From Feynman Proof of Maxwell Equations to Noncommutative Quantum Mechanics

In 1990, Dyson published a proof due to Feynman of the Maxwell equations assuming only the commutation relations between position and velocity. With this minimal assumption, Feynman never supposed the existence of Hamiltonian or Lagrangian formalism. In the present communication, we review the study of a relativistic particle using ``Feynman brackets.'' We show that Poincar\'e's magnetic angular momentum and Dirac magnetic monopole are the consequences of the structure of the Lorentz Lie algebra defined by the Feynman's brackets. Then, we extend these ideas to the dual momentum space by considering noncommutative quantum mechanics. In this context, we show that the noncommutativity of the coordinates is responsible for a new effect called the spin Hall effect. We also show its relation with the Berry phase notion. As a practical application, we found an unusual spin-orbit contribution of a nonrelativistic particle that could be experimentally tested. Another practical application is the Berry phase effect on the propagation of light in inhomogeneous media.Comment: Presented at the 3rd Feynman Festival (Collage Park, Maryland, U.S.A., August 2006

Semiclassical Dynamics of Electrons in Magnetic Bloch Bands: a Hamiltonian Approach

y formally diagonalizing with accuracy $\hbar$ the Hamiltonian of electrons in a crystal subject to electromagnetic perturbations, we resolve the debate on the Hamiltonian nature of semiclassical equations of motion with Berry-phase corrections, and therefore confirm the validity of the Liouville theorem. We show that both the position and momentum operators acquire a Berry-phase dependence, leading to a non-canonical Hamiltonian dynamics. The equations of motion turn out to be identical to the ones previously derived in the context of electron wave-packets dynamics.Comment: 4 page

Enhanced co-tolerance and co-sensitivity from long-term metal exposures of heterotrophic and autotrophic components of fluvial biofilms

Understanding the interactive effects of multiple stressors on ecosystems has started to become a major concern. The aim of our study was therefore to evaluate the consequences of a long-term exposure to environmental concentrations of Cu, Zn and As on the pollution induced community tolerance (PICT) of lotic biofilm communities in artificial indoor channels. Moreover, the specificity of the PICT was assessed by evaluating the positive and negative co-tolerance between these metals. Photosynthetic efficiency and substrate-induced respiration (SIR), targeting the autotrophic and heterotrophic communities respectively were used in short-term inhibition bioassays with Cu, Zn and As to assess sensitivities of preexposed biofilms to the metals tested. Diversity profiles of a phototrophic, eukaryotic and prokaryotic community in biofilms following the different treatments were determined and analyzed with principal component analysis. The results demonstrated that pre-exposure to metals induced structural shifts in the community and led to tolerance enhancements in the phototrophic and heterotrophic communities. On the other hand, whatever the functional parameter used (i.e. photosynthesis and SIR), communities exposed to Cu were more tolerant to Zn and vice versa. Furthermore, only phototrophic communities pre-exposed to As developed tolerance to Cu but not to Zn, whereas no co-tolerance between Cu and As was observed in the heterotrophic communities. Finally, phototrophic and heterotrophic communities exposed to Cu and Zn became more sensitive to As, reflecting a negative co tolerance between these metals. Overall, our findings support the fact that although the mode of action of the different metals is an important driver for the structure and thus the tolerance of the communities, it appears that the detoxification modes are the most important factors for the occurrence of positive or negative co-tolerance

Quantitative information flow, with a view

We put forward a general model intended for assessment of system security against passive eavesdroppers, both quantitatively ( how much information is leaked) and qualitatively ( what properties are leaked). To this purpose, we extend information hiding systems ( ihs ), a model where the secret-observable relation is represented as a noisy channel, with views : basically, partitions of the state-space. Given a view W and n independent observations of the system, one is interested in the probability that a Bayesian adversary wrongly predicts the class of W the underlying secret belongs to. We offer results that allow one to easily characterise the behaviour of this error probability as a function of the number of observations, in terms of the channel matrices defining the ihs and the view W . In particular, we provide expressions for the limit value as n → ∞, show by tight bounds that convergence is exponential, and also characterise the rate of convergence to predefined error thresholds. We then show a few instances of statistical attacks that can be assessed by a direct application of our model: attacks against modular exponentiation that exploit timing leaks, against anonymity in mix-nets and against privacy in sparse datasets

