note on coherent states and adiabatic connections curvatures we give a possible generalization to the example in the paper of zanardi and rasetti phys lett a 264 94 1999 for this explicit forms of adiabatic connection curvature etc are given we also discuss the possibility of another generalization of their model

geometric quantization of neumann type completely integrable hamiltonian systems the procedure of geometric quantization is developed for completely integrable dynamical systems on manifolds with exact symplectic structure these results are applied to neumann s nonharmonic oscillatory system on two dimensional sphere s2

control aspects of holonomic quantum computation a unifying framework for the control of quantum systems with non abelian holonomy is presented it is shown that from a control theoretic point of view holonomic quantum computation can be treated as a control system evolving on a principal fiber bundle an extension of methods developed for these classical systems may be applied to quantum holonomic systems to obtain insight into the control properties of such systems and to construct control algorithms for two established examples of the computing paradigm

small time controllability of systems on compact lie groups and spin angular momentum in this article we develop some general results on the properties of the reachable sets for right invariant bilinear systems with state varying on compact lie groups the main results consist of a characterization of the set of states reachable in arbitrary time from the identity of the group this under suitable assumptions is proved to be a lie subgroup of the underlying lie group we apply these results to the analysis of the controllability of particles with spin the results are motivated by and generalize the results in another work d d alessandro sys control lett 41 213 221 2000 where the specific model of a spin 12 particle system in an electro magnetic field was considered

on the hyperinvariant subspace problem iii abstract in two recent papers foias and pearcy j funct anal in press hamid et al indiana univ math j to appear the authors reduced the hyperinvariant subspace problem for operators on hilbert space to the question whether every c 00 bcp operator that is quasidiagonal and has spectrum the unit disc has a nontrivial hyperinvariant subspace n h s in this note we continue this study by showing with the help of a new equivalence relation that every operator whose spectrum is uncountable as well as every nonalgebraic operator with finite spectrum has a hyperlattice i e lattice of hyperinvariant subspaces that is isomorphic to the hyperlattice of a c 00 quasidiagonal bcp operator whose spectrum is the closed unit disc

the symplectic camel and phase space quantization we show that a result of symplectic topology gromov s non squeezing theorem also known as the principle of the symplectic camel can be used to quantize phase space in cells that quantization scheme leads to the correct energy levels for integrable systems and to maslov quantization of lagrangian manifolds by purely topological arguments we finally show that the argument leading to the proof of the non squeezing theorem leads to a classical form of heisenberg s inequalities

shift type invariant subspaces of contractions abstract using the sz nagy foias functional model it was shown in l kerchy injection of unilateral shifts into contractions with non vanishing unitary asymptotes acta sci math szeged 61 1995 443 476 that under certain conditions on a contraction t the natural embedding of a hardy space of vector valued functions into the corresponding l 2 space can be factored into the product of two transformations intertwining t with a unilateral shift and with an absolutely continuous unitary operator respectively the norm estimates in the factorization theorem of this paper are sharpened to their best possible form by essential improvements in the proof as a consequence we obtain that if the residual set of a contraction covers the whole unit circle then those invariant subspaces where the restriction is similar to the unilateral shift with a similarity constant arbitrarily close to 1 span the whole space furthermore the hyperinvariant subspace problem for asymptotically non vanishing contractions is reduced to these special circumstances

the worst parallel hanoi graphs abstract the towers of hanoi is a problem that has been extensively studied and frequently generalized in particular it has been generalized to be played on arbitrary directed graphs and using parallel moves of two types we ask what is the largest number of parallel moves in either of the two models that is required to move n disks from the starting node to the destination node not all directed graphs allow solving this problem we will call those graphs that do hanoi graphs in previous work we settled the question of what are the worst sequential hanoi graphs that is those graphs that require the largest number of sequential moves we also demonstrated that the characterization of sequential hanoi graphs carries over the parallel hanoi graphs here we determine the worst hanoi graphs provided parallel moves are allowed it turns out that for one of the two models of parallel moves the worst graphs are quite different from the worst sequential graphs while in the other model of parallelism there is little difference with the sequential situation

