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

Hepatocyte growth factor (HGF) receptor expression is inducible and is part of the delayed-early response to HGF.

The c-MET proto-oncogene encodes the tyrosine kinase receptor for hepatocyte growth factor (HGF), also known as scatter factor, a potent mitogen and motogen for epithelial cells. The level of the HGF receptor expressed by epithelial cells varies in different growth conditions, being lower in growth arrested confluent monolayers and higher in growing sparse cells. The amount of HGF receptor mRNA increases from 3- to 5-fold after stimulation of confluent monolayers by serum and up to 10-fold after stimulation of protein kinase C by 12-O-tetradecanoylphorbol-13-acetate (TPA). An increased level of the receptor mRNA was also observed after cell stimulation with nanomolar concentration of HGF itself. The effect was transient, dose, and time-dependent. Transcription of a reporter gene under control of the cloned 297 base pair c-MET promoter was also stimulated by serum, TPA, or HGF. The accumulation of specific mRNA is followed by appearance of the HGF receptor precursor protein, which is further processed to the receptor mature form. After HGF stimulation, HGF receptor expression follows c-FOS and c-JUN induction with a peak approximately 4 h. Pretreatment with the protein synthesis inhibitor puromycin strongly reduced the response to HGF, while cycloheximide alone increased the level of the receptor mRNA. These data show that c-MET behaves as a delayed early-response gene and suggest that the HGF response is autoamplified by inducing the specific receptor

ErbB2 receptor over-expression improves post-traumatic peripheral nerve regeneration in adult mice.

In a transgenic mice (BALB-neuT) over-expressing ErbB2 receptor, we investigated the adult mouse median nerve in physiological and pathological conditions. Results showed that, in physiological conditions, the grip function controlled by the median nerve in BALB-neuT mice was similar to wild-type (BALB/c). Stereological assessment of ErbB2-overexpressing intact nerves revealed no difference in number and size of myelinated fibers compared to wild-type mice. By contrast, after a nerve crush injury, the motor recovery was significantly faster in BALB-neuT compared to BALB/c mice. Moreover, stereological assessment revealed a significant higher number of regenerated myelinated fibers with a thinner axon and fiber diameter and myelin thickness in BALB-neuT mice. At day-2 post-injury, the level of the mRNAs coding for all the ErbB receptors and for the transmembrane (type III) Neuregulin 1 (NRG1) isoforms significantly decreased in both BALB/c and BALB-neuT mice, as shown by quantitative real time PCR. On the other hand, the level of the mRNAs coding for soluble NRG1 isoforms (type I/II, alpha and beta) increased at the same post-traumatic time point though, intriguingly, this response was significantly higher in BALB-neuT mice with respect to BALB/c mice. Altogether, these results suggest that constitutive ErbB2 receptor over-expression does not influence the physiological development of peripheral nerves, while it improve

A reformulation of Hamiltonian dynamics. A case study of the Jaynes-Cummings model.

Despite its great successes in describing the statistical aspects of experiments, quantum theory itself presents problems of interpretation, which arise from its indeterministic features and which are clearly seen, for example, in the unresolved measurement problem. Thus, concerning the foundations of quantum mechanics, there is an increasing impetus to try to reconstruct and to better understand the emergence of quantum mechanics from simpler structures beneath. We present a reformulation of Hamiltonian dynamics in such a way that the classical Liouville equation, after suitable tranformations, can be written in a way that almost reproduces the quantum mechanical von Neumann equation. Indeed, an unusual superoperator appearing in the transformed Liouville equation gives rise to the only substantial difference between the quantum and classical dynamics. This approach also gives the possibility of looking more carefully into the common and distinctive features of the classical and quantum dynamics. Some interesting considerations regarding the preparation of entangled states are pointed out. We then present this approach for a hydrogenic atom interacting with the electromagnetic field in the Coulomb gauge. Starting from the classical Liouville equation we derive for the atom-field system an evolution equation appearing as the usual quantum mechanical von Neumann equation modified by an extra term. From this general expression, by making approximations which are widely applied in quantum optics, we obtain the von Neumann equation for the Jaynes-Cummings model modified by an extra term. The Jaynes-Cummings model describes a simplified version of atom-field interaction. It has been widely studied experimentally and theoretically. In particular, it has been a usefull tool for investigating the evolution of entanglement between the atom and the electromagnetic field and has also been used for applications in quantum information. A review of the related cavity QED experiments performed in Paris is presented. The aim of the thesis is to study the way the extra term modifies the dynamics described by the Jaynes-Cummings hamiltonian and thus to what extent the dynamics of this quantum mechanical model can be derived from the classical Liouville equation

The number of Schwann cells is higher in BALB-neuT mice after regeneration.

<p>A, histognams showing the number of Schwann cells counted at electron microscopy. B, C representative electron images of transverse sections of regenerated median nerves of BALB/c and BALB-neuT mice respectively. Magnification: 10000×. Statistical significance: *p<0.05.</p

The number of Schwann cells is comparable between BALB/c and BALB-neuT mice.

<p>A, histognams showing the number of Schwann cells counted at electron microscopy. B, C representative electron images of transverse sections of uninjured median nerves of BALB/c and BALB-neuT mice respectively. Magnification: 10000×.</p

2 days after the crush injury, BALB-neuT mice express higher levels of ErbB2 protein.

<p>Western blot analysis showing ErbB2 expression in crushed nerves 2-days after injury. β-actin was used as a loading control. The ErbB2 expression is higher in BALB-neuT mice compared to BALB/c mice.</p