Mixmaster Chaoticity as Semiclassical Limit of the Canonical Quantum Dynamics

Within a cosmological framework, we provide a Hamiltonian analysis of the Mixmaster Universe dynamics on the base of a standard Arnowitt-Deser-Misner approach, showing how the chaotic behavior characterizing the evolution of the system near the cosmological singularity can be obtained as the semiclassical limit of the canonical quantization of the model in the same dynamical representation. The relation between this intrinsic chaotic behavior and the indeterministic quantum dynamics is inferred through the coincidence between the microcanonical probability distribution and the semiclassical quantum one.Comment: 9 pages, 1 figur

Dynamical system analysis for nonminimal torsion-matter coupled gravity

In this work, we perform a detailed dynamical analysis for the cosmological applications of a nonminimal torsion-matter coupled gravity. Two alternative formalisms are proposed, which enable one to choose between the easier approach for a given problem, and furthermore, we analyze six specific models. In general, we extract fixed points corresponding either to dark-matter dominated, scaling decelerated solutions, or to dark-energy dominated accelerated solutions. Additionally, we find that there is a small parameter region in which the model can experience the transition from the matter epoch to a dark-energy era. These features are in agreement with the observed universe evolution, and make the theory a successful candidate for the description of Nature.Comment: 11 pages, 3 figure

Dimensionful deformations of Poincare' symmetries for a Quantum Gravity without ideal observers

Quantum Mechanics is revisited as the appropriate theoretical framework for the description of the outcome of experiments that rely on the use of classical devices. In particular, it is emphasized that the limitations on the measurability of (pairs of conjugate) observables encoded in the formalism of Quantum Mechanics reproduce faithfully the ``classical-device limit'' of the corresponding limitations encountered in (real or gedanken) experimental setups. It is then argued that devices cannot behave classically in Quantum Gravity, and that this might raise serious problems for the search of a class of experiments described by theories obtained by ``applying Quantum Mechanics to Gravity.'' It is also observed that using heuristic/intuitive arguments based on the absence of classical devices one is led to consider some candidate Quantum-Gravity phenomena involving dimensionful deformations of the Poincare' symmetries.Comment: 7 pages, Latex. (This essay received an ``honorable mention'' from the Gravity Research Foundation, 1998-Ed.

NLO evolution of color dipoles

The small-$x$ deep inelastic scattering in the saturation region is governed by the non-linear evolution of Wilson-line operators. In the leading logarithmic approximation it is given by the BK equation for the evolution of color dipoles. In the next-to-leading order the BK equation gets contributions from quark and gluon loops as well as from the tree gluon diagrams with quadratic and cubic nonlinearities. We calculate the gluon contribution to small-x evolution of Wilson lines (the quark part was obtained earlier).Comment: 43 pages, 12 figure

Dark soliton collisions in superfluid Fermi gases

In this work dark soliton collisions in a one-dimensional superfluid Fermi gas are studied across the BEC-BCS crossover by means of a recently developed finite-temperature effective field theory [S. N. Klimin, J. Tempere, G. Lombardi, J. T. Devreese, Eur. Phys. J. B 88, 122 (2015)] . The evolution of two counter-propagating solitons is simulated numerically based on the theory's nonlinear equation of motion for the pair field. The resulting collisions are observed to introduce a spatial shift into the trajectories of the solitons. The magnitude of this shift is calculated and studied in different conditions of temperature and spin-imbalance. When moving away from the BEC-regime, the collisions are found to become inelastic, emitting the lost energy in the form of small-amplitude density oscillations. This inelasticity is quantified and its behavior analyzed and compared to the results of other works. The dispersion relation of the density oscillations is calculated and is demonstrated to show a good agreement with the spectrum of collective excitations of the superfluid

Strongly correlated metal interfaces in the Gutzwiller approximation

We study the effect of spatial inhomogeneity on the physics of a strongly correlated electron system exhibiting a metallic phase and a Mott insulating phase, represented by the simple Hubbard model. In three dimensions, we consider various geometries, including vacuum-metal-vacuum, a junction between a weakly and a strongly correlated metal, and finally the double junctions metal-Mott insulator-metal and metal-strongly correlated metal- metal. We applied to these problems the self-consistent Gutzwiller technique recently developed in our group, whose approximate nature is compensated by an extreme flexibility,ability to treat very large systems, and physical transparency. The main general result is a clear characterization of the position dependent metallic quasiparticle spectral weight. Its behavior at interfaces reveals the ubiquitous presence of exponential decays and crossovers, with decay lengths of clear physical significance. The decay length of metallic strength in a weakly-strongly correlated metal interface is due to poor screening in the strongly correlated side. The decay length of metallic strength from a metal into a Mott insulator (or into vacuum) is due to tunneling. In both cases, the decay length is a bulk property, and diverges with a critical exponent ($\sim 1/2$ in the present approximation, mean field in character) as the (continuous, paramagnetic) Mott transition is approached.Comment: 19 pages, 19 figure

Discrete Approximations of a Controlled Sweeping Process

The paper is devoted to the study of a new class of optimal control problems governed by the classical Moreau sweeping process with the new feature that the polyhe- dral moving set is not fixed while controlled by time-dependent functions. The dynamics of such problems is described by dissipative non-Lipschitzian differential inclusions with state constraints of equality and inequality types. It makes challenging and difficult their anal- ysis and optimization. In this paper we establish some existence results for the sweeping process under consideration and develop the method of discrete approximations that allows us to strongly approximate, in the W^{1,2} topology, optimal solutions of the continuous-type sweeping process by their discrete counterparts