singular kahler einstein metrics we study degenerate complex monge ampere equations of the form omega dd c f n e t f mu where omega is a big semi kahler form on a compact kahler manifold x of dimension n t in r and mu f omega n is a positive measure with density f in l p x omega n p 1 we prove the existence and unicity of continuous o plurisubharmonic solutions in case x is projective and omega psi omega where psi x to v is a proper birational morphism to a normal projective variety omega in ns r v is an ample class and mu has only algebraic singularities we prove that the solution is smooth in the regular locus of the equation we use these results to construct singular kahler einstein metrics of non positive curvature on projective klt pairs in particular on canonical models of algebraic varieties of general type

control design of uncertain quantum systems with fuzzy estimators an approach of control design using fuzzy estimators fes is proposed for quantum systems with uncertainties two types of quantum control problems are considered 1 control of a pure state quantum system in the presence of uncertainties and 2 control design of quantum systems with initial mixed states and uncertainties for the first type of tasks a partial feedback control scheme with an fe is presented to design controllers in this scheme an fe is trained to estimate the quantum state for feedback control of a quantum system and controlled projective measurement is used to assist in controlling the system for the second type of quantum control tasks a probabilistic fuzzy estimator pfe is trained to estimate the quantum state for control design of a quantum system with an initial mixed state and a corresponding control algorithm is proposed to design a control law that drives the system from the mixed state to a target pure state two examples of two spin 1 2 systems are also presented and analyzed to demonstrate the process of control design and potential applications of the proposed approach

identification of unknown parameters for a class of two level quantum systems this technical note studies the identification of unknown decoherence rates for a class of two level quantum systems undergoing spontaneous emission our previous work shows that estimates of the unknown decoherence rates can be obtained from the ensemble averages by imposing constant control and monitoring a sequence of identical systems continuously inspired by the work this technical note further investigates the identification based on a single quantum system it is shown that a mean ergodic solution exists for a single system under constant control and convergence to an ergodic process can be guaranteed by introducing some noise into the control signals the ensemble average can thus be replaced by the time average of a single system and the parameter estimate can be obtained from a single implementation

feedback control of quantum entanglement in a two spin system a pair of spins is the most simple quantum system that can exhibit entanglement a nonclassical property that plays an essential role in quantum information technologies in this paper feedback control problems of a symmetric two spin system conditioned on a continuous measurement are investigated in order to make some useful formulas in stochastic control theory directly applicable we first derive a two dimensional representation of the system we then prove that a feedback controller stabilizes an entangled state of the two spins almost globally with probability one furthermore it is demonstrated that some entangled states which correspond to nonequilibrium points of the dynamics are globally stabilized via feedback in the sense that the mean distance from a target can be reduced to an arbitrarily small value

stein compacts in levi flat hypersurfaces we explore connections between geometric properties of the levi foliation of a levi flat hypersurface m and holomorphic convexity of compact sets in m or bounded in part by m applications include extendability of cauchy riemann functions solvability of the b equation approximation of cauchy riemann and holomorphic functions and global regularity of the neumann operator

strong q convexity in uniform neighborhoods of subvarieties in coverings of complex spaces the main result is that for any projective compact analytic subset y of dimension q 0 in a reduced complex space x there is a neighborhood of y such that for any covering space upsilon colon widehat x to x in which widehat y equiv upsilon 1 y has no noncompact connected analytic subsets of pure dimension q with only compact irreducible components there exists a c exhaustion function varphi on widehat x which is strongly q convex on widehat omega upsilon 1 omega outside a uniform neighborhood of the q dimensional compact irreducible components of widehat y

