A path integral for classical dynamics, entanglement, and Jaynes-Cummings model at the quantum-classical divide

The Liouville equation differs from the von Neumann equation 'only' by a characteristic superoperator. We demonstrate this for Hamiltonian dynamics, in general, and for the Jaynes-Cummings model, in particular. -- Employing superspace (instead of Hilbert space), we describe time evolution of density matrices in terms of path integrals which are formally identical for quantum and classical mechanics. They only differ by the interaction contributing to the action. This allows to import tools developed for Feynman path integrals, in order to deal with superoperators instead of quantum mechanical commutators in real time evolution. Perturbation theory is derived. Besides applications in classical statistical physics, the "classical path integral" and the parallel study of classical and quantum evolution indicate new aspects of (dynamically assisted) entanglement (generation). Our findings suggest to distinguish 'intra'- from 'inter-space' entanglement.Comment: 22 pages; based on invited talk at Quantum 2010 - Advances in Foundations of Quantum mechanics and Quantum Information with Atoms and Photons (Torino, May 2010). To appear in Int. J. Qu. Inf

A novel layered topology of auxetic materials based on the tetrachiral honeycomb microstructure

Microstructured honeycomb materials may exhibit exotic, extreme and tailorable mechanical properties, suited for innovative technological applications in a variety of modern engineering fields. The paper is focused on analysing the directional auxeticity of tetrachiral materials, through analytical, numerical and experimental methods. Theoretical predictions about the global elastic properties have been successfully validated by performing tensile laboratory tests on tetrachiral samples, realized with high precision 3D printing technologies. Inspired by the kinematic behaviour of the tetrachiral material, a newly-design bi-layered topology, referred to as bi-tetrachiral material, has been theoretically conceived and mechanically modelled. The novel topology virtuously exploits the mutual collaboration between two tetrachiral layers with opposite chiralities. The bi-tetrachiral material has been verified to outperform the tetrachiral material in terms of global Young modulus and, as major achievement, to exhibit a remarkable auxetic behaviour. Specifically, experimental results, confirmed by parametric analytical and computational analyses, have highlighted the effective possibility to attain strongly negative Poisson ratios, identified as a peculiar global elastic property of the novel bi-layered topology

General linear dynamics - quantum, classical or hybrid

We describe our recent proposal of a path integral formulation of classical Hamiltonian dynamics. Which leads us here to a new attempt at hybrid dynamics, which concerns the direct coupling of classical and quantum mechanical degrees of freedom. This is of practical as well as of foundational interest and no fully satisfactory solution of this problem has been established to date. Related aspects will be observed in a general linear ensemble theory, which comprises classical and quantum dynamics in the form of Liouville and von Neumann equations, respectively, as special cases. Considering the simplest object characterized by a two-dimensional state-space, we illustrate how quantum mechanics is special in several respects among possible linear generalizations.Comment: 17 pages; based on invited talks at the conferences DICE2010 (Castiglioncello, Italia, Sept 13-17, 2010) and Quantum Field Theory and Gravity (Regensburg, Germany, Sept 28 - Oct 1, 2010

ErbB4 expression in neural progenitor cells (ST14A) is necessary to mediate neuregulin-1beta1-induced migration

Activation of the receptor tyrosine kinase ErbB4 leads to various cellular responses such as proliferation, survival, differentiation, and chemotaxis. Two pairs of naturally occurring ErbB4 isoforms differing in their juxtamembrane (JMa/JMb) and C termini (cyt1/cyt2) have been described. To examine the role of ErbB4 in neuron migration, we cloned and stably transfected each of the four ErbB4 isoforms in ST14A cells (a neural progenitor cell line derived from the striatum of embryonic day 14 rats) endogenously expressing the other members of the ErbB family: ErbB1, ErbB2, and ErbB3. Using immunoprecipitation assays, we showed that the neuregulin-1beta1 (NRG1beta1) stimulus induced ErbB4 tyrosine phosphorylation and phosphatidylinositol 3-kinase (PI3K) recruitment and activation (as demonstrated by Akt phosphorylation) either directly (ErbB4 cyt1 isoform) or indirectly (ErbB4 cyt2 isoform). We examined the ability of the four ErbB4 isoforms to induce chemotaxis and cell proliferation in response to NRG1beta1 stimulation. Using migration assays, we observed that only ErbB4-expressing cells stimulated with NRG1beta1 showed a significant increase in migration, whereas the growth rate remained unchanged. Additional assays showed that inhibition of PI3K (but not of phospholipase Cgamma) dramatically reduced migratory activity. Our data show that ErbB4 signaling via PI3K activation plays a fundamental role in controlling NRG1beta1-induced migration