antenna array pattern synthesis via convex optimization we show that a variety of antenna array pattern synthesis problems can be expressed as convex optimization problems which can be numerically solved with great efficiency by recently developed interior point methods the synthesis problems involve arrays with arbitrary geometry and element directivity constraints on far and near field patterns over narrow or broad frequency bandwidth and some important robustness constraints we show several numerical simulations for the particular problem of constraining the beampattern level of a simple array for adaptive and broadband arrays

quantum probabilities for time extended alternatives we study the probability assignment for the outcomes of time extended measurements we construct the class operator that incorporates the information about a generic time smeared quantity these class operators are employed for the construction of positive operator valued measures for the time averaged quantities the scheme highlights the distinction between velocity and momentum in quantum theory propositions about velocity and momentum are represented by different class operators hence they define different probability measures we provide some examples we study the classical limit and we construct probabilities for generalized time extended phase space variables

an anhomomorphic logic for quantum mechanics although various schemes for anhomomorphic logics for quantum mechanics have been considered in the past we shall mainly concentrate on the quadratic or grade 2 scheme in this scheme the grade 2 truth functions are called coevents we discuss properties of coevents projections on the space of coevents and the master observable we show that the set of projections forms an orthomodular poset we introduce the concept of precluding coevents and show that this is stronger than the previously studied concept of preclusive coevents precluding coevents are defined naturally in terms of the master observable a result that exhibits a duality between preclusive and precluding coevents is given some simple examples are presented

constrained least squares optimization in conformal array antenna synthesis the least mean square error of the constrained least squares optimization method is studied the phases of non zero goal values and the phases of non zero constraint values can be selected by a fast iteration for optimum fit to the goal function amplitude this kind of modified least squares optimization method opens up a fast and robust synthesis method for large conformal antenna arrays constraints can be written also for the element excitation amplitudes and a phase synthesis with predefined amplitudes can be done iterative weight correction technique is used for accurate sidelobe control synthesis examples of two dimensional elliptical and large three dimensional conformal antenna arrays are presented

the uncertainty principle on considere l existence et la regularite des solutions d equations aux derivees partielles la construction de solutions fondamentales explicites et les valeurs propres d operateurs de schrodinger

continuous time and consistent histories we discuss the use of histories labelled by a continuous time in the approach to consistent histories quantum theory in which propositions about the history of the system are represented by projection operators on a hilbert space this extends earlier work by two of us c j isham and n linden j math phys 36 5392 5408 1995 where we showed how a continuous time parameter leads to a history algebra that is isomorphic to the canonical algebra of a quantum field theory we describe how the appropriate representation of the history algebra may be chosen by requiring the existence of projection operators that represent propositions about the time average of the energy we also show that the history description of quantum mechanics contains an operator corresponding to velocity that is quite distinct from the momentum operator finally the discussion is extended to give a preliminary account of quantum field theory in this approach to the consistent histories formalism

poincare invariance for continuous time histories we show that the relativistic analog of the two types of time translation in a nonrelativistic history theory is the existence of two distinct poincare groups the internal poincare group is analogous to the one that arises in the standard canonical quantization scheme the external poincare group is similar to the group that arises in a lagrangian description of the standard theory in particular it performs explicit changes of the space time foliation that is implicitly assumed in standard canonical field theory

a joint optimization approach for the synthesis of large 4 d heterogeneous antenna arrays due to the inherent nonlinearity in the synthesis of large four dimensional 4 d heterogeneous arrays conventional pattern synthesis techniques are no longer suitable in this paper an effective joint optimization approach based on the combination of convex programming cp and differential evolution de algorithm is proposed by designing suitable time sequences of a 4 d heterogeneous array with uniform static amplitude excitations the original synthesis problem is simplified into two independent small problems which can be easily solved in two steps respectively in the first step the approach takes definite advantages from the convexity of the problem with respect to the static phase excitations and the switch on duration times these optimization variables become known and are fixed in the second step then the de algorithm is used to optimize the switch on time instants owing to the efficiency of the cp only 2 3 of the optimization variables need be solved in the first step while even fewer number of optimization variables are solved in the second step consequently the joint optimization of cp and de algorithm significantly improves the overall synthesis efficiency two numerical examples are presented to demonstrate the effectiveness of the proposed approach

