upper bounds on wavepacket spreading for random jacobi matrices a method is presented for proving upper bounds on the moments of the position operator when the dynamics of quantum wavepackets is governed by a random possibly correlated jacobi matrix as an application one obtains sharp upper bounds on the diffusion exponents for random polymer models coinciding with the lower bounds obtained in a prior work the second application is an elementary argument not using multiscale analysis or the aizenman molchanov method showing that under the condition of uniformly positive lyapunov exponents the moments of the position operator grow at most logarithmically in time

necessary and sufficient graphical conditions for formation control of unicycles the feasibility problem is studied of achieving a specified formation among a group of autonomous unicycles by local distributed control the directed graph defined by the information flow plays a key role it is proved that formation stabilization to a point is feasible if and only if the sensor digraph has a globally reachable node a similar result is given for formation stabilization to a line and to more general geometric arrangements

the fibonacci hamiltonian we consider the fibonacci hamiltonian the central model in the study of electronic properties of one dimensional quasicrystals and establish relations between its spectrum and spectral characteristics namely the optimal holder exponent of the integrated density of states the dimension of the density of states measure the dimension of the spectrum and the upper transport exponent and the dynamical properties of the fibonacci trace map such as dimensional characteristics of the non wandering hyperbolic set and its measure of maximal entropy as well as other equilibrium measures topological entropy multipliers of periodic orbits we also exhibit a connection between the spectral quantities and the thermodynamic pressure function as a result a detailed description of the spectral properties for all values of the coupling constant is obtained in contrast to all previous quantitative results which could be established only in the regime of small or large coupling in particular we show that the spectrum of this operator is a dynamically defined cantor set and that the density of states measure is exact dimensional this implies that all standard fractal dimensions coincide in each case we show that all the gaps of the spectrum allowed by the gap labeling theorem are open for all values of the coupling constant also we establish strict inequalities between the four spectral characteristics in question and provide the exact large coupling asymptotics of the dimension of the density of states measure for the other three quantities the large coupling asymptotics were known before

eigenvalue spacings and dynamical upper bounds for discrete one dimensional schrodinger operators we prove dynamical upper bounds for discrete one dimensional schrodinger operators in terms of various spacing properties of the eigenvalues of finite volume approximations we demonstrate the applicability of our approach by a study of the fibonacci hamiltonian

formation tracking of the second order multi agent systems using position only information via impulsive control with input delays in this paper the formation tracking problem for the second order multi agent system with and without input delay are investigated respectively the objective is to design the formation tracking algorithm such that a certain follower follows the trajectory of the leader while also maintains a certain desired geometric formation with other agents simultaneously the impulsive algorithms are designed by using only the relative position information of the neighbors for both the cases with and without the input delay by using properties of the laplacian matrix and combining the stability theory of impulsive systems necessary and sufficient conditions are derived to achieve the formation tracking of the second order multi agent system with and without the input delay respectively the numerical examples are given to illustrate the effectiveness of our theoretical results

solutions spectrum and dynamics for schrodinger operators on infinite domains 1 introduction and main results in this paper we investigate the relations between the rate of decay of solutions of schrodinger equations continuity properties of spectral measures of the corresponding operators and dynamical properties of the corresponding quantum systems the first main result of this paper shows that in great generality certain upper bounds on the rate of growth of l 2 norms of generalized eigenfunctions over expanding balls imply certain minimal singularity of the spectral measures consider an operator h v defined by the differential expression h v v x

dynamical upper bounds on wavepacket spreading we derive a general upper bound on the spreading rate of wavepackets in the framework of schrodinger time evolution our result consists of showing that a portion of the wavepacket cannot escape outside a ball whose size grows dynamically in time where the rate of this growth is determined by properties of the spectral measure and by spatial properties of solutions of an associated time independent schrodinger equation we also derive a new lower bound on the spreading rate which is strongly connected with our upper bound we apply these new bounds to the fibonacci hamiltonian the most studied one dimensional model of quasicrystals as a result we obtain for this model upper and lower dynamical bounds establishing wavepacket spreading rates which are intermediate between ballistic transport and localization the bounds have the same qualitative behavior in the limit of large coupling

