non markovian quantum feedback networks ii controlled flows the concept of a controlled flow of a dynamical system especially when the controlling process feeds information back about the system is of central importance in control engineering in this paper we build on the ideas presented by bouten and van handel quantum stochastics and information statistics filtering and control world scientific 2008 and develop a general theory of quantum feedback we elucidate the relationship between the controlling processes z and the measured processes y and to this end we make a distinction between what we call the input picture and the output picture we should note that the input output relations for the noise fields have additional terms not present in the standard theory but that the relationship between the control processes and measured processes themselves is internally consistent we do this for the two main cases of quadrature measurement and photon counting measurement the theory is general enough to include a modulating filter which post processes

analysis of the annular ring loaded circular disk microstrip antenna a rigorous analysis of the natural resonance frequencies and input impedance characteristics of an annular ring loaded arl circular disk microstrip antenna is presented using vector hankel transforms the problem is formulated in terms of vector dual integral equations galerkin s method is then used to solve the equations to obtain the resonance frequencies and the current distribution on the conductive patches arising from a probe excitation due to the singular nature of the current distribution the singularity subtraction method has been used to accelerate the convergence of basis function expansions experiments for determining resonance frequencies and input impedance characteristics of an arl circular disk microstrip antenna with various substrate thicknesses have been made the theoretical results are in good agreement with the experimental data even when the thickness of the substrate is 0 1 substrate wavelength it is shown that this theory can be used to analyze some microstrip antennas with an electrically thick substrate including the analysis of mutual coupling between conductive patches or between the path and the feed of a microstrip antenna

transfer function approach to quantum control part i dynamics of quantum feedback systems this paper gives a unified approach to feedback control theory of quantum mechanical systems of bosonic modes described by noncommutative operators a quantum optical closed loop including a plant and controller is developed and its fundamental structural properties are analyzed extensively from a purely quantum mechanical point of view in order to facilitate the use of control theory in microscopic world described by quantum theory in particular an input output description of quantum mechanical systems which is essential in describing the behavior of the feedback systems is fully formulated and developed this would then provide a powerful tool for quantum control and pave an avenue that connects control theory to quantum dynamics this paper is divided into two parts the first part is devoted to the basic formulation of quantum feedback control via quantum communication and local operations on an optical device cavity that can be regarded as a unit of quantum dynamics of bosonic modes the formulation introduced in this paper presents the feature intrinsic in quantum feedback systems based on quantum stochastic differential equations the input output description provides a basis for developing quantum feedback control through the transfer function representation of quantum feedback systems in the follow up paper the quantum mechanical representation of feedback is further elaborated to yield the control theoretical representation of fundamental notions of quantum theory uncertainty principle e g and some applications are presented

quantum feedback networks hamiltonian formulation a quantum network is an open system consisting of several component markovian input output subsystems interconnected by boson field channels carrying quantum stochastic signals generalizing the work of chebotarev and gregoratti we formulate the model description by prescribing a candidate hamiltonian for the network including details of the component systems the field channels their interconnections interactions and any time delays arising from the geometry of the network we show that the candidate is a symmetric operator and proceed modulo the proof of self adjointness the model is non markovian for finite time delays but in the limit where these delays vanish we recover a markov model and thereby deduce the rules for introducing feedback into arbitrary quantum networks the type of feedback considered includes that mediated by the use of beam splitters we are therefore able to give a system theoretic approach to introducing connections between quantum mechanical state based input output systems and give a unifying treatment using non commutative fractional linear or mobius transformations

non markovian quantum feedback networks i quantum transmission lines lossless bounded real property and limit markovian channels the purpose of this paper is to set out the problems of modeling quantum communication and signal processing where the communication between systems is via a non markovian channel this is a general feature of quantum transmission lines our ultimate objective is to extend the network rules that have been developed for markovian models to this end we recall the hamiltonian description of such non markov models of transmission lines and their quantization these have occurred in the context of non equilibrium thermodynamics but our interest is in the transmission lines as carriers of information rather than heat baths we show that there is an analytic scattering matrix associated with these models and that stability may be formulated in terms of the lossless bounded real property noting that the input and output fields do not separately satisfy a non self demolition principle we discuss the rigorous limit in which such models appear markov and so amenable to standard approaches of quantum filtering an

