components and also in the superspace formalisms. We find the solution for short- and long-range interactions through the imaginary time formalism path integral approach. The existence of critical points (classical and quantum) is analyzed and the corresponding critical dimensions are determined.

Local symmetries in gauge theories in a finite-dimensional setting

It is shown that the correct mathematical implementation of symmetry in the geometric formulation of classical field theory leads naturally beyond the concept of Lie groups and their actions on manifolds, out into the realm of Lie group bundles and, more generally, of Lie groupoids and their actions on fiber bundles. This applies not only to local symmetries, which lie at the heart of gauge theories, but is already true even for global symmetries when one allows for fields that are sections of bundles with (possibly) non-trivial topology or, even when these are topologically trivial, in the absence of a preferred trivialization. (C) 2012 Elsevier B.V. All rights reserved.

COMPLEXITY MEASURE: A QUANTUM INFORMATION APPROACH

In the past decades, all of the efforts at quantifying systems complexity with a general tool has usually relied on using Shannon's classical information framework to address the disorder of the system through the Boltzmann-Gibbs-Shannon entropy, or one of its extensions. However, in recent years, there were some attempts to tackle the quantification of algorithmic complexities in quantum systems based on the Kolmogorov algorithmic complexity, obtaining some discrepant results against the classical approach. Therefore, an approach to the complexity measure is proposed here, using the quantum information formalism, taking advantage of the generality of the classical-based complexities, and being capable of expressing these systems' complexity on other framework than its algorithmic counterparts. To do so, the Shiner-Davison-Landsberg (SDL) complexity framework is considered jointly with linear entropy for the density operators representing the analyzed systems formalism along with the tangle for the entanglement measure. The proposed measure is then applied in a family of maximally entangled mixed state.

Biocompatible Magnetic Microspheres for Use in PDT and Hyperthermia

Loaded microspheres with a silicon (IV) phthalocyanine derivative (NzPC) acting as a photosensitizer were prepared from polyhydroxybutyrate-co-valerate (PHBHV) and poly(ecaprolactone) (PCL) polymers using the emulsification solvent evaporation method (EE). The aim of our study was to prepare two systems of these biodegradable PHBHV/PCL microspheres. The first one containing only photosensitizer previously incorporated in the PHBHV and poly(ecaprolactone) (PCL) microspheres and the second one with the post magnetization of the DDS with magnetic nanoparticles. Magnetic fluid is successfully used for controlled incorporation of nanosized magnetic particles within the micron-sized template. This is the first time that we could get a successful pos incorporation of nanosized magnetic particles in a previously-prepared polymeric template. This procedure opens a great number of possibilities of post-functionalization of polymeric micro or nanoparticles with different bioactive materials. The NzPC release profile of the systems is ideal for PDT, the zeta potential and the size particle are stable upon aging in time. In vitro studies were evaluated using gingival fibroblastic cell line. The dark citotoxicity, the phototoxicity and the AC magnetic field assays of the as-prepared nanomagnetic composite were evaluated and the cellular viability analyzed by the classical test of MU.

Quantum spherical model with competing interactions

We analyse the phase diagram of a quantum mean spherical model in terms of the temperature T, a quantum parameter g, and the ratio p = -J(2)/J(1) where J(1) > 0 refers to ferromagnetic interactions between first-neighbour sites along the d directions of a hypercubic lattice, and J(2) < 0 is associated with competing anti ferromagnetic interactions between second neighbours along m <= d directions. We regain a number of known results for the classical version of this model, including the topology of the critical line in the g = 0 space, with a Lifshitz point at p = 1/4, for d > 2, and closed-form expressions for the decay of the pair correlations in one dimension. In the T = 0 phase diagram, there is a critical border, g(c) = g(c) (p) for d >= 2, with a singularity at the Lifshitz point if d < (m + 4)/2. We also establish upper and lower critical dimensions, and analyse the quantum critical behavior in the neighborhood of p = 1/4. 2012 (C) Elsevier B.V. All rights reserved.

Asymptotic integral kernel for ensembles of random normal matrices with radial potentials

The method of steepest descent is used to study the integral kernel of a family of normal random matrix ensembles with eigenvalue distribution P-N (z(1), ... , z(N)) = Z(N)(-1)e(-N)Sigma(N)(i=1) V-alpha(z(i)) Pi(1 <= i<j <= N) vertical bar z(i) - z(j)vertical bar(2), where V-alpha(z) = vertical bar z vertical bar(alpha), z epsilon C and alpha epsilon inverted left perpendicular0, infinity inverted right perpendicular. Asymptotic formulas with error estimate on sectors are obtained. A corollary of these expansions is a scaling limit for the n-point function in terms of the integral kernel for the classical Segal-Bargmann space. (C) 2012 American Institute of Physics. [http://dx.doi.org/10.1063/1.3688293]

Signatures of quantum phase transitions in parallel quantum dots: Crossover from local moment to underscreened spin-1 Kondo physics

We study a strongly interacting "quantum dot 1" and a weakly interacting "dot 2" connected in parallel to metallic leads. Gate voltages can drive the system between Kondo-quenched and non-Kondo free-moment phases separated by Kosterlitz-Thouless quantum phase transitions. Away from the immediate vicinity of the quantum phase transitions, the physical properties retain signatures of first-order transitions found previously to arise when dot 2 is strictly noninteracting. As interactions in dot 2 become stronger relative to the dot-lead coupling, the free moment in the non-Kondo phase evolves smoothly from an isolated spin-one-half in dot 1 to a many-body doublet arising from the incomplete Kondo compensation by the leads of a combined dot spin-one. These limits, which feature very different spin correlations between dot and lead electrons, can be distinguished by weak-bias conductance measurements performed at finite temperatures.