asymptotic behaviour and cyclic properties of weighted shifts on directed trees abstract in this paper we investigate a new class of bounded operators called weighted shifts on directed trees introduced recently in 11 this class is a natural generalization of the so called weighted bilateral unilateral and backward shift operators in the first part of the paper we calculate the asymptotic limit and the isometric asymptote of a contractive weighted shift on a directed tree and that of the adjoint then we use the asymptotic behaviour and similarity properties in order to obtain cyclicity results we also show that a weighted backward shift operator is cyclic if and only if there is at most one zero weight

first integrals and symmetries of time dependent hamiltonian systems in this paper first integrals of one dimensional time dependent hamiltonians h q p t are studied first of all it is shown that the second first integral j q h t t dq hp valid for autonomous hamiltonians h q p can be extended to the case of nonautonomous hamiltonians h q p t provided hp resp t is replaced with ip where i q p t is a first integral of h q p t resp a new time t j q i t t dq ip in a second part we derive a technique leading to a first integral i q p t from a lie symmetry as an example this technique together with the expression of the second first integral j q i t is used to completely integrate a special case of the linear harmonic oscillator with a time dependent frequency as a result lewis first integral is recovered from a lie symmetry in a way that generalizes the recent work of shivamoggi and muilenberg phys lett a 154 1 1991

solutions of a toda equations based on noncompact group su 1 1 and infinite dimensional grassmann manifolds special solutions of a toda equations are constructed based on noncompact group su 1 1 these solutions are derived from the holomorphic construction of infinite dimensional nonlinear grassmann models it is also shown that the solutions give a family of solutions of self dual einstein equations in a certain continuum limit

nonadiabatic holonomy operators in classical and quantum completely integrable systems given a completely integrable system we associate to any connection on a fiber bundle in invariant tori over a parameter manifold the classical and quantum holonomy operator generalized berry s phase factor without any adiabatic approximation

covariant hamilton equations for field theory we study the relations between the equations of first order lagrangian field theory on fibre bundles and the covariant hamilton equations on the finite dimensional polysymplectic phase space of covariant hamiltonian field theory if a lagrangian is hyperregular these equations are equivalent a degenerate lagrangian requires a set of associated hamiltonian forms in order to exhaust all solutions of the euler lagrange equations the case of quadratic degenerate lagrangians is studied in detail

hamiltonian time dependent mechanics the usual formulation of time dependent mechanics implies a given splitting y r m of an event space y this splitting however is broken by any time dependent transformation including transformations between inertial frames the goal is the frame covariant formulation of time dependent mechanics on a bundle y r whose fibration y m is not fixed its phase space is the vertical cotangent bundle v y provided with the canonical 3 form and the corresponding canonical poisson structure an event space of relativistic mechanics is a manifold z whose fibration z r is not fixed

on a question of leiss regarding the hanoi tower problem the tower of hanoi problem is generalized in such a way that the pegs are located at the vertices of a directed graph g and moves of disks may be made only along edges of g leiss obtained a complete characterization of graphs in which arbitrarily many disks can be moved from the source vertex s to the destination vertex d here we consider graphs which do not satisfy this characterization hence there is a bound on the number of disks which can be handled denote by gn the maximal such number as g varies over all such graphs with n vertices and s d vary over the vertices answering a question of leiss finite hanoi problems how many discs can be handled congr numer 44 1984 221 229 we prove that gn grows sub exponentially fast moreover there exists a constant c such that gn cn1 2 log2n for each n on the other hand for each e 0 there exists a constant ce 0 such that gn cen 1 2 e log2n for each n

on the quantization of presymplectic dynamical systems via coisotropic imbeddings we study certain aspects of the problem of quantizing a presymplectic dynamical system such a system is quantized by imbedding the presymplectic manifoldm under consideration into a symplectic manifoldx and then geometrically quantizing the latter it is known that this procedure will yield consistent results provided the imbeddingm x is coisotropic we show that such imbeddings always exist and are locally unique furthermore we investigate the extent to which the resulting quantum dynamics is independent of the choice of coisotropic imbedding that is we examine to what extent the presymplectic phase spacem determines the quantum representation space and the quantization of observables the quantization is carried out within the geometric quantization framework of kostant and souriau

