n body quantum scattering theory in two hilbert spaces vii real energy limits a study is made of the real energy limits of approximate solutions of the chandler gibson equations as well as the real energy limits of the approximate equations themselves it is proved that 1 the approximate time independent transition operator t z and an auxiliary operator m z when restricted to finite energy intervals are trace class operators and have limits in trace norm for almost all values of the real energy 2 the basic dynamical equation that determines the operator m z when restricted to the space of trace class operators has a real energy limit in trace norm for almost all values of the real energy 3 the real energy limit of m z is a solution of the real energy limit equation 4 the diagonal on shell elements of the kernels of the real energy limit of t z and of all solutions of the real energy limit equation exactly equal the on shell transition operator implying that the real energy limit equation uniquely determines the physical transition amplitude and 5 a s

radiation conditions and scattering theory for n particle hamiltonians the correct form of the angular part of radiation conditions is found in scattering problem forn particle quantum systems the estimates obtained allow us to give an elementary proof of asymptotic completeness for such systems in the framework of the theory of smooth perturbations

an efficient isogeometric solid shell formulation for geometrically nonlinear analysis of elastic shells abstract in this work an isogeometric solid shell model for geometrically nonlinear analyses is proposed it is based on a linear interpolation through the thickness and a nurbs interpolation on the middle surface of the shell for both the geometry and the displacement field the green lagrange strains are linearized along the thickness direction and a modified generalized constitutive matrix is adopted to easily eliminate thickness locking without introducing any additional unknowns and to model multi layered composite shells reduced integration schemes which take into account the high continuity of the shape functions are investigated to avoid interpolation locking and to increase the computational efficiency the relaxation of the constitutive equations at each integration point is adopted in the iterative scheme in order to reconstruct the equilibrium path using large steps and a low number of iterations even for very slender structures this strategy makes it possible to minimize the number of stiffness matrix evaluations and decompositions and it turns out to be particularly convenient in isogeometric analyses

geometrically nonlinear analysis of sandwich fgm and laminated composite degenerated shells using the isogeometric finite strip method abstract isogeometric analysis iga has become a strong tool for analysis of shell structures which can be considered as a powerful alternative to the standard finite element method fem besides several advantages of iga over fem in geometric nonlinear analysis of the shells it has some drawbacks corresponding to tensor product of b spline and nurbs surfaces one of the solutions to eliminate or at least reduce the effects of the mentioned shortcomings is to combine iga with the other methods such as fem in the present paper a novel version of the finite strip method fsm is developed to carry out the geometric nonlinear analysis which employs a combination of fem and iga in the transversal and longitudinal directions respectively and is named isogeometric b spline finite strip method ig sfsm the strip elements have been formulated based on the degenerated shell method for updated lagrangian ul approach then it is examined by some examples incorporating various geometries boundary conditions bcs and material properties such as laminated composites and sandwich fgms the results exhibited that to achieve the complicated nonlinear equilibrium paths of the shells ig sfsm requires a lower number of degrees of freedom dofs and consequently computational efforts comparing to the other common methods such as finite element and mesh free methods

structures of s matrices for three body schrodinger operators structures of the s matrix associated with the collision process from 2 clusters to 3 clusters are studied this s matrix is shown to have a continuous kernel except for 2 dimensional spheres on which 2 body subsystems have zero velocity on these spheres the s matrix has in general singularities whose existence arises from the zero eigenvalues and the zero resonances of the 2 body subsystems

isogeometric analysis using polynomial splines over hierarchical t meshes for two dimensional elastic solids isogeometric analysis has become a powerful alternative to standard finite elements due to its flexibility in handling complex geometries one of the major drawbacks of nurbs based isogeometric finite elements is the inefficiency of local refinement in this study we present an alternative to nurbs based isogeometric analysis that allows for local refinement the idea is based on polynomial splines and exploits the flexibility of t meshes for local refinement the shape functions satisfy important properties such as non negativity local support and partition of unity several numerical examples are used to demonstrate the reliability of the present method