the structure of decoherence functionals for von neumann quantum histories gell mann and hartle have proposed a significant generalization of quantum theory in which decoherence functionals perform a key role isham linden schreckenberg have given a penetrating analysis of decoherence functionals for l h where h is finite dimensional dimension greater than 2 in this note their conjecture on the significance of boundedness is verified in particular it is shown that when d is a bounded decoherence functional associated with a von neumann algebra a then provided a has no direct summand of type i2 d can be represented as the difference between semi innerproducts on a

calculation of sideband radiations in time modulated volumetric arrays and generalization of the power equation in this study sideband radiation sr power calculation for time modulated volumetric conformal arrays tmvas is investigated and a closed form formulation is derived the obtained formulation is combined with previous related works and a grid independent general representation of harmonic power radiation formulation is presented

are there realistically interpretable local theories although it rests on strongly established proofs the statement that no realistically interpretable local theory is compatible with some experimentally testable predictions of quantum mechanics seems at first sight to be incompatible with a few general ideas and clear cut statements occurring in recent theoretical work by griffiths omnes and ballentine and jarrett it is shown here that in fact none of the developments due to these authors can be considered as a realistically interpretable local theory so that there is no valid reason for suspecting that the existing proofs of the statement in question are all flawed

symmetry and history quantum theory an analog of wigner s theorem the basic ingredients of the consistent histories approach to quantum theory are a space up of history propositions and a space d of decoherence functionals in this article we consider such history quantum theories in the case where up is given by the set of projectors p v on some hilbert space v we define the notion of a physical symmetry of a history quantum theory pshqt and specify such objects exhaustively with the aid of an analog of wigner s theorem in order to prove this theorem we investigate the structure of d define the notion of an elementary decoherence functional and show that each decoherence functional can be expanded as a certain combination of these functionals we call two history quantum theories that are related by a pshqt physically equivalent and show explicitly in the case of history quantum mechanics how this notion is compatible with one that has appeared previously

on tracial operator representations of quantum decoherence functionals a general quantum history theory can be characterized by the space of histories and by the space of decoherence functionals in this note we consider the situation where the space of histories is given by the lattice of projection operators on an infinite dimensional hilbert space h we study operator representations for decoherence functionals on this space of histories we first give necessary and sufficient conditions for a decoherence functional being representable by a trace class operator on h h an infinite dimensional analogue of the isham linden schreckenberg representation for finite dimensions since this excludes many decoherence functionals of physical interest we then identify the large and physically important class of decoherence functionals which can be represented canonically by bounded operators on h h

consistent quantum realism a reply to bassi and ghirardi a recent claim by bassi and ghirardi that the consistent decoherent histories approach cannot provide a realistic interpretation of quantum theory is shown to be based upon a misunderstanding of the single framework rule they have replaced the correct rule with a principle which directly contradicts it it is their assumptions not those of the consistent histories approach which lead to a logical contradiction

completeness of decoherence functionals the basic ingredients of the consistent histories approach to a generalized quantum theory are histories and decoherence functionals the main aim of this program is to find and to study the behavior of consistent sets associated with a particular decoherence functional d in its recent formulation by isham quantum logic and the histories approach to quantum theory j math phys 35 2157 2185 1994 it is natural to identify the space up of propositions about histories with an orthoalgebra or lattice when up is given by the lattice of projectors p v in some hilbert space v consistent sets correspond to certain partitions of the unit operator in v into mutually orthogonal projectors 1 2 such that the function d is a probability distribution on the boolean algebra generated by 1 2 using the classification theorem for decoherence functionals proven in isham et al the classification of decoherence functionals an analog of gleason s theorem j math phys 35 6

stochastic description for open quantum systems abstract a linear quantum brownian motion model with a general spectral density function is considered in the framework of the influence functional formalism a langevin equation can be introduced to describe the system s fully quantum properties even beyond the semiclassical regime in particular we show that the reduced wigner function for the system can be formally written as a double average over both the initial conditions and the stochastic source of the langevin equation this is exploited to provide a derivation of the master equation for the reduced density matrix alternative to those existing in the literature furthermore we prove that all the correlation functions obtained in the context of the stochastic description associated to the langevin equation actually correspond to quantum correlation functions for system observables in doing so we also compute the closed time path generating functional of the open system