quantum dynamics via complex analysis methods general upper bounds without time averaging and tight lower bounds for the strongly coupled fibonacci hamiltonian abstract we develop further the approach to upper and lower bounds in quantum dynamics via complex analysis methods which was introduced by us in a sequence of earlier papers here we derive upper bounds for non time averaged outside probabilities and moments of the position operator from lower bounds for transfer matrices at complex energies moreover for the time averaged transport exponents we present improved lower bounds in the special case of the fibonacci hamiltonian these bounds lead to an optimal description of the time averaged spreading rate of the fast part of the wavepacket in the large coupling limit this provides the first example which demonstrates that the time averaged spreading rates may exceed the upper box counting dimension of the spectrum

brief paper synchronization in networks of identical linear systems the paper investigates the synchronization of a network of identical linear state space models under a possibly time varying and directed interconnection structure the main result is the construction of a dynamic output feedback coupling that achieves synchronization if the decoupled systems have no exponentially unstable mode and if the communication graph is uniformly connected the result can be interpreted as a generalization of classical consensus algorithms stronger conditions are shown to be sufficient but to some extent also necessary to ensure synchronization with the diffusive static output coupling often considered in the literature

fine structure of the zeros of orthogonal polynomials iv a priori bounds and clock behavior we prove locally uniform spacing for the zeros of orthogonal polynomials on the real line under weak conditions jacobi parameters approach the free ones and are of bounded variation we prove that for ergodic discrete schrodinger operators poisson behavior implies a positive lyapunov exponent both results depend on a priori bounds on eigenvalue spacings for which we provide several proofs

upper bounds in quantum dynamics of course the case of main interest is where h is given by l2 rd or 2 zd h is a schr dinger operator of the form a v and ip 0 is a localized wavepacket under the time evolution 1 the wavepacket i t will in general spread out with time finding quantitative bounds for this spreading in concrete cases and developing methods for proving such bounds has been the objective of a great number of papers in recent years one is often interested in the growth behavior of the moments of the position operator that is the function 11 x p 2 i 2 these questions are particularly complicated and interesting in situations where singular continuous spectra occur the discovery of the occurrence of such spectra for many models of physical relevance has triggered some activity on the quantum dynamical side for models with absolutely continuous spectra on the other hand quantum dynamical questions have been investigated much earlier in the context of scattering theory and have been answered to a great degree of satisfaction models with point spectrum or more restrictively models exhibiting anderson localization have also been investigated from a quantum dynamical point of view while it is not true in general that spectral localization implies dynamical localization 26 73 it has been shown that the three main approaches to spectral localization the fractional moment method 3 4 5 multi scale analysis 28 27 75 and the bourgain goldstein schlag method 12 37 yield dynamical localization as a by product 2 13 22 31 34 quantum dynamics for schr dinger operators with singular continuous spectra is much less understood the two primary examples motivated by physics are the harper model also known as the almost mathieu operator at critical cou pling which describes a bloch electron in a constant magnetic field with irrational flux through a unit cell and the fibonacci model which describes a standard one dimensional quasicrystal both models have been studied heavily in both the physics and mathematics communities

spectral and dynamical properties of certain random jacobi matrices with growing parameters in this paper a family of random jacobi matrices with off diagonal terms that exhibit power law growth is studied since the growth of the randomness is slower than that of these terms it is possible to use methods applied in the study of schr odinger operators with random decaying potentials a particular result of the analysis is the existence of operators with arbitrarily fast transport whose spectral measure is zero dimensional the results are applied to the infinite dumitriu edelman model 2002 and its spectral properties are analyzed

on the bundle of connections and the gauge orbit manifold in yang mills theory in an appropriate mathematical framework we supply a simple proof that the quotienting of the space of connections by the group of gauge transformations in yang mills theory is ac principal fibration the underlying quotient space the gauge orbit space is seen explicitly to be ac manifold modelled on a hilbert space