hamiltonian control of quantum dynamical semigroups stabilization and convergence speed we consider finite dimensional markovian open quantum systems and characterize the extent to which time independent hamiltonian control may allow to stabilize a target quantum state or subspace and optimize the resulting convergence speed for a generic lindblad master equation we introduce a dissipation induced decomposition of the associated hilbert space and show how it serves both as a tool to analyze global stability properties for given control resources and as the starting point to synthesize controls that ensure rapid convergence the resulting design principles are illustrated in realistic markovian control settings motivated by quantum information processing including quantum optical systems and nitrogen vacancy centers in diamond

minimal surfaces in minimally convex domains in this paper we prove that every conformal minimal immersion of a compact bordered riemann surface m into a minimally convex domain d r can be approximated uniformly on compacts in m m bm by proper complete conformal minimal immersions m d see theorems 1 1 1 7 and 1 9 we also obtain a rigidity theorem for complete immersed minimal surfaces of finite total curvature contained in a minimally convex domain in r see theorem 1 16 and we characterize the minimal surface hull of a compact set k in r for any n 3 by sequences of conformal minimal disks whose boundaries converge to k in the measure theoretic sense see corollary 5 6

locally conformal finite difference time domain techniques for particle in cell plasma simulation the dey mittra s dey r mitra a locally conformal finite difference time domain fdtd algorithm for modeling three dimensional perfectly conducting objects ieee microwave guided wave lett 7 273 1997 finite difference time domain partial cell method enables the modeling of irregularly shaped conducting surfaces while retaining second order accuracy we present an algorithm to extend this method to include charged particle emission and absorption in particle in cell codes several examples are presented that illustrate the possible improvements that can be realized using the new algorithm for problems relevant to plasma simulation

engineering stable discrete time quantum dynamics via a canonical qr decomposition we analyze the asymptotic behavior of discrete time markovian quantum systems with respect to a subspace of interest global asymptotic stability of subspaces is relevant to quantum information processing in particular for initializing the system in pure states or subspace codes we provide a linear algebraic characterization of the dynamical properties leading to invariance and attractivity of a given quantum subspace we then construct a design algorithm for discrete time feedback control that allows to stabilize a target subspace proving that if the control problem is feasible then the algorithm returns an effective control choice in order to prove this result a canonical qr matrix decomposition is derived and also used to establish the control scheme potential for the simulation of open system dynamics

wei norman equations for a unitary evolution the wei norman technique allows one to express the solution of a system of linear non autonomous differential equations in terms of product of exponentials with time dependent exponents being solutions of a system of nonlinear differential equations we show that in the unitary case i e when the solution of the linear system is given by a unitary evolution operator the nonlinear system by an appropriate choice of ordering can be reduced to a hierarchy of matrix riccati equations to this end we consider a general linear non autonomous dynamical system on the special linear group the unitary case of particular significance for quantum optimal control problems is then obtained by restriction to anti hermitian generators we also point to the connections of the obtained results with the theory of the so called lie systems

sliding mode control of two level quantum systems this paper proposes a robust control method based on sliding mode design for two level quantum systems with bounded uncertainties an eigenstate of the two level quantum system is identified as a sliding mode the objective is to design a control law to steer the system s state into the sliding mode domain and then maintain it in that domain when bounded uncertainties exist in the system hamiltonian we propose a controller design method using the lyapunov methodology and periodic projective measurements in particular we give conditions for designing such a control law which can guarantee the desired robustness in the presence of the uncertainties the sliding mode control method has potential applications to quantum information processing with uncertainties

the embedded curved boundary method for orthogonal simulation meshes a method for incorporating piecewise linear approximations to curved boundaries is developed for codes using orthogonal meshes the resulting method retains much of the fidelity of adaptive triangle meshes in 2d while retaining essentially all of the speed of traditional methods relying on banded matrix solutions we find this technique useful for situations lying between the crude but fast stairstep approximation and the elegant but slower adaptive mesh techniques this method provides a practical approach to problems such as space charge emission while retaining the simplicity and run time advantage of orthogonal mesh based codes examples from space charge limited flow between curved electrodes are given