identification of dynamical lie algebras for finite level quantum control systems the problem of identifying the dynamical lie algebras of finite level quantum systems subject to external control is considered with special emphasis on systems that are not completely controllable in particular it is shown that the dynamical lie algebra for an n level system with symmetrically coupled transitions such as a system with equally spaced energy levels and uniform transition dipole moments is a subalgebra of so n if n 2 1 and a subalgebra of sp if n 2 general criteria for obtaining either so 2 1 or sp are established

covariant geometric quantization of nonrelativistic time dependent mechanics we provide geometric quantization of the vertical cotangent bundle v q q r equipped with the canonical poisson structure and treated as a momentum phase space of nonrelativistic time dependent mechanics we show that this quantization is equivalent to fiberwise quantization of symplectic fibers of v q r and that the quantum algebra of time dependent mechanics is an instantwise algebra quantization of the classical evolution equation defines a connection on this instantwise algebra and describes quantum evolution in time dependent mechanics as a parallel transport

geometric quantization of time dependent completely integrable hamiltonian systems a time dependent completely integrable hamiltonian system is quantized with respect to time dependent action angle variables near an instantly compact regular invariant manifold its hamiltonian depends only on action variables and has a time independent countable energy spectrum

the worst hanoi graphs the towers of hanoi is a problem that has been extensively studied and frequently generalized we are interested in its generalization to arbitrary directed graphs and ask how many moves are required in a given graph to move n disks from the starting peg to the destination peg not all directed graphs allow solving this problem we will call those graphs that do hanoi graphs we settle the question of what are the hanoi graphs that require the largest number of moves

the relation between the berry and the anandan aharonov connections for u n bundles the geometric phase has been defined as the holonomy of two bundles with different base spaces and different connections in this article we establish the relation between the berry simon and the anandan aharonov definitions for a large class of cyclic hamiltonians with n fold degeneracy using the classifying theorem for principal fiber bundles

compression of quasianalytic spectral sets of cyclic contractions the class l0 h of cyclic quasianalytic contractions was studied in kerchy 2011 12 the subclass l1 h consists of those operators t in l0 h whose quasianalytic spectral set t covers the unit circle t the contractions in l1 h have rich invariant subspace lattices in this paper it is shown that for every operator t l0 h there exists an operator t1 l1 h commuting with t thus the hyperinvariant subspace problems for the two classes are equivalent the operator t1 is found as an h function of t the existence of an appropriate function compressing t to the whole circle is proved using potential theoretic tools by constructing a suitable regular compact set on t with absolutely continuous equilibrium measure

geometric quantization of mechanical systems with time dependent parameters quantum systems with adiabatic classical parameters are widely studied e g in the modern holonomic quantum computation we here provide complete geometric quantization of a hamiltonian system with time dependent parameters without the adiabatic assumption a hamiltonian of such a system is affine in the temporal derivative of parameter functions this leads to the geometric berry factor phenomena

constraints reduction and quantization theorems are proved that establish the unitary equivalence of the extended and reduced phase space quantizations of a constrained classical system with symmetry several examples are presented

on the geometric quantization of poisson manifolds in a paper by huebschmann j reine angew math 408 57 1990 the geometric quantization of poisson manifolds appears as a particular case of the quantization of poisson algebras here this quantization is presented straightforwardly the results include a geometric prequantization integrality condition and its discussion in particular cases such as dirac brackets an adaptation of the notion of a polarization and a construction of a quantum hilbert space and a computational example in the last section of the paper the general prequantization representations in the sense of urwin adv math 50 126 1983 are described for the poisson and jacobi manifolds

constraints in hamiltonian time dependent mechanics the key point of the study of constraints in hamiltonian time dependent mechanics lies in the fact that a poisson structure does not provide dynamic equations and a poisson bracket of constraints with a hamiltonian is ill defined we describe hamiltonian dynamics in terms of hamiltonian forms and connections on the vertical cotangent bundle v q r seen as a momentum phase space a poisson bracket v on v q is induced by the canonical poisson bracket t on the cotangent bundle t q with v an algebra of first and second class time dependent constraints is described but we use the pull back of the evolution equation onto t x and the bracket t in order to extend the constraint algorithm to time dependent constraints the case of lagrangian constraints of a degenerate almost regular lagrangian is studied in detail one can assign to this lagrangian l a set of hamiltonian forms which are not necessarily degenerate such that any solution of the corresponding hamilton equations which lives in the lag