symmetries of history quantum theories and decoherence functionals recently schreckenberg investigated symmetries in the context of history quantum theories in the case that the space of histories is given by the set of projectors on some finite dimensional hilbert space he obtained first a complete characterization of all physical symmetries of history quantum theories an analog of wigner s theorem and second a complete mathematical characterization of symmetries of single decoherence functionals in this paper we extend schreckenberg s results to the case where the underlying space of histories is given by the set of projectors on some infinite dimensional hilbert space

optimal polarization synthesis of arbitrary arrays with focused power pattern the joint synthesis of the spatial power pattern and polarization of arbitrary arrays is addressed specifically the proposed approach gives the solution to a frequently encountered problem namely the array design i e the determination of the radiating element weightings to achieve a pattern that is arbitrarily upper bounded while its polarization is optimized in a given angular region any state of polarization elliptical circular and linear can be synthesized and there is no restriction regarding the array geometry and element patterns the synthesis problem is rewritten as a convex optimization problem that is efficiently solved using readily available software this ensures the optimality of the proposed solution various numerical results are presented to validate the proposed method and illustrate its potentialities the synthesis of a sequentially rotated array is first addressed then a linear array of equispaced randomly oriented dipoles is considered finally a conformal and a planar array of patches where the mutual coupling effects are considered are synthesized to radiate a linear and a circular polarization

the arrival time distribution the extended probability approaches we present a calculation of the arrival time probability distribution based on the extended probability as proposed by hartle 2008 phys rev a 78 012108 we show that two cases of the arrival time probability distribution can be used first we use the path decomposition expansion to discuss a fine grained history for which a particle has a first crossing x 0 at time the arrival time probability related to the probability current is obtained second we consider that the arrival time distribution is modeled by the first photon emitted from a two level atom the basic atom laser model the partition dynamic of this system is discussed each history is in the form of a coarse grained history we confirm that the arrival time probability distribution computed by this method agrees with that computed via the probability of no photon detection crucially the resulting arrival time distributions can be obtained without the restriction of the consistency condition

efficiency constrained particle swarm optimization of a modified bernstein polynomial for conformal array excitation amplitude synthesis as various enabling technologies advance conformal phased arrays are finding more numerous applications because a conformal array is curved new far field pattern behaviors emerge and many of the traditional linear and planar phased array synthesis methods are not valid this paper starts by reviewing the equations for the far field of a curved phased array and provides a generalized definition of aperture efficiency appropriate for conformal arrays a modified bernstein polynomial defined with just five parameters is introduced which provides a flexible method to specify a variety of smooth unimodal amplitude distributions that are shown to give good sidelobe levels and aperture efficiencies by using particle swarm optimization of the modified bernstein polynomial parameters constrained to provide a specified aperture efficiency a family of aperture distributions and corresponding far field patterns is produced that allows aperture efficiency to be traded for sidelobe level

an effective hybrid approach for the optimal synthesis of monopulse antennas the problem of synthesizing optimal sum and difference patterns subject to arbitrary sidelobe bounds by means of a simple feeding network is dealt with it is shown how a hybrid optimization procedure properly acting on both clustering into subarrays and excitations of these latter greatly improves performances of known feeding architectures with respect to existing procedures results of the proposed technique which significantly outperform existing methods renew the interest of these simple feeding architectures and emphasize the effectiveness of this kind of hybrid procedures exploiting the convexity of the problem with respect to a part of the unknowns

sidelobe reduction in array pattern synthesis using genetic algorithm a simple and flexible genetic algorithm ga for pattern synthesis of antenna array with arbitrary geometric configuration is presented unlike conventional ga using binary coding and binary crossover this approach directly represents the array excitation weighting vectors as complex number chromosomes and uses decimal linear crossover without a crossover site compared with conventional gas this approach has a few advantages giving a clearer and simpler representation of the problem simplifying chromosome construction and totally avoiding binary encoding and decoding so as to simplify software programming and to reduce cpu time this method also allows us to impose constraints on phases and magnitudes of complex excitation coefficients for preferable implementation in practice using digital phase shifters and digital attenuators successful applications show that the approach can be used as a general tool for pattern synthesis of arbitrary arrays