power law bounds on transfer matrices and quantum dynamics in one dimension we present an approach to quantum dynamical lower bounds for discrete one dimensional schrodinger operators which is based on power law bounds on transfer matrices it suffices to have such bounds for a nonempty set of energies we apply this result to various models including the fibonacci hamiltonian

distributed estimation for moving target based on state consensus strategy this technical note studies the distributed estimation problem for a continuous time moving target under switching interconnection topologies a recursive distributed estimation algorithm is proposed by using state consensus strategy where a common gain is assigned to adjust the innovative and state consensus information for each sensor in the network under mild conditions on observability and connectivity the stability of the distributed estimation algorithm is analyzed an upper bound and lower bound for the total mean square estimation error tmsee are obtained by virtue of the common lyapunov method and kalman bucy filtering theory respectively then a numerical simulation is given to verify the effectiveness of the proposed algorithm

brief paper a connection between formation infeasibility and velocity alignment in kinematic multi agent systems in this paper a feedback control strategy that achieves convergence of a multi agent system to a desired formation configuration is proposed for both the cases of agents with single integrator and nonholonomic unicycle type kinematics when inter agent objectives that specify the desired formation cannot occur simultaneously in the state space the desired formation is infeasible it is shown that under certain assumptions formation infeasibility forces the agents velocity vectors to a common value at steady state this provides a connection between formation infeasibility and flocking behavior for the multi agent system we finally also obtain an analytic expression of the common velocity vector in the case of formation infeasibility

formation control of mobile agents based on distributed position estimation we propose a formation control strategy based on distributed position estimation for single integrator modeled agents by using relative position measurements under the proposed strategy the estimated and the actual formations globally exponentially converge to the actual and the desired formations respectively up to translation if and only if the interaction graph for the agents has a spanning tree a sufficient condition is provided for the case that the edge weights of the interaction graph are time varying further the proposed strategy is applied to formation control of unicycle like agents

connections with l p bounds on curvature we show by means of the implicit function theorem that coulomb gauges exist for fields over a ball inr n when the integrall n 2 field norm is sufficiently small we then are able to prove a weak compactness theorem for fields on compact manifolds withl p integral norms bounded p n 2

non representability of cohomology classes by bi invariant forms gauge and kac moody groups we give a necessary topological condition on a cohomology class of any lie group modelled on a frechet space to be representable by a bi invariant form on as a corollary we show that if for somed 0 then there exists a cohomology class in which cannot be represented by any bi invariant form in particular we conclude that there are many cohomology generators in general in the case of gauge groups and also kac moody groups which cannot be represented by bi invariant forms although very often they are representable by left invariant forms

almost periodic schrodinger operators iii the absolutely continuous spectrum in one dimension we studyh d2 dx2 v x withv x limit periodic e g v x ancos x 2n with an we prove that for a genericv and for generican in the explicit example h is a cantor nowhere dense perfect set for a dense set the spectrum is both cantor and purely absolutely continuous and therefore purely recurrent absolutely continuous

absolutely continuous convolutions of singular measures and an application to the square fibonacci hamiltonian author s damanik d gorodetski a solomyak b abstract 2015 we prove for the square fibonacci hamiltonian that the density of states measure is absolutely continuous for almost all pairs of small coupling constants this is obtained from a new result we establish about the absolute continuity of convolutions of measures arising in hyperbolic dynamics with exact dimensional measures

fractal dimensions and the phenomenon of intermittency in quantum dynamics we exhibit an intermittency phenomenon in quantum dynamics more precisely we derive new lower bounds for the moments of order p associated to the state t e it h and averaged in time between zero and t these lower bounds are expressed in terms of generalized fractal dimensions d 1 1 p d of the measure where d is the space dimension this improves previous results obtained in terms of hausdorff and packing dimension

dynamical upper bounds for one dimensional quasicrystals abstract following the killip kiselev last method we prove quantum dynamical upper bounds for discrete one dimensional schrodinger operators with sturmian potentials these bounds hold for sufficiently large coupling almost every rotation number and every phase