Interrupt Timed Automata: verification and expressiveness

We introduce the class of Interrupt Timed Automata (ITA), a subclass of hybrid automata well suited to the description of timed multi-task systems with interruptions in a single processor environment. While the reachability problem is undecidable for hybrid automata we show that it is decidable for ITA. More precisely we prove that the untimed language of an ITA is regular, by building a finite automaton as a generalized class graph. We then establish that the reachability problem for ITA is in NEXPTIME and in PTIME when the number of clocks is fixed. To prove the first result, we define a subclass ITA- of ITA, and show that (1) any ITA can be reduced to a language-equivalent automaton in ITA- and (2) the reachability problem in this subclass is in NEXPTIME (without any class graph). In the next step, we investigate the verification of real time properties over ITA. We prove that model checking SCL, a fragment of a timed linear time logic, is undecidable. On the other hand, we give model checking procedures for two fragments of timed branching time logic. We also compare the expressive power of classical timed automata and ITA and prove that the corresponding families of accepted languages are incomparable. The result also holds for languages accepted by controlled real-time automata (CRTA), that extend timed automata. We finally combine ITA with CRTA, in a model which encompasses both classes and show that the reachability problem is still decidable. Additionally we show that the languages of ITA are neither closed under complementation nor under intersection

Topological Force and Torque in Spin-Orbit Coupling System

The topological force and torque are investigated in the systems with spin-orbit coupling. Our results show that the topological force and torque appears as a pure relativistic quantum effect in an electromagnetic field. The origin of both topological force and torque is the Zitterbewegung effect. Considering nonlinear behaviors of spin-orbit coupling, we address possible phenomena driven by the topological forces.Comment: 4 page

Cell cycle-dependent and independent mating blocks ensure fungal zygote survival and ploidy maintenance.

To ensure genome stability, sexually reproducing organisms require that mating brings together exactly 2 haploid gametes and that meiosis occurs only in diploid zygotes. In the fission yeast Schizosaccharomyces pombe, fertilization triggers the Mei3-Pat1-Mei2 signaling cascade, which represses subsequent mating and initiates meiosis. Here, we establish a degron system to specifically degrade proteins postfusion and demonstrate that mating blocks not only safeguard zygote ploidy but also prevent lysis caused by aberrant fusion attempts. Using long-term imaging and flow-cytometry approaches, we identify previously unrecognized and independent roles for Mei3 and Mei2 in zygotes. We show that Mei3 promotes premeiotic S-phase independently of Mei2 and that cell cycle progression is both necessary and sufficient to reduce zygotic mating behaviors. Mei2 not only imposes the meiotic program and promotes the meiotic cycle, but also blocks mating behaviors independently of Mei3 and cell cycle progression. Thus, we find that fungi preserve zygote ploidy and survival by at least 2 mechanisms where the zygotic fate imposed by Mei2 and the cell cycle reentry triggered by Mei3 synergize to prevent zygotic mating

Lorentzian manifolds and scalar curvature invariants

We discuss (arbitrary-dimensional) Lorentzian manifolds and the scalar polynomial curvature invariants constructed from the Riemann tensor and its covariant derivatives. Recently, we have shown that in four dimensions a Lorentzian spacetime metric is either $\mathcal{I}$-non-degenerate, and hence locally characterized by its scalar polynomial curvature invariants, or is a degenerate Kundt spacetime. We present a number of results that generalize these results to higher dimensions and discuss their consequences and potential physical applications.Comment: submitted to CQ

Last passage percolation and traveling fronts

We consider a system of N particles with a stochastic dynamics introduced by Brunet and Derrida. The particles can be interpreted as last passage times in directed percolation on {1,...,N} of mean-field type. The particles remain grouped and move like a traveling wave, subject to discretization and driven by a random noise. As N increases, we obtain estimates for the speed of the front and its profile, for different laws of the driving noise. The Gumbel distribution plays a central role for the particle jumps, and we show that the scaling limit is a L\'evy process in this case. The case of bounded jumps yields a completely different behavior