entropy of random quantum states the authors use a simple generating function to calculate exactly the entropy of random quantum states for finite dimensional hilbert spaces over real complex and quaternionic scalars this allows them to extend their previous formula for the quantum correlation information of a state determination apparatus to include real and quaternionic von neumann analysers

separation of unistochastic matrices from the double stochastic ones recovery of a 3 3 unitary matrix from experimental data the aim of the paper is to provide a constructive method for recovering a unitary matrix from experimental data since there is a natural immersion of unitary matrices within the set of double stochastic ones the problem to solve is to find necessary and sufficient criteria that separate the two sets a complete solution is provided for the three dimensional case accompanied by a 2 test necessary for the reconstruction of a unitary matrix from error affected data

entropy and hadamard matrices the entropy of an orthogonal matrix is defined it provides a new interpretation of hadamard matrices as those that saturate the bound for entropy it appears to be a useful morse function on the group manifold it has sharp maximum and other saddle points the matrices corresponding to the maxima for three and five dimensions are presented they are integer matrices up to a rescaling

moment based evidence for simple rational valued hilbert schmidt generic 2 2 separability probabilities employing the hilbert schmidt measure we explicitly compute and analyze a number of determinantal product bivariate moments k pt n k n 0 1 2 3 with pt denoting the partial transpose for both generic 9 dimensional two rebit and generic 15 dimensional two qubit 1 density matrices the results are then incorporated into a general formula parameterized by k n and with the case 2 presumptively corresponding to generic 27 dimensional quaternionic systems holding the dyson index like parameter fixed the induced univariate moments pt n and pt n are inputted into a legendre polynomial based least squares probability distribution reconstruction algorithm of provost 2005 mathematica j 9 727 yielding specific separability probability estimates since as the number of inputted moments grows estimates based on the variable pt strongly decrease while ones employing pt strongly increase and converge faster the gaps between upper and lower estimates diminish yielding sharper and sharper bounds remarkably for 2 with the use of 2325 moments a separability probability lower bound 0 999 999 987 as large as is found for 1 based on 2415 moments a lower bound results that is 0 999 997 066 times as large as a simpler still fractional value that had previously been conjectured slater 2007 j phys a math theor 40 14279 furthermore for employing 3310 moments the lower bound is 0 999 955 times as large as a rational value previously considered slater 2010 j phys a math theor 43 195302

majorization entropic uncertainty relations entropic uncertainty relations in a finite dimensional hilbert space are investigated making use of the majorization technique we derive explicit lower bounds for the sum of r enyi entropies describing probability distributions associated with a given pure state expanded in eigenbases of two observables obtained bounds are expressed in terms of the largest singular values of submatrices of the unitary rotation matrix numerical simulations show that for a generic unitary matrix of size n 5 our bound is stronger than the well known result of maassen and uffink mu with a probability larger than 98 we also show that the bounds investigated are invariant under the dephasing and permutation operations finally we derive a classical analogue of the mu uncertainty relation which is formulated for stochastic transition matrices

intertwining operators associated to the group for any finite reflection group g on an euclidean space there is a parametrized commutative algebra of differential difference operators with as many parameters as there are conjugacy classes of reflections in g there exists a linear isomorphism on polynomials which intertwines this algebra with the algebra of partial differential operators with constant coefficients for all but a singular set of parameter values containing only certain negative rational numbers this paper constructs an integral transform implementing the intertwining operator for the group s3 the symmetric group on three objects for parameter value the transform is realized as an absolutely continuous measure on a compact subset of m2 r which contains the group as a subset of its boundary the construction of the integral formula involves integration over the unitary group u 3 associated to any finite reflection group g on an euclidean space there is a parametrized commutative algebra of differential difference operators with as many parameters as there are conjugacy classes of reflections in g it has been shown that there exists a linear isomorphism on polynomials which intertwines this algebra with the algebra of partial differential operators with constant coefficients for all but a singular set of parameter values this singular set contains only negative values and is closely linked to the zero set of the poincare series of g this paper constructs an integral transform implementing the intertwining map for the group s3 the symmetric group on three objects for positive parameter values previously this had been done only for the group z2 acting by sign change on r where the transform is a classical fractional integral the transform in this paper has its origin in the adjoint action of the unitary group u 3 on the linear space of real diagonal 3 x 3 matrices the complexification of the maximal torus this will lead to a transform realized as an absolutely continuous measure on a certain compact subset of m2 r here is a concise statement of the main result rephrased from formulas 5 1 5 6 the operator v intertwines the differential difference operators received by the editors august 22 1994 1991 mathematics subject classification primary 22e30 33c80 secondary 33c50 20b30

