7,478 research outputs found
Reconstructing Quantum Geometry from Quantum Information: Spin Networks as Harmonic Oscillators
Loop Quantum Gravity defines the quantum states of space geometry as spin
networks and describes their evolution in time. We reformulate spin networks in
terms of harmonic oscillators and show how the holographic degrees of freedom
of the theory are described as matrix models. This allow us to make a link with
non-commutative geometry and to look at the issue of the semi-classical limit
of LQG from a new perspective. This work is thought as part of a bigger project
of describing quantum geometry in quantum information terms.Comment: 16 pages, revtex, 3 figure
Lieb–Robinson bounds for open quantum systems with long-ranged interactions
We state and prove four types of Lieb–Robinson bounds valid for many-body open quantum systems with power law decaying interactions undergoing out of equilibrium dynamics. We also provide an introductory and self-contained discussion of the setting and tools necessary to prove these results. The results found here apply to physical systems in which both long-ranged interactions and dissipation are present, as commonly encountered in certain quantum simulators, such as Rydberg systems or Coulomb crystals formed by ions
D0-Branes As Light-Front Confined Quarks
We argue that different aspects of Light-Front QCD at confined phase can be
recovered by the Matrix Quantum Mechanics of D0-branes. The concerning Matrix
Quantum Mechanics is obtained from dimensional reduction of pure Yang-Mills
theory to 0+1 dimension. The aspects of QCD dynamics which are studied in
correspondence with D0-branes are: 1) phenomenological inter-quark potentials,
2) whiteness of hadrons and 3) scattering amplitudes. In addition, some other
issues such as the large-N behavior, the gravity--gauge theory relation and
also a possible justification for involving ``non-commutative coordinates'' in
a study of QCD bound-states are discussed.Comment: 26 pages, LaTeX file, 3 .eps figures; v2: language is improved; v3:
subsection 4.2 is changed- accepted for publication in EPJ.
New tools for Loop Quantum Gravity with applications to a simple model
Loop Quantum Gravity is now a well established approach to quantum gravity.
One of the main challenges still faced by the theory is constructing a
consistent dynamics which would lead back to the standard dynamics of the
gravitational field at large scales. Here we will review the recent U(N)
framework for Loop Quantum Gravity and the new spinor representation (that
provides a classical setting for the U(N) framework). Then, we will apply these
techniques to a simple model in order to propose a dynamics for a symmetry
reduced sector of the theory. Furthermore, we will explore certain analogies of
this model with Loop Quantum Cosmology.Comment: 4 pages, to appear in Proceedings of Spanish Relativity Meeting 2011
(ERE 2011) held in Madrid, Spai
6D superconformal theory as the theory of everything
We argue that the fundamental Theory of Everything is a conventional field
theory defined in the flat multidimensional bulk. Our Universe should be
obtained as a 3-brane classical solution in this theory. The renormalizability
of the fundamental theory implies that it involves higher derivatives (HD). It
should be supersymmetric (otherwise one cannot get rid of the huge induced
cosmological term) and probably conformal (otherwise one can hardly cope with
the problem of ghosts) . We present arguments that in conformal HD theories the
ghosts (which are inherent for HD theories) might be not so malignant. In
particular, we present a nontrivial QM HD model where ghosts are absent and the
spectrum has a well defined ground state. The requirement of superconformal
invariance restricts the dimension of the bulk to be D < 7. We suggest that the
TOE lives in six dimensions and enjoys the maximum N = (2,0) superconformal
symmetry. Unfortunately, no renormalizable field theory with this symmetry is
presently known. We construct and discuss an N = (1,0) 6D supersymmetric gauge
theory with four derivatives in the action. This theory involves a
dimensionless coupling constant and is renormalizable. At the tree level, the
theory enjoys conformal symmetry, but the latter is broken by quantum anomaly.
The sign of the beta function corresponds to the Landau zero situation.Comment: 15 pages, 2 figures, based on the talks in Gribov-75 memorial
workshop (Budapest, May 22-24) and the workshop "Supersymmetry and quantum
symmetries" (Dubna, July 27-31
The Physics of Communicability in Complex Networks
A fundamental problem in the study of complex networks is to provide
quantitative measures of correlation and information flow between different
parts of a system. To this end, several notions of communicability have been
introduced and applied to a wide variety of real-world networks in recent
years. Several such communicability functions are reviewed in this paper. It is
emphasized that communication and correlation in networks can take place
through many more routes than the shortest paths, a fact that may not have been
sufficiently appreciated in previously proposed correlation measures. In
contrast to these, the communicability measures reviewed in this paper are
defined by taking into account all possible routes between two nodes, assigning
smaller weights to longer ones. This point of view naturally leads to the
definition of communicability in terms of matrix functions, such as the
exponential, resolvent, and hyperbolic functions, in which the matrix argument
is either the adjacency matrix or the graph Laplacian associated with the
network. Considerable insight on communicability can be gained by modeling a
network as a system of oscillators and deriving physical interpretations, both
classical and quantum-mechanical, of various communicability functions.
Applications of communicability measures to the analysis of complex systems are
illustrated on a variety of biological, physical and social networks. The last
part of the paper is devoted to a review of the notion of locality in complex
networks and to computational aspects that by exploiting sparsity can greatly
reduce the computational efforts for the calculation of communicability
functions for large networks.Comment: Review Article. 90 pages, 14 figures. Contents: Introduction;
Communicability in Networks; Physical Analogies; Comparing Communicability
Functions; Communicability and the Analysis of Networks; Communicability and
Localization in Complex Networks; Computability of Communicability Functions;
Conclusions and Prespective
Rotational states in deformed nuclei: An analytic approach
The consequences of the spontaneous breaking of rotational symmetry are
investigated in a field theory model for deformed nuclei, based on simple
separable interactions. The crucial role of the Ward-Takahashi identities to
describe the rotational states is emphasized. We show explicitly how the rotor
picture emerges from the isoscalar Goldstone modes, and how the two-rotor model
emerges from the isovector scissors modes. As an application of the formalism,
we discuss the M1 sum rules in deformed nuclei, and make connection to
empirical information.Comment: 19 pages, 9 figure
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