quantum markovian subsystems invariance attractivity and control we characterize the dynamical behavior of continuous time markovian quantum systems with respect to a subsystem of interest markovian dynamics describes a wide class of open quantum systems of relevance to quantum information processing subsystem encodings offering a general pathway to faithfully represent quantum information we provide explicit linear algebraic characterizations of the notion of invariant and noiseless subsystem for markovian master equations under different robustness assumptions for model parameter and initial state variations the stronger concept of an attractive quantum subsystem is introduced and sufficient existence conditions are identified based on lyapunov s stability techniques as a main control application we address the potential of output feedback markovian control strategies for quantum pure state stabilization and noiseless subspace generation in particular explicit results for the synthesis of stabilizing semigroups and noiseless subspaces in finite dimensional markovian systems are obtained

non smooth lyapunov function based global stabilization for quantum filters this paper addresses the global stabilization problem for a class of quantum filters via non smooth lyapunov functions due to the intrinsic symmetric topology of filter state space the smooth controls synthesized via the classical lyapunov stochastic stability theory fail to obtain the global stabilizability because of the existence of the so called antipodal eigenstates as such for the first time we introduce a non smooth lyapunov like theory for generic stochastic nonlinear systems which includes a continuous lyapunov like theorem and a discontinuous lyapunov like theorem for stability in probability applying the non smooth lyapunov like theory switching control and continuous control in saturation form are constructed for the quantum filters with consideration of the sliding motion of filter state the non smooth property enables these controls to deal with the symmetric topology of filter state space and to solve the problem of global stabilization for quantum filters the eigenstate transferring is obtained as a special result distinguishing these non smooth lyapunov based controls from classical control approaches for quantum filters the effectiveness of the non smooth lyapunov based controls is illustrated through the control design for the spin 1 2 systems simulation results are presented and discussed to show the effectiveness of the controls

some q convexity properties of coverings of complex manifolds let c be a nowhere dense compact analytic subset of a 2 dimensional complex manifold x a result of napier is the construction of a neighborhood v of c such that for any covering space open image in new window in which open image in new window is holomorphically convex there is a c exhaustion function on open image in new window which is strictly plurisubharmonic on 1 v away from the compact irreducible components of open image in new window col oiu and v j itu obtained a q convex version of this result for c a q dimensional fiber of a proper surjective submersion x y the goal of this paper is a similar version for cprojective

brief paper discrete time controllability for feedback quantum dynamics controllability properties for discrete time markovian quantum dynamics are investigated we find that while in general the controlled system is not finite time controllable feedback control allows for arbitrary asymptotic state to state transitions under further assumptions on the form of the measurement we show that finite time controllability can be achieved in a time that is twice the dimension of the system and we provide an iterative procedure to design the unitary control actions

stabilizing quantum states by constructive design of open quantum dynamics based on recent work on the asymptotic behavior of controlled quantum markovian dynamics we show that any generic quantum state can be stabilized by devising constructively a simple lindblad gks generator that can achieve global asymptotic stability at the desired state the applicability of such result is demonstrated by designing a direct feedback strategy that achieves global stabilization of a qubit state encoded in a noise protected subspace

quantum measurement based feedback control a nonsmooth time delay control approach this paper addresses the problem of measurement based feedback control for quantum systems in which the time to compute the filter based control input is taken into account by considering the input delay it starts with a new lyapunov lasalle like theorem for delay dependent stochastic stability of a class of time delay stochastic nonlinear systems nonsmooth time delay control is then constructed to compensate for the control computation time which is known but arbitrarily long while globally stabilizing the quantum filters almost surely the nonsmooth property enables the control to deal with the symmetric topology of filter state space the effectiveness of the proposed control is illustrated through the global stabilization of the spin 1 2 systems simulation results are presented and discussed to show the effectiveness of the proposed control

