Constraining spacetime torsion with LAGEOS

We compute the corrections to the orbital Lense-Thirring effect (or frame-dragging) in the presence of spacetime torsion. We analyze the motion of a test body in the gravitational field of a rotating axisymmetric massive body, using the parametrized framework of Mao, Tegmark, Guth and Cabi. In the cases of autoparallel and extremal trajectories, we derive the specific approximate expression of the corresponding system of ordinary differential equations, which are then solved with methods of Celestial Mechanics. We calculate the secular variations of the longitudes of the node and of the pericenter. We also show how the LAser GEOdynamics Satellites (LAGEOS) can be used to constrain torsion parameters. We report the experimental constraints obtained using both the nodes and perigee measurements of the orbital Lense-Thirring effect. This makes LAGEOS and Gravity Probe B complementary frame-dragging and torsion experiments, since they constrain three different combinations of torsion parameters.     

Dynamical phases of the Hindmarsh-Rose neuronal model: studies of the transition from bursting to spiking chaos

The dynamical phases of the Hindmarsh-Rose neuronal model are analyzed in detail by varying the external current I. For increasing current values, the model exhibits a peculiar cascade of nonchaotic and chaotic period-adding bifurcations leading the system from the silent regime to a chaotic state dominated by bursting events. At higher I-values, this phase is substituted by a regime of continuous chaotic spiking and finally via an inverse period doubling cascade the system returns to silence. The analysis is focused on the transition between the two chaotic phases displayed by the model: one dominated by spiking dynamics and the other by bursts. At the transition an abrupt shrinking of the attractor size associated with a sharp peak in the maximal Lyapunov exponent is observable. However, the transition appears to be continuous and smoothed out over a finite current interval, where bursts and spikes coexist. The beginning of the transition (from the bursting side) is signaled from a structural modification in the interspike interval return map. This change in the map shape is associated with the disappearance of the family of solutions responsible for the onset of the bursting chaos. The successive passage from bursting to spiking chaos is associated with a progressive pruning of unstable long-lasting bursts.     

Nonequilibrium invariant measure under heat flow

We provide an explicit representation of the nonequilibrium invariant measure for a chain of harmonic oscillators with conservative noise in the presence of stationary heat flow. By first determining the covariance matrix, we are able to express the measure as the product of Gaussian distributions aligned along some collective modes that are spatially localized with power-law tails. Numerical studies show that such a representation applies also to a purely deterministic model, the quartic Fermi-Pasta-Ulam chain.     

Interpolation by type I factors and the flip automorphism

Given two von Neumann algebras $\text{A}$ ?$\text{B}$ we study the relation between the existence of an interpolating type I factor $\text{F}$, namely $\text{A}$ ?$\text{F}$ ?$\text{B}$, the implementability of the flip automorphism of $\text{A}$ ? $\text{A}$ by a unitary in $\text{B}$ ? $\text{B}$, and the statistical independence of $\text{A}$ and $\text{B}$′ ($\text{A}$ and $\text{B}$′ generate a $\text{W}$¹-tensor product). As an application in Q.F.T. we derive in a natural way a structure theorem of Buchholz for the von Neumann algebras of local observables associated to free fields.     

Extensions of automorphisms and gauge symmetries

We characterize the automorphisms of aC ^*-algebra which extend to automorphisms of the crossed product by a compact group dual. The case where the inclusion is equipped with a group of automorphisms commuting with the dual action is also treated. These results are applied to the analysis of broken gauge symmetries in Quantum Field Theory to draw conclusions on the structure of the degenerate vacua on the field algebra.Dedicated to Huzihiro ArakiResearch supported by MURST and CNR, GNAFA