quantum chaos an entropy approach a new definition of the entropy of a given dynamical system and of an instrument describing the measurement process is proposed within the operational approach to quantum mechanics it generalizes other definitions of entropy in both the classical and quantum cases the kolmogorov sinai ks entropy is obtained for a classical system and the sharp measurement instrument for a quantum system and a coherent states instrument a new quantity coherent states entropy is defined it may be used to measure chaos in quantum mechanics the following correspondence principle is proved the upper limit of the coherent states entropy of a quantum map as 0 is less than or equal to the ks entropy of the corresponding classical map chaos umpire sits and by decision more imbroils the fray by which he reigns next him high arbiter chance governs all john milton paradise lost book ii

decoherence and linear entropy increase in the quantum baker s map we show that the coarse grained quantum baker s map exhibits a linear entropy increase at an asymptotic rate given by the kolmogorov sinai entropy of the classical chaotic baker s map the starting point of our analysis is a symbolic representation of the map on a string of n qubits i e an n bit register of a quantum computer to coarse grain the quantum evolution we make use of the decoherent histories formalism as a by product we show that the condition of medium decoherence holds asymptotically for the coarse grained quantum baker s map

continuous time histories observables probabilities phase space structure and the classical limit the continuous time histories program stems from the consistent histories approach to quantum theory and aims to provide a fully covariant formalism for quantum mechanics in this paper we examine some structural points of the formalism we demonstrate a general construction of history hilbert spaces and identify a large class of time averaged observables we pay particular attention to the construction of the decoherence functional the object that encodes probability information in the continuous time limit and its relation to the temporal structure of the theory phase space observables are introduced through the study of general representations of the history group which is the analog of the canonical group in the formalism we can also define a closed time path ctp generating functional for each observable which encodes the information of its correlation functions the phase space version of the ctp generating functional leads to the implementation of wigner weyl transforms that gives a description of quantum theory solely in terms of phase space histories these results allow the identification of an algorithm for going to the classical stochastic limit for a generic quantum system

two derivations of the master equation of quantum brownian motion central to many discussion of decoherence is a master equation for the reduced density matrix of a massive particle experiencing scattering from its surrounding environment such as that of joos and zeh such master equations enjoy a close relationship with spontaneous localization models like the grw model the aim of this paper is to present two derivations of the master equation the first derivation is a pedagogical model designed to illustrate the origins of the master equation as simply as possible focusing on physical principles and without the complications of s matrix theory this derivation may serve as a useful tutorial example for students attempting to learn this subject area the second is the opposite a very general derivation using non relativistic many body field theory it reduces to the equation of the type given by joos and zeh in the one particle sector but correcting certain numerical factors which have recently become significant in connection with experimental tests of decoherence this master equation also emphasizes the role of local number density as the preferred basis for decoherence in this model

logical reformulation of quantum mechanics iv projectors in semiclassical physics this is a technical paper providing the proofs of three useful theorems playing a central role in two kinds of physical applications an explicit logical and mathematical formulation of the interpretation of quantum mechanics and the corresponding description of irreversibility the appendix contains a brief mathematical introduction to microlocal analysis three theorems are derived in the text a associating a projector in hilbert space with a macroscopic regular cell in classical phase space b specifying the algebra of the projectors associated with different cells c showing the connection between the classical motion of cells and the schrodinger evolution of projectors for a class of regular hamiltonians corresponding approximately to deterministic systems as described within the framework of quantum mechanics applications to the interpretation of quantum mechanics are given and the consequences for irreversibility will be given later

numerical evidence for approximate consistency and markovianity of some quantum histories in a class of finite closed spin systems closed quantum systems obey the schrodinger equation whereas nonequilibrium behavior of many systems is routinely described in terms of classical markovian stochastic processes evidently there are fundamental differences between those two types of behavior we discuss the conditions under which the unitary dynamics may be mapped onto pertinent classical stochastic processes this is first principally addressed based on the notions of consistency and markovianity numerical data are presented that show that the above conditions are to good approximation fulfilled for heisenberg type spin models comprising 12 20 spins the accuracy to which these conditions are met increases with system size