ground state stabilization of quantum finite level systems by dissipation control by dissipation or environment engineering constitutes an important methodology within quantum coherent control which was proposed to improve the robustness and scalability of quantum control systems the system environment coupling often considered to be detrimental to quantum coherence also provides the means to steer the system to desired states this paper aims to develop the theory for engineering of the dissipation based on a ground state lyapunov stability analysis of open quantum systems via a heisenberg picture approach in particular lyapunov stability conditions expressed as operator inequalities allow a purely algebraic treatment of the environment engineering problem which facilitates the integration of quantum components into a large scale quantum system and draws an explicit connection to the classical theory of vector lyapunov functions and decomposition aggregation methods for control of complex systems this leads to tractable algebraic conditions concerning the ground state stability and scalability of quantum systems the implications of the results in relation to dissipative quantum computing and state engineering are also discussed in this paper

representation and network synthesis for a class of mixed quantum classical linear stochastic systems the purpose of this paper is to present a network realization theory for a class of mixed quantum classical linear stochastic systems two forms the standard form and the general form of this class of linear mixed quantum classical systems are proposed necessary and sufficient conditions for their physical realizability are derived based on these physical realizability conditions a network synthesis theory for this class of linear mixed quantum classical systems is developed which clearly exhibits the quantum component the classical component and their interface an example is used to illustrate the theory presented in this paper

controllability properties for finite dimensional quantum markovian master equations various notions from geometric control theory are used to characterize the behavior of the markovian master equation for n level quantum mechanical systems driven by unitary control and to describe the structure of the sets of reachable states it is shown that the system can be accessible but neither small time controllable nor controllable in finite time in particular if the generators of quantum dynamical semigroups are unital then the reachable sets admit easy characterizations as they monotonically grow in time the two level case is treated in detail

decoherence free linear quantum subsystems this paper provides a general theory for characterizing and constructing a decoherence free df subsystem for an infinite dimensional linear open quantum system the main idea is that based on the heisenberg picture of the dynamics rather than the commonly taken schrodinger picture the notions of controllability and observability in control theory are employed to characterize a df subsystem a particularly useful result is a general if and only if condition for a linear system to have a df component this condition is used to demonstrate how to actually construct a df dynamics in some specific examples it is also shown that as in the finite dimensional case we are able to do coherent manipulation and preservation of a state of a df subsystem

more explicit formulas for the matrix exponential abstract the matrix exponential plays an important role in the study of dynamical systems and linear systems an elementary method is discussed for computing eta for general a c n n it is shown that this method can be applied to generate explicit formulas for eta in various forms using this method some well known formulas are rederived and some new formulas are also derived as applications explicit formulas for n 3 or n 4 are given in each case a characterization of eta is also made based on the entries of a alone

decompositions of hilbert spaces stability analysis and convergence probabilities for discrete time quantum dynamical semigroups we investigate convergence properties of discrete time semigroup quantum dynamics including asymptotic stability probability and speed of convergence to pure states and subspaces these properties are of interest in both the analysis of uncontrolled evolutions and the engineering of controlled dynamics for quantum information processing our results include two hilbert space decompositions that allow for deciding the stability of the subspace of interest and for estimating of the speed of convergence as well as a formula to obtain the limit probability distribution for a set of orthogonal invariant subspaces

on the integrability of systems of nonlinear ordinary differential equations with superposition principles a new class of solvable nonlinear dynamical systems has been recently identified by the requirement that the ordinary differential equations ode s describing each member of this class possess nonlinear superposition principles these systems of ode s are generally not derived from a hamiltonian and are classified by associated pairs of lie algebras of vector fields in this paper all such systems of n 3 ode s are integrated in a unified way by finding explicit integrals for them and relating them all to a pivotal member of their class the projective riccati equations moreover by perturbing two parametrically driven projective riccati equations thus making them nonsolvable in the above sense evidence is discovered of chaotic behavior on the poincare surface of section in the form of sensitive dependence on initial conditions near a boundary separating bounded from unbounded motion