the complete heyting algebra of subsystems and contextuality the finite set of subsystems of a finite quantum system with variables in z n is studied as a heyting algebra the physical meaning of the logical connectives is discussed it is shown that disjunction of subsystems is more general concept than superposition consequently the quantum probabilities related to commuting projectors in the subsystems are incompatible with associativity of the join in the heyting algebra unless if the variables belong to the same chain this leads to contextuality which in the present formalism has as contexts the chains in the heyting algebra logical bell inequalities which contain heyting factors are discussed the formalism is also applied to the infinite set of all finite quantum systems which is appropriately enlarged in order to become a complete heyting algebra

stationary scattering in the semi classical limit for a schrodinger operator in a gauge field abstract we study the classical limit of the stationary scattering theory for a schrodinger operator in a compactly supported gauge field we show that under suitable hypotheses on the associated classical flow the scattering amplitude has a complete asymptotic expansion in the semi classical parameter and we determine the main term of this expansion

persistence of embedded eigenvalues we consider conditions under which an embedded eigenvalue of a self adjoint operator remains embedded under small perturbations in the case of a simple eigenvalue embedded in continuous spectrum of multiplicity m infinity we show that in favorable situations the set of small perturbations of a suitable banach space which do not remove the eigenvalue form a smooth submanifold of codimension in we also have results regarding the cases when the eigenvalue is degenerate or when the multiplicity of the continuous spectrum is infinite

mourre s method and smoothing properties of dispersive equations abstract the purpose of this paper is to point out that mourre s method in spectral theory is useful and powerful in studying the smoothing effect of dispersive equations especially we will see that the smoothing effect is a quite general phenomenon even for operators with variable coefficients

scattering matrices in many body scattering in this paper we show that generalized eigenfunctions of many body hamiltonians h with short range two body interactions have distributional asymptotics at non threshold channels the leading terms of the asymptotics can be used to define a scattering matrix and we show that this is the same up to normalization as that arising from the standard wave operator approach we also prove the existence of local distributional asymptotics for locally approximate generalized eigenfunctions in the more general setting of short range perturbations of a scattering metric defined by melrose in 13

asymptotic completeness for long range many particle systems with stark effect ii we prove the existence and the asymptotic completeness of the dollard type modified wave operators for many particle stark hamiltonians with long range potentials

smoothing effects and dispersion of singularities for the schrodinger evolution group we describe smoothing effects and dispersion of singularities for the schrodinger evolution group in the weighted sobolev spaces under a fairly general assumption on the potential it is shown that all singularities in the wavefunction vanish instantly whenever the initial state has sufficient decay we measure the regularity gained by the wavefunction by the decay property of the initial state no assumptions on the regularity of the initial state are imposed throughout the paper

local quasi hidden variable modelling and violations of bell type inequalities by a multipartite quantum state we introduce for a general correlation scenario a new simulation model a local quasi hidden variable lqhv model where locality and the measure theoretic construction inherent to a local hidden variable lhv model are preserved but positivity of a simulation measure is dropped we specify a necessary and sufficient condition for lqhv modelling and based on this prove that every quantum correlation scenario admits a lqhv simulation via the lqhv approach we construct analogs of bell type inequalities for an n partite quantum state and find a new analytical upper bound on the maximal violation by an n partite quantum state of s1 sn setting bell type inequalities either on correlation functions or on joint probabilities and for outcomes of an arbitrary spectral type discrete or continuous this general analytical upper bound is expressed in terms of the new state dilation characteristics introduced in the present paper and not only traces quantum states admitting an s1 sn setting lhv de

isogeometric analysis with trimming technique for problems of arbitrary complex topology trimming technique is a powerful and efficacious way of endowing an arbitrary complex topology to cad files created by using nurbs in the present work it is shown that any complex multiply connected nurbs domain can be described by using trimming curves only isogeometric analysis for linear elasticity problems of complex topology described in this way is presented for fully communicative interaction between cad and cae a specific searching algorithm and an integration scheme of trimmed elements are introduced to utilize the iges files exported from cad system for isogeometric analysis schemes for imposing essential and traction boundary conditions on trimming curves are presented it has been demonstrated that with the presented schemes trimmed cases in any complicated situations can be successfully treated with the examples of complex topology that could be described by employing trimming curves only effectiveness and robustness of present method are demonstrated