quantum dynamics without the wavefunction when suitably generalized and interpreted the path integral offers an alternative to the more familiar quantal formalism based on state vectors self adjoint operators and external observers mathematically one generalizes the path integral as propagator to a quantal measure on the space of all conceivable worlds and this generalized measure expresses the dynamics or law of motion of the theory much as wiener measure expresses the dynamics of brownian motion within such histories based schemes new and more realistic possibilities open up for resolving the philosophical problems of the state vector formalism in particular one can dispense with the need for external agents by locating the predictive content of in its sets of measure zero such sets are to be precluded but unrestricted application of this rule engenders contradictions one possible response would remove the contradictions by circumscribing the application of the preclusion concept another response more in the tradition of quantum logic would accommodate the contradictions by dualizing to a space of co events and effectively identifying reality with an element of this dual space

a bell inequality analog in quantum measure theory one obtains bell s inequalities if one posits a hypothetical joint probability distribution or measure whose marginals yield the probabilities produced by the spin measurements in question the existence of a joint measure is in turn equivalent to a certain causality condition known as screening off we show that if one assumes more generally a joint quantal measure or decoherence functional one obtains instead an analogous inequality weaker by a factor of the proof of this tsirel son inequality is geometrical and rests on the possibility of associating a hilbert space to any strongly positive quantal measure these results lead both to a question does a joint measure follow from some quantal analog of screening off and to the observation that non contextual hidden variables are viable in histories based quantum mechanics even if they are excluded classically

quantum equilibrium and the origin of absolute uncertainty what is randomness probability certainty knowledge these are old and difficult questions and we shall not focus on them here nonetheless we shall obtain sharp striking conclusions concerning the relationship between these concepts

linearly positive histories probabilities for a robust family of sequences of quantum events non negative probabilities that obey the sum rules may be assigned to a much wider family of sets of histories than decohering histories the resulting linearly positive histories avoid the highly restrictive decoherence conditions and yet give the same probabilities when those conditions apply thus linearly positive histories are a broad extension of decohering histories moreover the resulting theory is manifestly time reversal invariant

the classical limit for a class of quantum baker s maps we show that the class of quantum baker s maps defined by schack and caves have the proper classical limit provided the number of momentum bits approaches infinity this is done by deriving a semi classical approximation to the coherent state propagator

boundedness of solutions to a class of coercive systems with morrey data abstract we prove global essential boundedness of the weak solutions u w 0 1 p r n to the quasilinear system div a x u d u b x u d u the principal part a x u d u of the differential operator is componentwise coercive and supports controlled growths with respect to u and d u while the lower order term b x u d u exhibits componentwise controlled gradient growth the x behaviour of the nonlinearities is governed in terms of morrey spaces

electromagnetic inverse scattering of multiple two dimensional perfectly conducting objects by the differential evolution strategy electromagnetic inverse scattering of multiple two dimensional 2 d perfectly conducting objects with transverse magnetic tm wave incidence by the differential evolution strategy des is presented the governing electric field integral equations for the scattering problem are expressed as surface integral over the cylinder contours the cylinder contours are approximately represented by closed cubic b splines local shape functions in local polar coordinate system the inverse problem is to locate the cylinders and to reconstruct their shape with or without a priori knowledge of the number of cylinders it is cast into an optimization problem and is solved using the des both synthetic and real reconstructions are carried out the reconstruction results agree with the true profiles very well comparison with the real coded genetic algorithm has been carried out it has been observed that the des outperforms the real coded genetic algorithm

an effective approach for the optimal focusing of array fields subject to arbitrary upper bounds a new approach to the optimal focusing of array fields subject to arbitrary upper bounds is presented the approach formulates the problem as the minimization of a linear function in a convex set unlike other approaches this one guarantees the achievement of the global optimum by using local optimization techniques and can moreover deal with any convex constraint on the unknowns such as near field constraints optimization is performed by two ad hoc developed solution algorithms which exploit the geometrical characteristics of the problem at hand thus leading to extremely effective and computationally efficient numerical codes an extensive numerical analysis has been performed in all cases of linear planar and circular arc arrays the enhanced performance of the proposed technique with respect to the solution algorithms available in the literature fully confirms the effectiveness of the approach

the action operator for continuous time histories we define the action operator for the consistent histories formalism as the quantum analog of the classical action functional for the simple harmonic oscillator case we conclude that the action operator is the generator of time transformations and is associated with the two types of time evolution of the standard quantum theory the wave packet reduction and the unitary time evolution we construct the corresponding classical histories and demonstrate the relevance with the quantum histories finally we show the relation of the action operator to the decoherence functional