adaptive resummation of markovian quantum dynamics in this thesis we derive a highly convergent nonperturbative expansion of markovian open quantum dynamics it is based on a splitting of the incoherent dynamics into periods of continuous evolution and abrupt jumps and attains its favorable convergence properties from an adaptive resummation of this so called jump expansion by means of the long standing problems of spatial particle detection and landau zener tunneling in the presence of dephasing we show that this adaptive resummation technique facilitates new highly accurate analytic approximations of markovian open systems the open landau zener model leads us to propose an efficient and robust incoherent control technique for the isomerization reaction of the visual pigment protein rhodopsin besides leading to approximate analytic descriptions of markovian open quantum dynamics the adaptive resummation of the jump expansion implies an efficient numerical simulation method we spell out the corresponding numerical algorithm by means of monte carlo integration of the relevant terms in the jump expansion and demonstrate it in a set of paradigmatic open quantum systems

analysis and synthesis of attractive quantum markovian dynamics we propose a general framework for investigating a large class of stabilization problems in markovian quantum systems building on the notions of invariant and attractive quantum subsystem we characterize attractive subspaces by exploring the structure of the invariant sets for the dynamics our general analysis results are exploited to assess the ability of open loop hamiltonian and output feedback control strategies to synthesize markovian generators which stabilize a target subsystem subspace or pure state in particular we provide an algebraic characterization of the manifold of stabilizable pure states in arbitrary finite dimensional markovian systems that leads to a constructive strategy for designing the relevant controllers implications for stabilization of entangled pure states are addressed by example

cohomology of q convex spaces in top degrees it is shown that every strongly q complete subvariety of a complex analytic space has a fundamental system of strongly q complete neighborhoods as a consequence we find a simple proof of ohsawa s result that every non compact irreducible n dimensional analytic space is strongly n complete finally it is shown that l cohomology theory readily implies ohsawa s hodge decomposition and lefschetz isomorphism theorems for absolutely q convex manifolds

algorithms for interpolation and localization in irregular 2d meshes abstract in numerical simulations of power systems discrete models and mesh free models are very often used simultaneously for example in particle in cell pic codes the aim of this paper is to introduce new techniques for interpolation as well as for localization in irregular fourpoint meshes these algorithms extend the existing methods for regular grids to grids consisting of non equidistant convex four point meshes they were developed in order to obtain short cpu times and possible vectorization

modeling and control of quantum systems an introduction the scope of this work is to provide a self contained introduction to a selection of basic theoretical aspects in the modeling and control of quantum mechanical systems as well as a brief survey on the main approaches to control synthesis while part of the existing theory especially in the open loop setting stems directly from classical control theory most notably geometric control and optimal control a number of tools specifically tailored for quantum systems have been developed since the 1980s in order to take into account their distinctive features the probabilistic nature of atomic scale physical systems the effect of dissipation and the irreversible character of the measurements have all proved to be critical in feedback design problems the relevant dynamical models for both closed and open quantum systems are presented along with the main results on their controllability and stability a brief review of several currently available control design methods is meant to provide the interested reader with a roadmap for further studies

on the solution of the riccati equation by the taylor matrix method in this paper we suggest a matrix method to solve the riccati differential equation in terms of taylor polynomials this method is based on first taking the truncated taylor series of the function in equations and then substituting their matrix forms into the given equation hence the result matrix equation can be solved and the unknown taylor coefficients can be found approximately the solution is calculated in the form of a series with easily computable components the numerical results show the effectiveness of the method for this type of equation comparing the methodology with some known techniques shows that the present approach is relatively easy and highly accurate