spectral and scattering theory in perturbed stratified fluids ii transmission problems and exterior domains abstract the spectral and scattering theory of the acoustic propagator in perturbed stratified fluids is studied in the cases of transmission problems and of exterior domains

on the virial theorem in quantum mechanics we review the various assumptions under which abstract versions of the quantum mechanical virial theorem have been proved we point out a relationship between the virial theorem for a pair of operators h a and the regularity properties of the map we give an example showing that the statement of the virial theorem in cfks is incorrect

resolvent smoothness and local decay at low energies for the standard model of non relativistic qed we consider an atom interacting with the quantized electromagnetic field in the standard model of non relativistic qed the nucleus is supposed to be fixed we prove smoothness of the resolvent and local decay of the photon dynamics for quantum states in a spectral interval i just above the ground state energy our results are uniform with respect to i their proofs are based on abstract mourre s theory a mourre inequality established by frohlich griesemer and sigal see frohlich et al 2008 14 hardy type estimates in fock space and a low energy dyadic decomposition

linear inviscid damping and enhanced viscous dissipation of shear flows by using the conjugate operator method abstract we study the large time behavior of solutions to two dimensional euler and navier stokes equations linearized about shear flows of the mixing layer type in the unbounded channel t r under a simple spectral stability assumption on a self adjoint operator we prove a local form of the linear inviscid damping that is uniform with respect to small viscosity we also prove a local form of the enhanced viscous dissipation that takes place at times of order 1 3 being the small viscosity to prove these results we use a hamiltonian approach following the conjugate operator method developed in the study of schrodinger operators combined with a hypocoercivity argument to handle the viscous case

decay estimates and strichartz estimates of fourth order schrodinger operator abstract we study time decay estimates of the fourth order schrodinger operator h 2 v x in r d for d 3 and d 5 we analyze the low energy and high energy behaviour of resolvent r h z and then derive the jensen kato dispersion decay estimate and local decay estimate for e i t h p a c under suitable spectrum assumptions of h based on jensen kato type decay estimate and local decay estimate we obtain the l 1 l estimate of e i t h p a c in 3 dimension by ginibre argument and also establish the endpoint global strichartz estimates of e i t h p a c for d 5 furthermore using the local decay estimate and the georgescu larenas soffer conjugate operator method we prove the jensen kato type decay estimates for some functions of h

absence of singular continuous spectrum for certain self adjoint operators we give a sufficient condition for a self adjoint operator to have the following properties in a neighborhood of a pointe of its spectrum a its point spectrum is finite b its singular continuous spectrum is empty c its resolvent satisfies a class of a priori estimates

quantum probabilities as dempster shafer probabilities in the lattice of subspaces the orthocomplemented modular lattice of subspaces l h d of a quantum system with d dimensional hilbert space h d is considered a generalized additivity relation which holds for kolmogorov probabilities is violated by quantum probabilities in the full lattice l h d it is only valid within the boolean subalgebras of l h d this suggests the use of more general than kolmogorov probability theories and here the dempster shafer probability theory is adopted an operator d h1 h2 which quantifies deviations from kolmogorov probability theory is introduced and it is shown to be intimately related to the commutator of the projectors p h1 p h2 to the subspaces h1 h2 as an application it is shown that the proof of the inequalities of clauser horne shimony and holt for a system of two spin 1 2 particles is valid for kolmogorov probabilities but it is not valid for dempster shafer probabilities the violation of these inequalities in experiments supports the interpretation of quantum proba

on inverse scattering for then body schrodinger equation abstract we consider the generalized n body schrodinger operator h q x q x a a v a x a x r d x a x a r d x a x a with short range regular interactions we obtain in particular the following results 1 we give new formulas and proofs relating high energy asymptotics in a weak sense of the scattering operators with the same cluster decomposition a for and and the x ray transform pi defined on the set of all lines in x a with nonsingular directions of the effective potentials i x a x a x a these results significantly clarify some of those given in the literature 2 we describe completely ker p and give a method for reconstruction of i mod ker p from pi 3 we prove pointwise high energy asymptotics for the two cluster two cluster scattering amplitudes f with the fourier transform i in the leading term for the case when the cluster decomposition for and is the same 4 we give several additional results for the case of perturbed stratified medium when q x v a x a v b x b x a x 1 x b x 1 x d x and each v c x c rapidly decreases as x c c a b our results including proofs in some cases significantly simplify methods of high energy inverse scattering for the n body schrodinger operator given earlier by wang and by enss and weder