blended ausm method for all speeds and all grid aspect ratios an ausm based discretization method using an explicit third order discretization for the convective part and a line implicit central discretization for the acoustic part and for the diffusive part has been developed for incompressible and low speed compressible navier stokes equations the lines are chosen in the direction of the gridpoints with shortest connection the semi implicit line method is used in multistage form because of the explicit third order discretization of the convective part multigrid is used as acceleration technique because of the implicit treatment of the acoustic and the diffusive terms the stiffness otherwise caused by high aspect ratio cells is removed low mach number stiffness is treated by a preconditioning technique to ensure physical correct behavior of the discretization for vanishing mach number extreme care has been taken for vanishing mach number stabilization terms are added to the mass flux pressure and temperature stabilization terms are necessary the coefficients of these terms are chosen so that correct scaling with mach number is obtained a blend of the low speed algorithm with the original ausm algorithm developed for high speed applications has been constructed so that the resulting algorithm can be used at all speeds

locality for quantum systems on graphs depends on the number field adapting a definition of aaronson and ambainis 2005 theory comput 1 47 79 we call a quantum dynamics on a digraph saturated z local if the nonzero transition amplitudes specifying the unitary evolution are in exact correspondence with the directed edges including loops of the digraph this idea appears recurrently in a variety of contexts including angular momentum quantum chaos and combinatorial matrix theory complete characterization of the digraph properties that allow such a process to exist is a long standing open question that can also be formulated in terms of minimum rank problems we prove that saturated z local dynamics involving complex amplitudes occur on a proper superset of the digraphs that allow restriction to the real numbers or even further the rationals consequently among these fields complex numbers guarantee the largest possible choice of topologies supporting a discrete quantum evolution a similar construction separates complex numbers from the skew field of quaternions the result proposes a concrete ground for distinguishing between complex and quaternionic quantum mechanics

embedded function approach for turbulent flow prediction in conventional prediction methods for turbulent flow influence on surface properties very small mesh sizes and considerable computational effort is required to adequately resolve the intense velocity and temperature profile variations that occur in the wall layer region in this study an approach is described wherein an outer region numerical solution is smoothly matched to a set of embedded analytic profile functions in the near wall region these wall layer profile functions having been derived through consideration of the coherent structure of the time dependent near wall flow provide analytic expressions for the mean velocity and enthalpy profiles in the wall layer the concept is demonstrated through example applications to turbulent boundary layer flows in two dimensions the technique is shown to be very efficient and it is demonstrated that a reduction of approximately half the mesh points across the 2 d layer may be realized as compared to conventional methods with no degradation in accuracy

all teleportation and dense coding schemes we establish a one to one correspondence between 1 quantum teleportation schemes 2 dense coding schemes 3 orthonormal bases of maximally entangled vectors 4 orthonormal bases of unitary operators with respect to the hilbert schmidt scalar product and 5 depolarizing operations whose kraus operators can be chosen to be unitary the teleportation and dense coding schemes are assumed to be tight in the sense that all hilbert spaces involved have the same finite dimension d and the classical channel involved distinguishes d 2 signals a general construction procedure for orthonormal bases of unitaries involving latin squares and complex hadamard matrices is also presented

defect stream function law of the wall wake method for turbulent boundary layers a law of the wall law of the wake formulation for the inner part of the boundary layer is presented that greatly simplifies the computational task near the wall and eliminates the need for an eddy viscosity model in this region the eddy viscosity model in the outer part of the boundary layer is arbitrary formulations for both equilibrium and nonequilibrium boundary layers are presented and results are compared with previous methods for equilibrium boundary layers

unitary stochastic matrix ensembles and spectral statistics we propose to study unitary matrix ensembles defined in terms of unitary stochastic transition matrices associated with markov processes on graphs we argue that the spectral statistics of such an ensemble after ensemble averaging depends crucially on the spectral gap between the leading and subleading eigenvalue of the underlying transition matrix it is conjectured that unitary stochastic ensembles follow one of the three standard ensembles of random matrix theory in the limit of infinite matrix size n if the spectral gap of the corresponding transition matrices closes slower than 1 n the hypothesis is tested by considering several model systems ranging from binary graphs to uniformly and non uniformly connected star graphs and diffusive networks in arbitrary dimensions