tame sets dominating maps and complex tori a discrete subset of c n is said to be tame if there is an automorphism of c n taking the given discrete subset to a subset of a complex line such tame sets are known to allow interpolation by automorphisms we give here a fairly general sufficient condition for a discrete set to be tame in a related direction we show that for certain discrete sets in c n there is an injective holomorphic map from c n into itself whose image avoids an e neighborhood of the discrete set among other things this is used to show that given any complex n torus and any finite set in this torus there exist an open set containing the finite set and a locally biholomorphic map from c n into the complement of this open set

on realization theory of quantum linear systems the purpose of this paper is to study the realization theory of quantum linear systems it is shown that for a general quantum linear system its controllability and observability are equivalent and they can be checked by means of a simple matrix rank condition based on controllability and observability a specific realization is proposed for general quantum linear systems in which an uncontrollable and unobservable subspace is identified when restricted to the passive case it is found that a realization is minimal if and only if it is hurwitz stable computational methods are proposed to find the cardinality of minimal realizations of a quantum linear passive system it is found that the transfer function g s of a quantum linear passive system can be written as a fractional form in terms of a matrix function s moreover g s is lossless bounded real if and only if s is lossless positive real a type of realization for multi input multi output quantum linear passive systems is derived which is related to its controllability and observability decomposition two realizations namely the independent oscillator realization and the chain mode realization are proposed for single input single output quantum linear passive systems and it is shown that under the assumption of minimal realization the independent oscillator realization is unique and these two realizations are related to the lossless positive real matrix function s

the hartogs extension theorem on n 1 complete complex spaces employing morse theory for the global control of monodromy and the method of analytic discs for local extension we establish a version of the global hartogs extension theorem in a singular setting for every domain d of an n 1 complete normal complex space x of pure dimension n 2 and for every compact set k in d such that d k is connected holomorphic or meromorphic functions in d k extend holomorphically or meromorphically to d normality is an unvavoidable assumption for holomorphic extension but we show that meromorphic extension holds on a reduced globally irreducible not necessarily normal x of pure dimension n 2 provided that the regular part of d k is connected

high gain observer for a class of non triangular systems this paper presents a high gain observer for a class of mimo nonlinear systems involving some uncertainties the latter is particularly composed of cascade subsystems where each subsystem is associated with a subset of the output variables and assumes a triangular dependence on its own state variables and may depend on the state variables of all other subsystems the main contribution consists in extending the available results to allow more interconnections between the subsystems of fundamental interest it is shown that the underlying observation error exponentially converges to zero in the absence of uncertainties moreover the observation error can be made as small as desired by properly specifying the observer design parameter in the case where uncertainties are considered

algebraic solution of the lindblad equation for a collection of multilevel systems coupled to independent environments we consider the lindblad equation for a collection of multilevel systems coupled to independent environments the equation is symmetric under the exchange of the labels associated with each system and thus the open system dynamics takes place in the permutation symmetric subspace of the operator space the dimension of this space grows polynomially with the number of systems we construct a basis of this space and a set of superoperators whose action on this basis is easily specified for a given number of levels m these superoperators are written in terms of a bosonic realization of the generators of the lie algebra in some cases these results enable finding an analytic solution of the master equation using known lie algebraic methods to demonstrate this we obtain an analytic expression for the state operator of a collection of three level atoms coupled to independent radiation baths when analytic solutions are difficult to find the basis and the superoperators can be used to considerably reduce the computational resources required for simulations

robust procedures for converting among lindblad kraus and matrix representations of quantum dynamical semigroups given a quantum dynamical semigroup expressed as an exponential superoperator acting on a space of n dimensional density operators eigenvalue methods are presented by which canonical kraus and lindblad operator sum representations can be computed these methods provide a mathematical basis on which to develop novel algorithms for quantum process tomography the statistical estimation of superoperators and their generators from a wide variety of experimental data theoretical arguments and numerical simulations are presented which imply that these algorithms will be quite robust in the presence of random errors in the data