analysis of a plane wave excited subwavelength circular aperture in a planar conducting screen illuminating a multilayer uniaxial sample a spectral domain analysis is presented of a plane wave excited subwavelength circular aperture in a planar perfectly conducting screen in close proximity to a multilayer stack which may comprise uniaxially anisotropic slices the formulation employs the bethe bouwkamp aperture model for the general case of oblique incidence and it combines the hankel transform method with a transmission line network analogue of the medium which facilitates the inclusion of any number of material layers the electromagnetic fields are expressed in terms of one dimensional 1 d hankel transform integrals which are efficiently evaluated by a numerical quadrature along a suitably selected path with convergence acceleration by extrapolation sample numerical results are presented to demonstrate the validity of the method and its utility in the modeling of multilayer near field lenses and aperture type probes of near field optical microscopy

the hamiltonian operator associated with some quantum stochastic evolutions we consider the hamiltonian operator associated to the quantum stochastic differential equation introduced by hudson and parthasarathy to describe a quantum mechanical evolution in the presence of a quantum noise we characterize such a hamiltonian in the case of arbitrary multiplicity and bounded coefficients we find an essentially self adjoint restriction of the operator and in particular we provide an explicit construction of a dense set of vectors belonging to its domain

asymptotic green s function of a surface magnetic current element on a perfect electric conductor plane covered by a lossy dielectric substrate published analyses of radiation modeling for slot structures on dielectric substrate are empirical or numerical this paper proposes exact analytical asymptotic expressions of the far field green s functions of a surface magnetic current element on a perfect electric conductor plane covered by a lossy dielectric substrate of finite thickness from these expressions the radiation pattern of both the space wave and surface wave far away from an arbitrary shaped slot antenna structure can be calculated provided the source distribution across the slot is known the potentials used in the analysis are defined and their boundary conditions are expressed the helmholtz equation is solved in the laplace domain and the solutions are transformed into the space domain using the inverse hankel transform and steepest descent method the influences of the substrate thickness and dielectric constant are analyzed using the calculated expressions the model is validated by comparison with surface wave and space wave measurements and with numerical results obtained from a commercial electromagnetic simulator

hankel transform domain analysis of open circular microstrip radiating structures a full wave analysis of a circular disk conductor printed on a dielectric substrate backed by a ground plane is presented the method is based on the galerkin s method applied in the hankel transform domain and is numerically quite efficient several numerical examples are compared with available experimental data the agreement is found to be quite good and the validity of the present method is confirmed

an annular slot antenna on a dielectric half space the radiation properties of both singly and multiply fed annular slot antennas on a dielectric air interface have been analyzed using galerkin s method applied in the hankel transform domain the validity of our method has been confirmed through comparison with both theoretical and experimental results the magic slot configuration has also been studied the polarization diversity of this radiator makes it suitable for implementing a quasioptical balanced mixer

vector hankel transform analysis of annular ring microstrip antenna a rigorous analysis of the resonant frequency characteristics of an annular ring conductor printed on a dielectric substrate backed by a ground plane is presented the problem is cast into a set of vector dual integral equations by using vector hankel transform vht galerkin s method is then applied to compute the resonant frequencies of both transverse magnetic modes tm 11 and tm 12 of the microstrip antenna the real part of the resonant frequency shift of the tm 11 mode increases with increasing dielectric thickness in contrast to the tm 12 mode while the tm 11 mode has a high q it is a poor radiating mode the tm 12 mode is more suitable for antenna applications for a probe excitation the input impedance is obtained using single mode approximation for both the tm 11 and tm 12 modes it is shown that the tm 12 mode of the annular ring has a greater bandwidth than the tm 11 mode

the series product and its application to quantum feedforward and feedback networks the purpose of this paper is to present simple and general algebraic methods for describing series connections in quantum networks these methods build on and generalize existing methods for series or cascade connections by allowing for more general interfaces and by introducing an efficient algebraic tool the series product we also introduce another product which we call the concatenation product that is useful for assembling and representing systems without necessarily having connections we show how the concatenation and series products can be used to describe feedforward and feedback networks a selection of examples from the quantum control literature are analyzed to illustrate the utility of our network modeling methodology

spectral method of moments for planar structures with azimuthal symmetry an efficient method of moments formulation is proposed for the analysis of planar structures in the presence of azimuthally symmetric fields boundary integral equations are derived for tm and te polarizations assuming as a reference structure a metal plate with a finite number of concentric annular slots placed above a stratified medium the equations are discretized with a galerkin testing scheme in the fourier bessel domain adopting suitable sub domain basis functions that ensure a very rapid convergence of the involved spectral integrals numerical validation is provided by comparison with state of art simulation software considering planar antennas with omnidirectional radiation patterns in order to show the accuracy of the proposed formulation