random bistochastic matrices ensembles of random stochastic and bistochastic matrices are investigated while all columns of a random stochastic matrix can be chosen independently the rows and columns of a bistochastic matrix have to be correlated we evaluate the probability measure induced into the birkhoff polytope of bistochastic matrices by applying the sinkhorn algorithm to a given ensemble of random stochastic matrices for matrices of order n 2 we derive explicit formulae for the probability distributions induced by random stochastic matrices with columns distributed according to the dirichlet distribution for arbitrary n we construct an initial ensemble of stochastic matrices which allows one to generate random bistochastic matrices according to a distribution locally flat at the center of the birkhoff polytope the value of the probability density at this point enables us to obtain an estimation of the volume of the birkhoff polytope consistent with recent asymptotic results

on the reconstruction of a unitary matrix from its moduli we study the problem of reconstructing a unitary matrix from the knowledge of the moduli of its matrix elements first in the case of a symmetric matrix which could be thes matrix forn coupled channels second in the case of a non symmetric matrix like the cabibbo kobayashi maskawa matrix forn generations of quarks and leptons in the symmetric case we find conditions under which the problem has 2 n 2 3n 2 solutions differing in a non trivial way but also situations where one has continuous ambiguities

simultaneous solution algorithms for eulerian eulerian gas solid flow models stability analysis and convergence behaviour of a point and a plane solver simultaneous solution algorithms for eulerian eulerian gas solid flow models are presented and their stability analyzed the integration algorithms are based on dual time stepping with fourth order runge kutta in pseudo time the domain is solved point or plane wise the discretization of the inviscid terms is based on a low mach limit of the multi phase preconditioned advection upstream splitting method mp ausmp the numerical stability of the simultaneous solution algorithms is analyzed in 2d with the fourier method stability results are compared with the convergence behaviour of 3d riser simulations the impact of the grid aspect ratio preconditioning artificial dissipation and the treatment of the source terms is investigated a particular advantage of the simultaneous solution algorithms is that they allow a fully implicit treatment of the source terms which are of crucial importance for the eulerian eulerian gas solid flow models and their solution the numerical stability of the optimal simultaneous solution algorithm is analyzed for different solids volume fractions and gas solid slip velocities furthermore the effect of the grid resolution on the convergence behaviour and the simulation results is investigated finally simulations of the bottom zone of a pilot scale riser with a side solids inlet are experimentally validated

volume of the set of unistochastic matrices of order 3 and the mean jarlskog invariant a bistochastic matrix b of size n is called unistochastic if there exists a unitary u such that bij uij 2 for i j 1 n the set u3 of all unistochastic matrices of order n 3 forms a proper subset of the birkhoff polytope which contains all bistochastic doubly stochastic matrices we compute the volume of the set u3 with respect to the flat lebesgue measure and analytically evaluate the mean entropy of an unistochastic matrix of this order we also analyze the jarlskog invariant j defined for any unitary matrix of order three and derive its probability distribution for the ensemble of matrices distributed with respect to the haar measure on u 3 and for the ensemble which generates the flat measure on the set of unistochastic matrices for both measures the probability of finding j smaller than the value observed for the cabbibo kobayashi maskawa matrix which describes the violation of the cp parity is shown to be small similar statistical reasoning may also be applied to the maki nakagawa sakata matrix which plays role in describing the neutrino oscillations some conjectures are made concerning analogous probability measures in the space of unitary matrices in higher dimensions

random unistochastic matrices an ensemble of random unistochastic orthostochastic matrices is defined by taking squared moduli of elements of random unitary orthogonal matrices distributed according to the haar measure on u n or o n an ensemble of symmetric unistochastic matrices is obtained with use of unitary symmetric matrices pertaining to the circular orthogonal ensemble we study the distribution of complex eigenvalues of bistochastic unistochastic and orthostochastic matrices in the complex plane we compute averages entropy traces over the ensembles of unistochastic matrices and present inequalities concerning the entropies of products of bistochastic matrices

product of two diagonal entries of a 3 by 3 normal matrix abstract the set of product of two diagonal entries of 3 by 3 normal matrices unitarily similar to a diagonal matrix is a triangle if the diagonal entries form an acute angled triangle inscribed to the unit circle

