Random Time-Dependent Quantum Walks

We consider the discrete time unitary dynamics given by a quantum walk on the lattice $\Z^d$ performed by a quantum particle with internal degree of freedom, called coin state, according to the following iterated rule: a unitary update of the coin state takes place, followed by a shift on the lattice, conditioned on the coin state of the particle. We study the large time behavior of the quantum mechanical probability distribution of the position observable in $\Z^d$ when the sequence of unitary updates is given by an i.i.d. sequence of random matrices. When averaged over the randomness, this distribution is shown to display a drift proportional to the time and its centered counterpart is shown to display a diffusive behavior with a diffusion matrix we compute. A moderate deviation principle is also proven to hold for the averaged distribution and the limit of the suitably rescaled corresponding characteristic function is shown to satisfy a diffusion equation. A generalization to unitary updates distributed according to a Markov process is also provided. An example of i.i.d. random updates for which the analysis of the distribution can be performed without averaging is worked out. The distribution also displays a deterministic drift proportional to time and its centered counterpart gives rise to a random diffusion matrix whose law we compute. A large deviation principle is shown to hold for this example. We finally show that, in general, the expectation of the random diffusion matrix equals the diffusion matrix of the averaged distribution.Comment: Typos and minor errors corrected. To appear In Communications in Mathematical Physic

Correlated Markov Quantum Walks

We consider the discrete time unitary dynamics given by a quantum walk on $\Z^d$ performed by a particle with internal degree of freedom, called coin state, according to the following iterated rule: a unitary update of the coin state takes place, followed by a shift on the lattice, conditioned on the coin state of the particle. We study the large time behavior of the quantum mechanical probability distribution of the position observable in $\Z^d$ for random updates of the coin states of the following form. The random sequences of unitary updates are given by a site dependent function of a Markov chain in time, with the following properties: on each site, they share the same stationnary Markovian distribution and, for each fixed time, they form a deterministic periodic pattern on the lattice. We prove a Feynman-Kac formula to express the characteristic function of the averaged distribution over the randomness at time $n$ in terms of the nth power of an operator $M$. By analyzing the spectrum of $M$, we show that this distribution posesses a drift proportional to the time and its centered counterpart displays a diffusive behavior with a diffusion matrix we compute. Moderate and large deviations principles are also proven to hold for the averaged distribution and the limit of the suitably rescaled corresponding characteristic function is shown to satisfy a diffusion equation. An example of random updates for which the analysis of the distribution can be performed without averaging is worked out. The random distribution displays a deterministic drift proportional to time and its centered counterpart gives rise to a random diffusion matrix whose law we compute. We complete the picture by presenting an uncorrelated example.Comment: 37 pages. arXiv admin note: substantial text overlap with arXiv:1010.400

The Plasma Membrane Calcium ATPases and Their Role as Major New Players in Human Disease.

The Ca2+ extrusion function of the four mammalian isoforms of the plasma membrane calcium ATPases (PMCAs) is well established. There is also ever-increasing detail known of their roles in global and local Ca2+ homeostasis and intracellular Ca2+ signaling in a wide variety of cell types and tissues. It is becoming clear that the spatiotemporal patterns of expression of the PMCAs and the fact that their abundances and relative expression levels vary from cell type to cell type both reflect and impact on their specific functions in these cells. Over recent years it has become increasingly apparent that these genes have potentially significant roles in human health and disease, with PMCAs1-4 being associated with cardiovascular diseases, deafness, autism, ataxia, adenoma, and malarial resistance. This review will bring together evidence of the variety of tissue-specific functions of PMCAs and will highlight the roles these genes play in regulating normal physiological functions and the considerable impact the genes have on human disease

A Two-Stage Model for Lipid Modulation of the Activity of Integral Membrane Proteins

Lipid-protein interactions play an essential role in the regulation of biological function of integral membrane proteins; however, the underlying molecular mechanisms are not fully understood. Here we explore the modulation by phospholipids of the enzymatic activity of the plasma membrane calcium pump reconstituted in detergent-phospholipid mixed micelles of variable composition. The presence of increasing quantities of phospholipids in the micelles produced a cooperative increase in the ATPase activity of the enzyme. This activation effect was reversible and depended on the phospholipid/detergent ratio and not on the total lipid concentration. Enzyme activation was accompanied by a small structural change at the transmembrane domain reported by 1-aniline-8-naphtalenesulfonate fluorescence. In addition, the composition of the amphipilic environment sensed by the protein was evaluated by measuring the relative affinity of the assayed phospholipid for the transmembrane surface of the protein. The obtained results allow us to postulate a two-stage mechanistic model explaining the modulation of protein activity based on the exchange among non-structural amphiphiles at the hydrophobic transmembrane surface, and a lipid-induced conformational change. The model allowed to obtain a cooperativity coefficient reporting on the efficiency of the transduction step between lipid adsorption and catalytic site activation. This model can be easily applied to other phospholipid/detergent mixtures as well to other membrane proteins. The systematic quantitative evaluation of these systems could contribute to gain insight into the structure-activity relationships between proteins and lipids in biological membranes

Spectroscopic analysis of halothane binding to the plasma membrane Ca2+-ATPase.

The intrinsic tryptophan (Trp) fluorescence of the plasma membrane Ca2+-ATPase (PMCA) is significantly quenched by halothane, a volatile anesthetic common in clinical practice. It has been proposed that halothane inhibition of the Ca2+-ATPase activity results from conformational changes following anesthetic binding in the enzyme. We have investigated whether the observed quenching reflects halothane binding to PMCA. We have shown that the quenching is dose dependent and saturable and can be fitted to a binding curve with an equilibrium constant K(Hal) = 2.1 mM, a concentration at which the anesthetic approximately half-maximally inhibits the Ca2+-ATPase activity. The relatively low sensitivity of halothane quenching of Trp fluorescence to the concentration of phosphatidylcholine and detergent in the PMCA preparation concurs with the quenching resulting from anesthetic binding in the PMCA molecule. Analysis of the Trp fluorescence quenching by acrylamide indicates that the Trp residues are not considerably exposed to the solvent (Stern-Volmer quenching constant of 2.9 M(-1)) and do not differ significantly in their accessibility to halothane. Other volatile anesthetics, diethyl ether and diisopropyl ether, reduce the quenching caused by halothane in a dose-dependent manner, suggesting halothane displacement from its binding site(s). These observations indicate that halothane quenching of intrinsic Trp fluorescence of PMCA results from anesthetic binding to the protein. The analysis, used as a complementary approach, provides new information to the still rudimentary understanding of the process of anesthetic interaction with membrane proteins

Growth and characterization of chalcopyrite nanocrystals beyond conventional thin films

A dry method for the growth of highly structured Cu containing chalcopyrite material on solid substrates, based on the use of metallic precursors, is described. Nanocrystals, sub micrometer polycrystalline dots, and macroscopic clusters have be grown, either as isolated units or alternatively as embedded structures in a matrix of a binary chalcogenide compound, by adjusting processing parameters. Vapor liquid solid VLS induced growth has been used for the growth of chalcopyrite nanowires. Examples of material characterization by scanning probe techniques are shown, demonstrating the suitability of the proposed growth metho

Mechanical properties of anodic aluminum oxide for MEMS applications

Aluminum oxide features good electrical properties such as high dielectric constant and high breakdown voltage. During these last years it has been introduced for the fabrication of metal oxide semiconductor and metal insulator metal capacitors. In the present paper, the mechanical properties of anodic Al2O3 are addressed as well as its interest for microelectromechanical system applications including membranes or cantilevers for humidity, flow, pressure, or biological sensors