a new proof of the propagation theorem for n body quantum systems a new proof of i sigal s and a soffer s propagation theorem is given this theorem describes a large class of operators which are kato smooth with respect to ann body schrodinger operator

asymptotic completeness for n body short range quantum systems a new proof we give an alternative geometrical proof of asymptotic completeness for an arbitrary number of quantum particles interacting through shortrange pair potentials it relies on an estimate showing that the intercluster motion concentrates asymptotically on classical trajectories

the shape resonance for a class of schrodinger operatorsh 2 2m v onl 2 n with potentials having minima embedded in the continuum of the spectrum and non trapping tails we show the existence of shape resonances exponentially close to the real axis as 0 the resonant energies are given by a convergent perturbation expansion in powers of a parameter exhibiting the expected exponentially small behaviour for tunneling

isogeometric topology optimization using trimmed spline surfaces in the present work a new spline based topology optimization using trimmed spline surfaces and the isogeometric analysis is proposed in the proposed approach the trimmed surface analysis which can treat topologically complex spline surfaces using trimming information provided by cad systems is employed for structural response analysis and sensitivity calculation in the topology optimization the outer and inner boundaries of design models are represented by a spline surface and trimming curves design variables used in this approach are the coordinates of control points of a spline surface and those of trimming curves new sensitivity formulations for the control points in the trimmed surface analysis are proposed and their efficiency and accuracy are verified the creation of new inner fronts during optimization is allowed for the topological flexibility an inner front merging algorithm is also presented the proposed spline based topology optimization is used to solve some benchmarking problems design space dependency which is one of serious shortcomings in conventional topology optimization approaches is naturally eliminated by the proposed spline based optimization design dependent load problems which are difficult to treat with conventional grid based topology optimization methods are easily dealt with by the proposed one it is also shown that post processing effort for converting to cad model is eliminated by using the same spline information in numerical analysis and design optimization

a simplified kirchhoff love large deformation model for elastic shells and its effective isogeometric formulation abstract isogeometric kirchhoff love elements have received an increasing attention in geometrically nonlinear analysis of elastic shells nevertheless some difficulties still remain among the others the highly nonlinear expression of the strain measure which leads to a complicated and costly computation of the discrete operators and the existence of locking which prevents the use of coarse meshes for slender shells and low order nurbs are key issues that need to be addressed in this work exploiting the hypothesis of small membrane strains we propose a simplified strain measure with a third order polynomial dependence on the displacement variables which allows an efficient evaluation of the discrete quantities numerical results show practically no difference to the original model even for very large displacements and composite structures patch wise reduced integrations are then investigated to deal with membrane locking in large deformation problems an optimal integration scheme for third order c 2 nurbs in terms of accuracy and efficiency is identified finally the recently proposed newton method with mixed integration points is used for the solution of the discrete nonlinear equations with a great reduction of the iterative burden with respect to the standard newton scheme

propagation estimates for n body schroedinger operators we prove propagation estimates of strong type for long rangen body hamiltonians emphasis is on phase space analysis in the free channel region

the n particle scattering problem asymptotic completeness for short range systems on demontre la completude asymptotique pour des systemes de mecanique quantique a courte portee constitues d un nombre arbitraire de particules

spectral analysis of second order elliptic operators on noncompact manifolds on demontre l estimation de mourre et les bornes qui y sont reliees pour une classe d operateurs elliptiques qui inclut des laplaciens pour des quotients cofinis et coinfinis d espaces hyperboliques