information is a physical entity abstract this paper associated with a broader conference talk on the fundamental physical limits of information handling emphasizes the aspects still least appreciated information is not an abstract entity but exists only through a physical representation thus tying it to all the restrictions and possibilities of our real physical universe the mathematician s vision of an unlimited sequence of totally reliable operations is unlikely to be implementable in this real universe speculative remarks about the possible impact of that on the ultimate nature of the laws of physics are included

on the relationship between complex potentials and strings of projection operators it is of interest in a variety of contexts and in particular in the arrival time problem to consider the quantum state obtained through unitary evolution of an initial state regularly interspersed with periodic projections onto the positive x axis pulsed measurements echanobe del campo and muga have given a compelling but heuristic argument that the state thus obtained is approximately equivalent to the state obtained by evolving in the presence of a certain complex potential of step function form in this paper with the help of the path decomposition expansion of the associated propagators we give a detailed derivation of this approximate equivalence the propagator for the complex potential is known so the bulk of the derivation consists of an approximate evaluation of the propagator for the free particle interspersed with periodic position projections this approximate equivalence may be used to show that to produce significant reflection the projections must act at time spacing less than e where e is the energy scale of the initial state

beampattern synthesis for linear and planar arrays with antenna selection by convex optimization a convex optimization based beampattern synthesis method with antenna selection is proposed for linear and planar arrays conjugate symmetric beamforming weights are used so that the upper and non convex lower bound constraints on the beampattern can be convex thus a mainlobe of an arbitrary beamwidth and response ripple can be obtained this method can achieve completely arbitrary sidelobe levels by minimizing a re weighted objective function based on the magnitudes of the elements in the beamforming weight vector iteratively the proposed method selects certain antennas in an array to satisfy the prescribed beampattern specifications precisely interestingly a sparse array with fewer antennas compared to other methods is produced this method can design non uniformly spaced arrays with inter element spacings larger than one half wavelength without the appearance of grating lobes in the resulting beampattern simulations are shown using arrays of up to a few hundred antennas to illustrate the practicality of the proposed method

popescu rohrlich boxes in quantum measure theory two results are proved at the quantal level in sorkin s hierarchy of measure theories one is a strengthening of an existing bound on the correlations in the epr bohm set up under the assumption that the probabilities admit a strongly positive joint quantal measure it is also proved that any set of no signalling probabilities for two distant experimenters with a choice of two alternative experiments each and two possible outcomes per experiment admits a joint quantal measure though one that is not necessarily strongly positive

super quantum measures on effect algebras with the riesz decomposition properties we give one basis of the space of super quantum measures on finite effect algebras with the riesz decomposition properties rdp for short then we prove that the super quantum measures and quantum interference functions on finite effect algebras with the rdp are determined each other at last we investigate the relationships between the super quantum measures and the diagonally positive signed measures on finite effect algebras with the rdp in detail

physical symmetries of quantum histories gell mann and hartle have proposed a significant generalisation of quantum theory in which decoherence functionals play a key role physical symmetries of quantum history systems are shown under mild physical assumptions to correspond to isometric jordan automorphisms of the underlying von neumann algebra unitary representations of groups of symmetries of quadratic forms over operator algebras are discussed and related to symmetries of decoherence functionals

logical reformulation of quantum mechanics i foundations the basic rules of quantum mechanics are reformulated they deal primarily with individual systems and do not assume that every ket may represent a physical state the customary kinematic and dynamic rules then allow to construct consistent boolean logics describing the history of a system following essentially griffiths proposal logical implication is defined within these logics the multiplicity of which reflects the complementary principle only one interpretative rule of quantum mechanics is necessary in such a framework it states that these logics providebona fide foundations for the description of a quantum system and for reasoning about it one attempts to build up classical physics including classical logic on these quantum foundations the resulting theory of measurement needs not to statea priori that the eigenvalues of an observable have to be the results of individual measurements nor to assume wave packet reduction both these properties can be obtained as consequences of the basic rules one also needs not to postulate that every observable is measurable even in principle a proposition calculus is obtained allowing in principle the replacement of the discussion of problems concerned with the practical interpretation of experiments by due calculations