Evolution of a dense neutrino gas in matter and electromagnetic field

We describe the system of massive Weyl fields propagating in a background matter and interacting with an external electromagnetic field. The interaction with an electromagnetic field is due to the presence of anomalous magnetic moments. To canonically quantize this system first we develop the classical field theory treatment of Weyl spinors in frames of the Hamilton formalism which accounts for the external fields. Then, on the basis of the exact solution of the wave equation for a massive Weyl field in a background matter we obtain the effective Hamiltonian for the description of spin-flavor oscillations of Majorana neutrinos in matter and a magnetic field. Finally, we incorporate in our analysis the neutrino self-interaction which is essential when the neutrino density is sufficiently high. We also discuss the applicability of our results for the studies of collective effects in spin-flavor oscillations of supernova neutrinos in a dense matter and a strong magnetic field. (C) 2011 Elsevier B.V. All rights reserved.

Modelling Mathematical Reasoning in Physics Education

Many findings from research as well as reports from teachers describe students' problem solving strategies as manipulation of formulas by rote. The resulting dissatisfaction with quantitative physical textbook problems seems to influence the attitude towards the role of mathematics in physics education in general. Mathematics is often seen as a tool for calculation which hinders a conceptual understanding of physical principles. However, the role of mathematics cannot be reduced to this technical aspect. Hence, instead of putting mathematics away we delve into the nature of physical science to reveal the strong conceptual relationship between mathematics and physics. Moreover, we suggest that, for both prospective teaching and further research, a focus on deeply exploring such interdependency can significantly improve the understanding of physics. To provide a suitable basis, we develop a new model which can be used for analysing different levels of mathematical reasoning within physics. It is also a guideline for shifting the attention from technical to structural mathematical skills while teaching physics. We demonstrate its applicability for analysing physical-mathematical reasoning processes with an example.

Cosmological measure with volume averaging and the vacuum energy problem

In this paper, we give a possible solution to the cosmological constant problem. It is shown that the traditional approach, based on volume weighting of probabilities, leads to an incoherent conclusion: the probability that a randomly chosen observer measures Lambda = 0 is exactly equal to 1. Using an alternative, volume averaging measure, instead of volume weighting can explain why the cosmological constant is non-zero.

Generalized non-commutative inflation

Non-commutative geometry indicates a deformation of the energy-momentum dispersion relation f (E) = E/pc (not equal 1) for massless particles. This distorted energy-momentum relation can affect the radiation-dominated phase of the universe at sufficiently high temperature. This prompted the idea of non-commutative inflation by Alexander et al (2003 Phys. Rev. D 67 081301) and Koh and Brandenberger (2007 JCAP06(2007) 021 and JCAP11(2007) 013). These authors studied a one-parameter family of a non-relativistic dispersion relation that leads to inflation: the a family of curves f (E) = 1 + (lambda E)(alpha). We show here how the conceptually different structure of symmetries of non-commutative spaces can lead, in a mathematically consistent way, to the fundamental equations of non-commutative inflation driven by radiation. We describe how this structure can be considered independently of (but including) the idea of non-commutative spaces as a starting point of the general inflationary deformation of SL(2, C). We analyze the conditions on the dispersion relation that leads to inflation as a set of inequalities which plays the same role as the slow-roll conditions on the potential of a scalar field. We study conditions for a possible numerical approach to obtain a general one-parameter family of dispersion relations that lead to successful inflation.

Integral form of Yang-Mills equations and its gauge invariant conserved charges

Despite the fact that the integral form of the equations of classical electrodynamics is well known, the same is not true for non-Abelian gauge theories. The aim of the present paper is threefold. First, we present the integral form of the classical Yang-Mills equations in the presence of sources and then use it to solve the long-standing problem of constructing conserved charges, for any field configuration, which are invariant under general gauge transformations and not only under transformations that go to a constant at spatial infinity. The construction is based on concepts in loop spaces and on a generalization of the non-Abelian Stokes theorem for two-form connections. The third goal of the paper is to present the integral form of the self-dual Yang-Mills equations and calculate the conserved charges associated with them. The charges are explicitly evaluated for the cases of monopoles, dyons, instantons and merons, and we show that in many cases those charges must be quantized. Our results are important in the understanding of global properties of non-Abelian gauge theories.

Statistical physics approach to dendritic computation: The excitable-wave mean-field approximation

We analytically study the input-output properties of a neuron whose active dendritic tree, modeled as a Cayley tree of excitable elements, is subjected to Poisson stimulus. Both single-site and two-site mean-field approximations incorrectly predict a nonequilibrium phase transition which is not allowed in the model. We propose an excitable-wave mean-field approximation which shows good agreement with previously published simulation results [Gollo et al., PLoS Comput. Biol. 5, e1000402 (2009)] and accounts for finite-size effects. We also discuss the relevance of our results to experiments in neuroscience, emphasizing the role of active dendrites in the enhancement of dynamic range and in gain control modulation.