spectral theory of time periodic many body systems we study the spectrum of the monodromy operator for an n body quantum system in a time periodic external field with time mean equal to zero this includes ac stark and circularly polarized fields and pair potentials with a local singularity up to and including the coulomb singularity in the framework of floquet theory we prove a local commutator estimate and use it to prove a limiting absorption principle for the floquet hamiltonian as well as exponential decay estimates on non threshold eigenfunctions these two results are then used to obtain a second order perturbation theory for embedded eigenvalues the principal tool is a new extended mourre theory

propagation of singularities in many body scattering in the presence of bound states abstract in this paper we describe the propagation of singularities of tempered distributional solutions u s of h u 0 where h is a many body hamiltonian h v 0 v a v a and is not a threshold of h under the assumption that the inter particle e g two body interactions v a are real valued polyhomogeneous symbols of order 1 e g coulomb type with the singularity at the origin removed here the term singularity refers to a microlocal description of the lack of decay at infinity thus we prove that the set of singularities of u is a union of maximally extended broken bicharacteristics of h these are curves in the characteristic variety of h which can be quite complicated due to the existence of bound states we use this result to describe the wave front relation of the s matrices we also analyze lagrangian properties of this relation which shows that the relation is not too large in terms of its dimension

local time decay of high energy scattering states for the schrodinger equation on considere l operateur de schrodinger h h 0 v s v l dans l espace de hilbert 7b h l 2 r n n n ou h 0 c 0 r n et v s et v l sont des fonctions a valeurs reelles satisfaisant certaines conditions

spectral analysis of n body schrodinger operators for a large class of two body potentials we solve two of the main problems in the spectral analysis of multiparticle quantum hamiltonians explicitly we prove that the point spectrum lies in a closed countable set and describe that set in terms of the eigenvalues of hamiltonians of subsystems and that there is no singular continuous spectrum we accomplish this by extending mourre s work on three body problems to n body problems

scattering for schrodinger operators in a class of domains with non compact boundaries abstract schrodinger operators in a class of domains with asymptotic cones are considered a generalized fourier transform representing the absolutely continuous part of the schrodinger operator as multiplication by 2 in the asymptotic cone is constructed wave operators relating the free laplacian to schrodinger operators are computed using the generalized fourier transform the wave operators relating schrodinger operators acting in domains with the same asymptotic cone are computed and shown to be complete

on the determination of the path direction for arc length methods in the presence of bifurcations and snap backs abstract this paper discusses the choice of the sign of the incremental load factor in the predictor solution phase of arc length methods it is shown that the criterion recently proposed by y t feng d peric d r j owen determination of travel directions in path following methods mathl and comput modelling 21 1995 43 59 a new criterion for determination of initial loading parameter in arc length methods comput struct 58 1996 479 485 produces a reliable path direction prediction even in the presence of bifurcations and or snap backs when some popular criteria may fail to predict the continuation direction the robustness of the criterion is illustrated in a numerical example where finite element solutions are obtained to a structural stability problem characterised by the existence of several bifurcation paths and snap back phenomena

high frequency limit of the helmholtz equation with variable refraction index abstract we study the high frequency limit of the helmholtz equation with variable refraction index and a source term concentrated near a p dimensional affine subspace under some conditions we first derive uniform estimates in besov spaces for the solutions then we prove that the semi classical measure associated with these solutions satisfies the stationary liouville equation with an explicit source term and has certain radiation property at infinity

adaptive isogeometric analysis by local h refinement with t splines isogeometric analysis based on non uniform rational b splines nurbs as basis functions preserves the exact geometry but suffers from the drawback of a rectangular grid of control points in the parameter space which renders a purely local refinement impossible this paper demonstrates how this difficulty can be overcome by using t splines instead t splines allow the introduction of so called t junctions which are related to hanging nodes in the standard fem obeying a few straightforward rules rectangular patches in the parameter space of the t splines can be subdivided and thus a local refinement becomes feasible while still preserving the exact geometry furthermore it is shown how state of the art a posteriori error estimation techniques can be combined with refinement by t splines numerical examples underline the potential of isogeometric analysis with t splines and give hints for further developments