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 use of subsectional spline basis functions for efficient calculation of the rcs of a microstrip array of concentric annular rings over a wide frequency band the use of b splines in the radial direction is described for efficient calculation of the radar cross section rcs of a microstrip annular ring or array of concentric annular rings over a wide frequency band galerkin s method in the vector hankel transform vht domain is used to calculate the induced current density on the annular patches an algorithm is presented for a fast and accurate calculation of the scalar hankel transforms of b splines on an arbitrary nonuniform grid which plays an important role in the numerical calculation of the reaction integrals containing the scalar hankel transforms of b splines the accuracy and computational efficiency of the method and the convergence of the rcs results with respect to the number of segments along the radial direction are studied for some annular ring and concentric ring patches

canonical basis for type a4 i monomial elements the global crystal basis or canonical basis plays an important role in the theory of the quantum groups and their representations the tight monomials are the simplest elements in the canonical basis based on lusztig and xi s work the regions of tight monomials in quantized enveloping algebra of type a4 are determined in this paper 2003 elsevier science usa all rights reserved

the stratonovich formulation of quantum feedback network rules we express the rules for forming quantum feedback networks using the stratonovich form of quantum stochastic calculus rather than the it or slh j e gough and m r james quantum feedback networks hamiltonian formulation commun math phys 287 1109 2009 j e gough and m r james the series product and its application to quantum feedforward and feedback networks ieee trans autom control 54 2530 2009 form remarkably the feedback reduction rule implies that we obtain the schur complement of the matrix of stratonovich coupling operators where we short out the internal input output coefficients

tight monomials and the monomial basis property abstract we generalize a criterion for tight monomials of quantum enveloping algebras associated with symmetric generalized cartan matrices and a monomial basis property of those associated with symmetric classical cartan matrices to their respective symmetrizable case we then link the two by establishing that a tight monomial is necessarily a monomial defined by a weakly distinguished word as an application we develop an algorithm to compute all tight monomials in the rank 2 dynkin case

efficient and accurate computation of an annular slot on a dielectric half space an efficient and accurate method of analysis for an annular slot radiating on a dielectric half space is presented the result involves neither singularity nor any numerical integration and therefore is computationally very efficient and easy to implement numerically the method is very rigorous and general and should find applications in other related configurations

quantum dissipative systems and feedback control design by interconnection the purpose of this paper is to extend j c willems theory of dissipative systems to open quantum systems described by quantum noise models this theory which combines ideas from quantum physics and control theory provides useful methods for analysis and design of dissipative quantum systems we describe the interaction of the plant and a class of external systems called exosystems in terms of feedback networks of interconnected open quantum systems our results include an infinitesimal characterization of the dissipation property which generalizes the well known positive real and bounded real lemmas and is used to study some properties of quantum dissipative systems we also show how to formulate control design problems using network models for open quantum systems which implements willems control by interconnection for open quantum systems this control design formulation includes for example standard problems of stabilization regulation and robust control

characteristic operator functions for quantum input plant output models and coherent control we introduce the characteristic operator as the generalization of the usual concept of a transfer function of linear input plant output systems to arbitrary quantum nonlinear markovian input output models this is intended as a tool in the characterization of quantum feedback control systems that fits in with the general theory of networks the definition exploits the linearity of noise differentials in both the plant heisenberg equations of motion and the differential form of the input output relations mathematically the characteristic operator is a matrix of dimension equal to the number of outputs times the number of inputs which must coincide but with entries that are operators of the plant system in this sense the characteristic operator retains details of the effective plant dynamical structure and is an essentially quantum object we illustrate the relevance to model reduction and simplification definition by showing that the convergence of the characteristic operator in adiabatic eliminatio

canonical basis for typeb2 abstract a quantized enveloping algebra has a remarkable basis called the canonical basis or global crystal basis for type a 2 the canonical basis is described explicitly the purpose of this paper is to find the canonical basis for type b 2 the main result is theorem 2 2

singular perturbation approximations for a class of linear quantum systems this technical note considers the use of singular perturbation approximations for a class of linear quantum systems arising in the area of linear quantum optics the technical note presents results on the physical realizability properties of the approximate system arising from singular perturbation model reduction

quantum ito s formula and stochastic evolutions using only the boson canonical commutation relations and the riemann lebesgue integral we construct a simple theory of stochastic integrals and differentials with respect to the basic field operator processes this leads to a noncommutative ito product formula a realisation of the classical poisson process in fock space which gives a noncommutative central limit theorem the construction of solutions of certain noncommutative stochastic differential equations and finally to the integration of certain irreversible equations of motion governed by semigroups of completely positive maps the classical ito product formula for stochastic differentials with respect to brownian motion and the poisson process is a special case