a relative oka grauert principle for holomorphic submersions over 1 convex spaces this paper presents the proof of the relative oka grauert principle for holomorphic submersions over 1 convex spaces using conic neighbourhoods of holomorphic sections over 1 convex spaces a proof of a version of cartan s theorem a for 1 convex spaces is also given

feedback control of quantum state reduction feedback control of quantum mechanical systems must take into account the probabilistic nature of quantum measurement we formulate quantum feedback control as a problem of stochastic nonlinear control by considering separately a quantum filtering problem and a state feedback control problem for the filter we explore the use of stochastic lyapunov techniques for the design of feedback controllers for quantum spin systems and demonstrate the possibility of stabilizing one outcome of a quantum measurement with unit probability

structural decomposition for quantum two level systems an input output model of a two level quantum system in the heisenberg picture is of bilinear form with constant system matrices which allows the introduction of the concepts of controllability and observability in analogy with those of quantum linear systems by means of the notions of controllability and observability coordinate transformations which are rotation matrices can be constructed explicitly that transform an input output model to a new one the new input output model enables us to investigate many interesting properties of the two level quantum system such as steady state solutions to the lindblad master equation quantum decoherence free df subspaces quantum non demolition qnd variables and the realization of quantum back action evading bae measurements the physical system in wang and wiseman 2001 is re studied to illustrate the results presented in this paper

sur la l 2 cohomologie des varietes a courbure negative we give a topological interpretation of the space of l2 harmonic forms on finite volume manifolds with sufficiently pinched negative curvature we give examples showing that this interpretation fails if the curvature is not sufficiently pinched and that our result is sharp with respect to the pinching constants the method consists first in comparing l2 cohomology with weighted l2 cohomology thanks to previuos works done by t ohsawa and then in identifying these weighted spaces

stabilization of stochastic quantum dynamics via open and closed loop control in this paper we investigate parametrization free solutions of the problem of quantum pure state preparation and subspace stabilization by means of hamiltonian control continuous measurement and quantum feedback in the presence of a markovian environment in particular we show that whenever suitable dissipative effects are induced either by the unmonitored environment or by non hermitian measurements there is no need for feedback as open loop time invariant control is sufficient to achieve stabilization of the target set in probability constructive necessary and sufficient conditions on the form of the control hamiltonian can be provided in this case when time invariant control is not sufficient state stabilization can be attained by the addition of filtering based feedback control

plurisubharmonic functions in calibrated geometry and q convexity let m be a kahler manifold an integrable function varphi on m is called q plurisubharmonic if the current dd c varphi wedge omega q 1 is positive we prove that varphi is q plurisubharmonic if and only if varphi is subharmonic on all q dimensional complex subvarieties we prove that a q plurisubharmonic function is q convex and admits a local approximation by smooth q plurisubharmonic functions for any closed subvariety z subset m dim mathbb c z leq q 1 there exists a strictly q plurisubharmonic function in a neighbourhood of z this result is known for q convex functions this theorem is used to give a new proof of sibony s lemma on integrability of positive closed p p forms which are integrable outside of a complex subvariety of codimension p 1

notes on sliding mode control of two level quantum systems in dong d and petersen i r 2012 sliding mode control of two level quantum systems automatica 48 725 735 a sliding mode control approach has been proposed for two level quantum systems to deal with bounded uncertainties in the system hamiltonian this paper further extends these results in two directions one extension is to consider the effect of uncertainties during the process of driving the system s state back to the sliding mode domain from outside and we propose two approaches to accomplish this control task the other extension generalizes the previous design approach to consider uncertainties described as perturbations in the free hamiltonian