complex probabilities on r n as real probabilities on c n and an application to path integrals we establish a necessary and sufficient condition for averages over complex valued weight functions on r n to be represented as statistical averages over real non negative probability weights on c n using this result we show that many path integrals for time ordered expectation values of bosonic degrees of freedom in real valued time can be expressed as statistical averages over ensembles of paths with complex valued coordinates and then speculate on possible consequences of this result for the relation between quantum and classical mechanics

contrary quantum histories and contrary inferences abstract in the context of the quantum histories approach to quantum mechanics we define a contrary relation between quantum histories generalizing the standard definition of contrary quantum properties using this contrary relation we study the possibility of inferring contrary quantum histories we consider the quantum histories approach with three different consistency conditions weak medium and global consistency conditions for the first two conditions we show that it is possible to infer contrary histories from different families of histories in accordance with previous results for global consistency condition we prove that it is not possible to infer contrary histories

can a quantum state over time resemble a quantum state at a single time the standard formalism of quantum theory treats space and time in fundamentally different ways in particular a composite system at a given time is represented by a joint state but the formalism does not prescribe a joint state for a composite of systems at different times if there were a way of defining such a joint state this would potentially permit a more even handed treatment of space and time and would strengthen the existing analogy between quantum states and classical probability distributions under the assumption that the joint state over time is an operator on the tensor product of single time hilbert spaces we analyse various proposals for such a joint state including one due to leifer and spekkens one due to fitzsimons jones and vedral and another based on discrete wigner functions finding various problems with each we identify five criteria for a quantum joint state over time to satisfy if it is to play a role similar to the standard joint state for a composite system that it is a hermitian operator on the tensor product of the single time hilbert spaces that it represents probabilistic mixing appropriately that it has the appropriate classical limit that it has the appropriate single time marginals that composing over multiple time steps is associative we show that no construction satisfies all these requirements if hermiticity is dropped then there is an essentially unique construction that satisfies the remaining four criteria

consistent histories and the interpretation of quantum mechanics the usual formula for transition probabilities in nonrelativistic quantum mechanics is generalized to yield conditional probabilities for selected sequences of events at several different times called consistent histories through a criterion which ensures that within limits which are explicitly defined within the formalism classical rules for probabilities are satisfied the interpretive scheme which results is applicable to closed isolated quantum systems is explicitly independent of the sense of time i e past and future can be interchanged has no need for wave function collapse makes no reference to processes of measurement though it can be used to analyze such processes and can be applied to sequences of microscopic or macroscopic events or both as long as the mathematical condition of consistency is satisfied when applied to appropriate macroscopic events it appears to yield the same answers as other interpretative schemes for standard quantum mechanics though from a different point of view which avoids the conceptual difficulties which are sometimes thought to require reference to conscious observers or classical apparatus

boundedness and differentiability for nonlinear elliptic systems we consider the elliptic system div aj x u vu bj x u vu j 1 n and an obstacle problem for a similar system of variational inequalities the functions a4 and s3 satisfy certain ellipticity and boundedness conditions with a p admissible weight w and exponent 1 p 2 the growth of b3 in ivul and lul is of order p 1 we show that weak solutions of the above systems are locally bounded and differentiable almost everywhere in the classical sense

how to calculate decoherence matrices numerically abstract a central object in the interpretation of quantum mechanics of closed systems is the decoherence matrix but only for a very small number of models one is able to give explicit expressions for its elements so numerical methods are required unfortunately the dimensions of these matrices are usually very high which makes also a direct numerical calculation impossible in this paper i will develop an algorithm that combines the numerical calculation of the elements of the decoherence matrix with a permanent estimation if the chosen histories are almost decoherent the algorithm will provide the diagonal and maybe some near to diagonal elements only in this case within numerical errors we can assume that all not calculated elements are smaller than a given threshold if the histories are coherent the algorithm has to calculate too much data there exist too much non vanishing elements and the success depends mainly on the available computer time as an example i apply this procedure to the caldeira leggett model

becchi rouet stora tyutin quantization of histories electrodynamics this article is a continuation of earlier work where a classical history theory of pure electrodynamics was developed in which the history fields have five components the extra component is associated with an extra constraint thus enlarging the gauge group of histories electrodynamics in this article we quantize the classical theory developed previously by two methods first we quantize the reduced classical history space to obtain a reduced quantum history theory second we quantize the classical brst extended history space and use the becchi rouet stora tyutin charge to define a cohomological quantum history theory finally we show that the reduced history theory is isomorphic as a history theory to the cohomological history theory