non commutative markov chains and multi analytic operators journal of mathematical analysis and applications volume 364 issue 1 1 april 2010 pages 275 288

transfer function approach to quantum control part ii control concepts and applications based on the stochastic differential equation of quantum mechanical feedback obtained in the first part of this paper detailed control concepts and applications are discussed for quantum systems interacting with a noncommutative noise source a feedback system in our framework is purely nonclassical in the sense that feedback control is performed via local operation and quantum communication through a quantum channel the role of the controller is to alter the quantum dynamic characteristics of the plant through entanglement shared between the plant and controller by sending quantum states that is modulated by the hamiltonian on the controller the input output relation of quantum systems provides a natural extension of control theory to the quantum domain this enables one to present a control theoretical interpretation of some fundamental quantum mechanical notions such as the uncertainty principle but also to find applications of ideas and tools of control theory one of the most important applications is the production of squeezed states which has been an important issue of quantum theory in relation to quantum computation and quantum communication the method proposed here reduces the application to a conventional noise reduction problem with feedback the h sub spl infin control then leads to complete squeezing

coherent feedback control of linear quantum optical systems via squeezing and phase shift the purpose of this paper is to present a theoretic and numerical study of utiliz ing squeezing and phase shift in coherent feedback control of linear quantum optical systems a quadrature representation with built in phase shifters is proposed for such systems fundamen tal structural characterizations of linear quantum optical systems are derived in terms of the new quadrature representation these results reveal considerable insights into the issue of the physical realizability of such quantum systems the problem of coherent quantum linear quadratic gaussian lqg feedback control studied in h i nurdin m r james and i r petersen automatica ifac 45 2009 pp 1837 1846 g zhang and m r james ieee trans automat control 56 2011 pp 1535 1550 is reinvestigated in depth first the optimization methods in these papers are extended to a multistep optimization algorithm which utilizes ideal squeezers second a two stage optimization approach is proposed on the basis of controller parametrization numerical studies show that closed loop systems designed via the second approach may offer lqg control performance even better than that when the closed loop systems are in the vacuum state when ideal squeezers in a closed loop system are replaced by more realistic degenerate parametric amplifiers a sufficient condition is derived for the asymptotic stability of the resultant new closed loop system the issue of performance convergence is also discussed in the lqg control setting

an introduction to quantum filtering this paper provides an introduction to quantum filtering theory an introduction to quantum probability theory is given focusing on the spectral theorem and the conditional expectation as a least squares estimate and culminating in the construction of wiener and poisson processes on the fock space we describe the quantum ito calculus and its use in the modeling of physical systems we use both reference probability and innovations methods to obtain quantum filtering equations for system probe models from quantum optics

brief paper cascade cavity realization for a class of complex transfer functions arising in coherent quantum feedback control this paper presents a realization algorithm for a class of complex transfer function matrices corresponding to physically realizable linear quantum systems the aim of the realization algorithm is to enable a coherent quantum feedback controller which has been synthesized using methods such as quantum h control or quantum lqg control to be constructed using optical components such as cavities and phase shifters the class of linear quantum systems under consideration are passive linear quantum systems which can be described purely in terms of annihilation operators the proposed algorithm enables a complex transfer function matrix to be realized as a pure cascade connection involving only cavities and phase shifters

direct and indirect couplings in coherent feedback control of linear quantum systems the purpose of this paper is to study and design direct and indirect couplings for use in coherent feedback control of a class of linear quantum stochastic systems a general physical model for a nominal linear quantum system coupled directly and indirectly to external systems is presented fundamental properties of stability dissipation passivity and gain for this class of linear quantum models are presented and characterized using complex lyapunov equations and linear matrix inequalities lmis coherent h and lqg synthesis methods are extended to accommodate direct couplings using multistep optimization examples are given to illustrate the results

analysis of a circular microstrip disk antenna with a thick dielectric substrate the problem of a circular microstrip disk excited by a probe is solved using rigorous analysis the disk is assumed to have zero thickness and the current on the probe is taken to be uniform using vector hankel transforms the problem is formulated in terms of vector dual integral equations from which the unknown current can be solved for due to the singular nature of the current distribution arising from probe excitation the direct application of galerkin s basis function expansion method gives a slowly convergent result therefore the singular part of the current is removed since the singularity is known a priori the unknown current to be solved for is then regular and tenable to galerkin s method of analysis it is shown that this analysis agrees with the single mode approximation when the dielectric substrate layer is thin and that it deviates from the single mode approximation when the substrate layer is thick excellent agreement of both the computed real and imaginary parts of the input impedance with experimental data is noted the radiation patterns and the current distributions on the disk are also presented