generic pure quantum states as steady states of quasi local dissipative dynamics we investigate whether a generic pure state on a multipartite quantum system can be the unique asymptotic steady state of locality constrained purely dissipative markovian dynamics in the tripartite setting we show that the problem is equivalent to characterizing the solution space of a set of linear equations and establish that the set of pure states obeying the above property has either measure zero or measure one solely depending on the subsystems dimension a complete analytical characterization is given when the central subsystem is a qubit in the n partite case we provide conditions on the subsystems size and the nature of the locality constraint under which random pure states cannot be quasi locally stabilized generically also allowing for the possibility to approximately stabilize entangled pure states that cannot be exact steady states in settings where stabilizability is generic our results offer insights into the extent to which random pure states may arise as unique ground states of frustration free parent hamiltonians we further argue that to a high probability pure quantum states sampled from a t design enjoy the same stabilizability properties of haar random ones as long as suitable dimension constraints are obeyed and t is sufficiently large lastly we demonstrate a connection between the tasks of quasi local state stabilization and unique state reconstruction from local tomographic information and provide a constructive procedure for determining a generic n partite pure state based only on knowledge of the support of any two of the reduced density matrices of about half the parties improving over existing results

slanted conducting boundaries and field emission of particles in an electromagnetic particle simulation code abstract a method to handle slanted perfectly conducting boundaries in electromagnetic particle simulation codes is described modifications to standard algorithms for the electromagnetic field advance charge and current densities particle destruction and field averaging are discussed in addition a new model for field emission from conducting boundary surfaces is described particles can be emitted from conformal or slanted surfaces and also from certain types of corners results of the new models on several problems involving slanted surfaces are presented

holomorphic flexibility properties of complex manifolds we obtain results on approximation of holomorphic maps by algebraic maps the jet transversality theorem for holomorphic and algebraic maps between certain classes of manifolds and the homotopy principle for holomorphic submersions of stein manifolds to certain algebraic manifolds

a transcendental approach to kollar s injectivity theorem ii we treat kollar s injectivity theorem from the analytic or differential geometric viewpoint more precisely we give a curvature condition which implies kollar type cohomology injectivity theorems our main theorem is formulated for a compact kahler manifold but the proof uses the space of harmonic forms on a zariski open set with a suitable complete kahler metric we need neither covering tricks desingularizations nor leray s spectral sequence

rapid lyapunov control of finite dimensional quantum systems abstract rapid state control of quantum systems is significant in reducing the influence of relaxation or decoherence caused by the environment and enhancing the capability in dealing with uncertainties in the model and control process bang bang lyapunov control can speed up the control process but cannot guarantee convergence to a target state this paper proposes two classes of new lyapunov control methods that can achieve rapidly convergent control for quantum states one class is switching lyapunov control where the control law is designed by switching between bang bang lyapunov control and standard lyapunov control the other class is approximate bang bang lyapunov control where we propose two special control functions which are continuously differentiable and yet have a bang bang type property related stability results are given and a construction method for the degrees of freedom in the lyapunov function is presented to guarantee rapid convergence to a target eigenstate being isolated in the invariant set several numerical examples demonstrate that the proposed methods can achieve improved performance for rapid state control of quantum systems

an exponential quantum projection filter for open quantum systems an approximate exponential quantum projection filtering scheme is developed for a class of open quantum systems described by hudson parthasarathy quantum stochastic differential equations aiming to reduce the computational burden associated with online calculation of the quantum filter by using a differential geometric approach the quantum trajectory is constrained in a finite dimensional differentiable manifold consisting of an unnormalized exponential family of quantum density operators and an exponential quantum projection filter is then formulated as a number of stochastic differential equations satisfied by the finite dimensional coordinate system of this manifold a convenient design of the differentiable manifold is also presented through reduction of the local approximation errors which yields a simplification of the quantum projection filter equations it is shown that the computational cost can be significantly reduced by using the quantum projection filter instead of the quantum filter it is also shown that when the quantum projection filtering approach is applied to a class of open quantum systems that asymptotically converge to a pure state the input to state stability of the corresponding exponential quantum projection filter can be established simulation results from an atomic ensemble system example are provided to illustrate the performance of the projection filtering scheme it is expected that the proposed approach can be used in developing more efficient quantum control methods