Diagonal Riccati Stability and Applications

We consider the question of diagonal Riccati stability for a pair of real matrices A, B. A necessary and sufficient condition for diagonal Riccati stability is derived and applications of this to two distinct cases are presented. We also describe some motivations for this question arising in the theory of generalised Lotka-Volterra systems

Spin noise of itinerant fermions

We develop a theory of spin noise spectroscopy of itinerant, noninteracting, spin-carrying fermions in different regimes of temperature and disorder. We use kinetic equations for the density matrix in spin variables. We find a general result with a clear physical interpretation, and discuss its dependence on temperature, the size of the system, and applied magnetic field. We consider two classes of experimental probes: 1. electron-spin-resonance (ESR)-type measurements, in which the probe response to a uniform magnetization increases linearly with the volume sampled, and 2. optical Kerr/Faraday rotation-type measurements, in which the probe response to a uniform magnetization increases linearly with the length of the light propagation in the sample, but is independent of the cross section of the light beam. Our theory provides a framework for interpreting recent experiments on atomic gases and conduction electrons in semiconductors and provides a baseline for identifying the effects of interactions on spin noise spectroscopy

Analysis of a hadron beam in five-dimensional phase space

We conduct a detailed measurement and analysis of a hadron beam in five-dimensional phase space at the Spallation Neutron Source Beam Test Facility. The measurement's resolution and dynamic range are sufficient to image sharp, high-dimensional features in low-density regions of phase space. To facilitate the complex task of feature identification in the five-dimensional phase space, we develop several analysis and visualization techniques, including non-planar slicing. We use these techniques to examine the transverse dependence of longitudinal hollowing and longitudinal dependence of transverse hollowing in the distribution. This analysis strengthens the claim that low-dimensional projections do not adequately characterize high-dimensional phase space distributions in low-energy hadron acceleratorsComment: 13 pages; 15 figures; submitted to Physical Review Accelerators and Beams (PRAB

Noise spectroscopy and interlayer phase-coherence in bilayer quantum Hall systems

Bilayer quantum Hall systems develop strong interlayer phase-coherence when the distance between layers is comparable to the typical distance between electrons within a layer. The phase-coherent state has until now been investigated primarily via transport measurements. We argue here that interlayer current and charge-imbalance noise studies in these systems will be able to address some of the key experimental questions. We show that the characteristic frequency of current-noise is that of the zero wavevector collective mode, which is sensitive to the degree of order in the system. Local electric potential noise measured in a plane above the bilayer system on the other hand is sensitive to finite-wavevector collective modes and hence to the soft-magnetoroton picture of the order-disorder phase transition.Comment: 5 pages, 2 figure

On analysis of Persidskii systems and their implementations using LMIs

International audienceThe conditions of (integral) input-to-state stability and input-output-to-state stability are established for a class of generalized Persidskii systems. The proposed conditions are formulated using linear matrix inequalities. Based on these results the conditions of convergence are derived for discretizations of this class of models obtained by the explicit and the implicit Euler methods. The proposed theory is finally applied to design a robust stabilization control

Averaging method for the stability analysis of strongly nonlinear mechanical systems

International audienceA mechanical system under strongly nonlinear potential and dissipative forces, with nonlinear nonstationary perturbations having zero mean values, is studied. Proposing a special construction of Lyapunov function, the conditions are found, under which the perturbations do not influence the asymptotic stability of the trivial equilibrium position of the system. These conditions include the requirements on asymptotic stability of the disturbance-free system and the relations of the nonlinearity orders between potential and dissipative forces. The developed approach is extended to the problem of monoaxial stabilization of a rigid body

Progress toward the P\mathcal{P}, T\mathcal{T}-odd Faraday effect: Light absorption by atoms briefly interacting with a laser beam

We investigate the process of photon absorption by atoms or molecules shortly interacting with a laser beam in the dipole approximation. Assuming that the interaction time $\tau$ is much smaller than the lifetime of the corresponding excited state, we examine the absorption probability as a function of $\tau$. Besides, we incorporate Doppler broadening due to nonzero temperature of the atoms (molecules). It is demonstrated that in the case of a zero detuning and without Doppler broadening, the absorption probability is quadratic in $\tau$. Once Doppler broadening is taken into account or the laser beam is off from the resonant frequency, the absorption probability becomes linear in $\tau$. Our findings are expected to be important for experimental studies in optical cells or cavities where atoms or molecules traverse continuous laser beams. The experimental prospects of searching for the electric dipole moment (EDM) of the electron are discussed in detail

Design of Finite/Fixed-time ISS-Lyapunov Functions for Mechanical Systems

Submitted to Mathematics of Control, Signals, and SystemsInternational audienceFor a canonical form of mechanical system dened through gradients of potential energy and dissipative terms, the conditions of nite-time and xed-time (integral) input-to-state stability are derived by nding suitable Lyapunov functions. The proposed stability conditions are constructive, which is demonstrated in several applications

Discretization of Homogeneous Systems Using Euler Method with a State-Dependent Step

International audienceNumeric approximations to the solutions of asymptotically stable homogeneous systems by Euler method, with a step of discretization scaled by the state norm, are investigated (for the explicit and implicit integration schemes). It is proven that for a sufficiently small discretization step the convergence of the approximating solutions to zero can be guaranteed globally in a finite or a fixed time depending on the degree of homogeneity of the system, but in an infinite number of discretization iterations. The maximal admissible step can be estimated by analyzing the system properties on the sphere. It is shown that the absolute and relative errors of the discretizations are globally bounded functions, thus the approximations approaching the solutions with the step converging to zero. In addition, it is established that the proposed discretization approach preserves robustness with respect to exogenous perturbations. Efficiency of the designed discretization algorithms is demonstrated in simulations