spectral and scattering theory for differential and hankel operators abstract we consider a class of hankel operators h realized in the space l 2 r as integral operators with kernels h t s where h t p ln t t 1 and p x x n p n 1 x n 1 p 0 is an arbitrary real polynomial of degree n this class contains the classical carleman operator when n 0 we show that a hankel operator h in this class can be reduced by an explicit unitary transformation essentially by the mellin transform to a differential operator a v q d v in the space l 2 r here q x x n q n 1 x n 1 q 0 is a polynomial determined by p x and v 1 2 cosh 1 2 is the universal function then the operator a v q d v reduces by the generalized liouville transform to the standard differential operator b d n b n 1 x d n 1 b 0 x with the coefficients b m x m 0 n 1 decaying sufficiently rapidly as x this allows us to use the results of spectral theory of differential operators for the study of spectral properties of generalized carleman operators in particular we show that the absolutely continuous spectrum of h is simple and coincides with r if n is odd and it has multiplicity 2 and coincides with 0 if n 2 is even the singular continuous spectrum of h is empty and its eigenvalues may accumulate to the point 0 only as a by product of our considerations we develop spectral theory of a new class of degenerate differential operators a v q d v where q x is an arbitrary real polynomial and v is an almost arbitrary real function decaying at infinity

schrodinger operators in the twentieth century this paper reviews the past fifty years of work on spectral theory and related issues in nonrelativistic quantum mechanics

asymptotic completeness for 3 particle long range systems we prove asymptotic completeness for 3 particle systems with pair potentials satisfying the virial condition and decreasing at infinity as for 1 2

schrodinger operators with an electric field and random or deterministic potentials we prove that the schrodinger operatorh d2 dx2 v x f x has purely absolutely continuous spectrum for arbitrary constant external fieldf for a large class of potentials this result applies to many periodic almost periodic and random potentials and in particular to random wells of independent depth for which we prove that whenf 0 the spectrum is almost surely pure point with exponentially decaying eigenfunctions

long range scattering for higher order schrodinger operators abstract this paper is concerned with the scattering problem for the higher order schrodinger operator m v x where v x is a long range potential at this moment the classical wave operators do not exist so we provide one kind of modified wave operators and show the existence and the asymptotic completeness of such wave operators as well as the expression of the corresponding scattering operator

nonlocality as well as rejection of realism are only sufficient but non necessary conditions for violation of bell s inequality in this review we remind the viewpoint that violation of bell s inequality might be interpreted not only as an evidence of the alternative either nonlocality or death of reality under the assumption the quantum mechanics is incomplete violation of bell s type inequalities is a well known sufficient condition of probabilistic incompatibility of random variables impossibility to realize them on a single probability space thus in fact we should take into account an additional interpretation of violation of bell s inequality a few pairs of random variables two dimensional vector variables involved in the epr bohm experiment are incompatible they could not be realized on a single kolmogorov probability space thus one can choose between a completeness of quantum mechanics b nonlocality c death of reality d non kolmogorovness in any event violation of bell s inequality has a variety of possible interpretations hence it could not be used to obtain the definite conclusion on the relation between quantum and classical models

scattering theory for a class of fermionic pauli fierz models abstract the scattering theory for a class of fermionic pauli fierz models is considered we give a proof of the asymptotic completeness of the dynamics in the case of massive fermions the result applied to the hamiltonian of a quantized spin 1 2 dirac particle interacting with an external field through a cutoff yukawa interaction and to the hamiltonian of a system of finitely many confined particles coupled to a fermionic field with a quadratic interaction

absolute continuity of the floquet spectrum for a nonlinearly forced harmonic oscillator we prove that the floquet spectrum of the time periodic schrodinger equation corresponding to a mildly nonlinear resonant forcing is purely absolutely continuous for suitably small

the scattering amplitude for the schrodinger equation with a long range potential we consider the schrodinger operator with a long range potential v x in the space our goal is to study spectral properties of the corresponding scattering matrix and a diagonal singularity of its kernel the scattering amplitude it turns out that in contrast to the short range case the dirac function singularity of at the diagonal disappears and the spectrum of the scattering matrix covers the whole unit circle for an asymptotically homogeneous function v x of order we show that typically where the module w and the phase are asymptotically homogeneous functions as of orders and respectively leading terms of asymptotics of w and at are calculated in the case 1 our results generalize in the limit the well known formula of gordon and mott