Gravity and the quantum: Are they reconcilable?

General relativity and quantum mechanics are not consistent with each other. This conflict stems from the very fundamental principles on which these theories are grounded. General relativity, on one hand, is based on the equivalence principle, whose strong version establishes the local equivalence between gravitation and inertia. Quantum mechanics, on the other hand, is fundamentally based on the uncertainty principle, which is essentially nonlocal. This difference precludes the existence of a quantum version of the strong equivalence principle, and consequently of a quantum version of general relativity. Furthermore, there are compelling experimental evidences that a quantum object in the presence of a gravitational field violates the weak equivalence principle. Now it so happens that, in addition to general relativity, gravitation has an alternative, though equivalent, description, given by teleparallel gravity, a gauge theory for the translation group. In this theory torsion, instead of curvature, is assumed to represent the gravitational field. These two descriptions lead to the same classical results, but are conceptually different. In general relativity, curvature geometrizes the interaction while torsion, in teleparallel gravity, acts as a force, similar to the Lorentz force of electrodynamics. Because of this peculiar property, teleparallel gravity describes the gravitational interaction without requiring any of the equivalence principle versions. The replacement of general relativity by teleparallel gravity may, in consequence, lead to a conceptual reconciliation of gravitation with quantum mechanics. © 2006 American Institute of Physics.

Análise comparativa de alguns sistemas dinâmicos clássicos e quânticos

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

A study of the dynamics of quantum correlations

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

The structure of non-abelian kinks

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Quasimodular instanton partition function and the elliptic solution of Korteweg-de Vries equations

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Dynamics of classical particles in oval or elliptic billiards with a dispersing mechanism

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Quantum Discord for d circle times 2 Systems

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Integrable deformations of strings on symmetric spaces

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

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]

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.

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.

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.

Decoherence of quantum kinematical correlations: Elastic scattering of identical particles

We include the dynamics of the angular straggling process in the angular distributions of Mott scattering of heavy ions. We model the passage of an incoming nucleus through a target as a diffusion process. It is then possible to derive a simple and physically transparent expression for the angular dispersion due to the straggling. The angular dispersion should be folded with the theoretical Mott cross section to see its effect on the amplitude of the Mott oscillations. Our results agree very well with data of Pb-208 + Pb-208 scattering. We define the "classical" limit as the limit when the angular dispersion due to straggling becomes comparable with the Mott oscillation period and get the disappearance of quantum interference occurring at the limit 0.050 root xi Z(4)/E-3/2 >= 1, where xi stands for the target thickness, Z is the system's charge, and E is the center-of-mass energy. The experiments on lead are very close to this limit. We show that the kinematical correlations due to the identity of the particles is maintained, as it should be, and the action of the environment is to reduce the fringe visibility.

Quantum deformation of the angular distributions of synchrotron radiation. Emission from particles in the first excited state

The exact expressions for the characteristics of synchrotron radiation of charged particles in the first excited state are obtained in analytical form using quantum theory methods. We performed a detailed analysis of the angular distribution structure of radiation power and its polarization for particles with spin 0 and 1/2. It is shown that the exact quantum calculations lead to results that differ substantially from the predictions of classical theory.

Reconstructing Quantum Field Theory from an Educational Perspective

The research work concerns the analysis of the foundations of Quantum Field Theory carried out from an educational perspective. The whole research has been driven by two questions: • How the concept of object changes when moving from classical to contemporary physics? • How are the concepts of field and interaction shaped and conceptualized within contemporary physics? What makes quantum field and interaction similar to and what makes them different from the classical ones? The whole work has been developed through several studies: 1. A study aimed to analyze the formal and conceptual structures characterizing the description of the continuous systems that remain invariant in the transition from classical to contemporary physics. 2. A study aimed to analyze the changes in the meanings of the concepts of field and interaction in the transition to quantum field theory. 3. A detailed study of the Klein-Gordon equation aimed at analyzing, in a case considered emblematic, some interpretative (conceptual and didactical) problems in the concept of field that the university textbooks do not address explicitly. 4. A study concerning the application of the “Discipline-Culture” Model elaborated by I. Galili to the analysis of the Klein-Gordon equation, in order to reconstruct the meanings of the equation from a cultural perspective. 5. A critical analysis, in the light of the results of the studies mentioned above, of the existing proposals for teaching basic concepts of Quantum Field Theory and particle physics at the secondary school level or in introductory physics university courses.