the classification of decoherence functionals an analog of gleason s theorem gell mann and hartle have proposed a significant generalization of quantum theory with a scheme whose basic ingredients are histories and decoherence functionals within this scheme it is natural to identify the space up of propositions about histories with an orthoalgebra or lattice this raises the important problem of classifying the decoherence functionals in the case where up is the lattice of projectors p v in some hilbert space v in effect one seeks the history analog of gleason s famous theorem in standard quantum theory in the present article the solution to this problem for the case where v is finite dimensional is presented in particular it is shown that every decoherence functional d p v can be written in the form d trv v x for some operator x on the tensor product space v v

from classical to quantum mechanics how to translate physical ideas into mathematical language following previous works by e prugovecki physica a 91a 202 1978 and stochastic quantum mechanics and quantum space time reidel dordrecht 1986 on common features of classical and quantum mechanics we develop a unified mathematical framework for classical and quantum mechanics based on l2 spaces over classical phase space in order to investigate to what extent quantum mechanics can be obtained as a simple modification of classical mechanics on both logical and analytical levels to obtain this unified framework we split quantum theory in two parts i general quantum axiomatics a system is described by a state in a hilbert space observables are self adjoints operators and so on and ii quantum mechanics proper that specifies the hilbert space as l2 rn the heisenberg rule pi qj i ij with p i the free hamiltonian h 2 2m and so on we show that general quantum axiomatics up to a supplementary axiom of classicity can be used as a nonstandard mathematical ground to formula

decoherent histories and realism we reconsider the decoherent histories approach to quantum mechanics and analyze some problems related to its interpretation which we believe have not been adequately clarified by its proponents we put forward some assumptions which in our opinion are necessary for a realistic interpretation of the probabilities that the formalism attaches to decoherent histories we prove that such assumptions unless one limits the set of the decoherent families which can be taken into account lead to a logical contradiction the line of reasoning we follow is conceptually different from other arguments which have been presented and which have been rejected by the supporters of the decoherent histories approach the conclusion is that the decoherent histories approach to be considered as an interesting realistic alternative to the orthodox interpretation of quantum mechanics requires the identification of a mathematically precise criterion to characterize an appropriate set of decoherent families which does not give rise to any problem

a topos formulation of history quantum theory topos theory has been suggested by doring and isham as an alternative mathematical structure with which to formulate physical theories in particular it has been used to reformulate standard quantum mechanics in such a way that a novel type of logic is used to represent propositions in this paper we extend this formulation to include temporally ordered collections of propositions as opposed to single time propositions that is to say we have developed a quantum history formalism in the language of topos theory where truth values can be assigned to temporal propositions we analyze the extent to which such truth values can be derived from the truth values of the constituent single time propositions

about the notion of truth in quantum mechanics the meaning of truth in quantum mechanics is considered in order to respond to some objections raised by b d espagnat against a logical interpretation of quantum mechanics recently proposed by the author a complete answer is given it is shown that not only can factual data be said to be true but also some of their logical consequences so that the definition of truth given by heisenberg is both extended and refined some nontrue but reliable propositions may also be used but they are somewhat arbitrary because of the complementarity principle for instance the propositions expressing wave packet reduction can be either true or reliable according to the case under study separability is also discussed as far as the true properties of an individual system are concerned quantum mechanics is separable

pattern synthesis of narrowband conformal arrays using iterative second order cone programming a new design method is proposed for the power or shaped beam pattern synthesis problem of narrowband conformal arrays where only the magnitude response is specified the proposed method iteratively linearizes the non convex power pattern function to obtain a convex subproblem in the design variables which can be solved optimally using second order cone programming socp in addition a wide variety of magnitude constraints such as non convex lower bound magnitude constraints can be incorporated an efficient technique for determining a reasonably good initial guess to the problem is also proposed to further improve the reliability of the method computer simulations show that the initial guesses so obtained converge to satisfactory solutions while satisfying various prescribed magnitude constraints design results show that the performance of the proposed method is comparable to the optimal solution previously obtained for uniform linear arrays with isotropic elements moreover we show by means of examples that the proposed method is also applicable to general non convex power pattern synthesis problems involving arbitrary array geometries arbitrary polarization characteristics and mutual coupling effect