a multigrid semi implicit line method for viscous incompressible and low mach number flows on high aspect ratio grids abstract discretization of viscous incompressible and viscous low mach number flows often leads to a system of equations which is very difficult to solve there are two reasons first the use of high aspect ratio grids results in a very numerically anisotropic behaviour of the diffusive and acoustic terms and second in low mach number flow the ratio of the convective and acoustic eigenvalues of the inviscid system becomes very high we implemented an ausm based discretization method using an explicit third order discretization for the convective part and a line implicit central discretization for the acoustic part and for the diffusive part the lines are chosen in the direction of the grid points with shortest connection the preconditioned semi implicit line method is used in multistage form because of the explicit third order discretization of the convective part multigrid is used as an acceleration technique it is shown that the convergence is very good independent of grid aspect ratio and mach number

development of low diffusion flux splitting methods for dense gas solid flows the development of a class of low diffusion upwinding methods for computing dense gas solid flows is presented in this work an artificial compressibility low mach preconditioning strategy is developed for a hyperbolic two phase flow equation system consisting of separate solids and gas momentum and continuity equations the eigenvalues of this system are used to devise extensions of the ausm 1 and ldfss 2 flux splitting methods that provide high resolution capturing of bubble growth and collapse in gas solid fluidized beds applications to several problems in fluidization are presented

preconditioned methods for solving the incompressible low speed compressible equations abstract acceleration methods are presented for solving the steady state incompressible equations these systems are preconditioned by introducing artificial time derivatives which allow for a faster convergence to the steady state we also consider the compressible equations in conservation form with slow flow two arbitrary functions and are introduced in the general preconditioning an analysis of this system is presented and an optimal value for is determined given a constant it is further sown that the resultant incompressible equations form a symmetric hyperbolic system and so are well posed several generalizations to the compressible equations are presented which extend previous results

birkhoff s polytope and unistochastic matrices n 3 and n 4 the set of bistochastic or doubly stochastic n n matrices is a convex set called birkhoff s polytope which we describe in some detail our problem is to characterize the set of unistochastic matrices as a subset of birkhoff s polytope for n 3 we present fairly complete results for n 4 partial results are obtained an interesting difference between the two cases is that there is a ball of unistochastic matrices around the van der waerden matrix for n 3 while this is not the case for n 4

families of line graphs and their quantization any directed graph g with n vertices and j edges has an associated line graph l g where the j edges form the vertices of l g we show that the non zero eigenvalues of the adjacency matrices are the same for all graphs of such a family ln g we give necessary and sufficient conditions for a line graph to be quantisable and demonstrate that the spectra of associated quantum propagators follow the predictions of random matrices under very general conditions line graphs may therefore serve as models to study the semiclassical limit of large matrix size of a quantum dynamics on graphs with fixed classical behaviour

a new flux splitting scheme a new flux splitting scheme is proposed the scheme is remarkably simple and yet its accuracy rivals and in some cases surpasses that of roe s solver in the euler and navier stokes solutions carried out in this study the scheme is robust and converges as fast as the roe splitting we propose an appropriately defined cell face advection mach number using values from the two straddling cells via associated characteristic speeds this interface mach number is then used to determine the upwind extrapolation for the convective quantities accordingly the name of the scheme is coined as the advection upstream splitting method ausm we also introduce a new pressure splitting which is shown to behave successfully yielding much smoother results than other existing pressure splittings of particular interest is the supersonic blunt body problem in which the roe scheme gives anomalous solutions the ausm produces correct solutions without difficulty for a wide range of flow conditions as well as grids

classical 1d maps quantum graphs and ensembles of unitary matrices we study a certain class of classical one dimensional piecewise linear maps for these systems we introduce an infinite family of markov partitions in equal cells the symbolic dynamics generated by these systems is described by bi stochastic doubly stochastic matrices we analyse the structure of graphs generated from the corresponding symbolic dynamics we demonstrate that the spectra of quantized graphs corresponding to the regular classical systems have locally poissonian statistics while quantized graphs derived from classically chaotic systems display statistical properties characteristic of the circular unitary ensemble even though the corresponding unitary matrices are sparse

preconditioning applied to variable and constant density flows a time derivative preconditioning of the navier stokes equations suitable for both variable and constant density fluids is developed the ideas of low mach number preconditioning and artificial compressibility are combined into a unified approach designed to enhance convergence rates of density based time marching schemes for solving flows of incompressible and variable density fluids at all speeds the preconditioning is coupled with a dual time stepping scheme implemented within an explicit multistage algorithm for solving time accurate flows the resultant time integration scheme is used in conjunction with a finite volume discretization designed for unstructured solution adaptive mesh topologies this method is shown to provide accurate steady state solutions for transonic and low speed flow of variable density fluids the time accurate solution of unsteady incompressible flow is also demonstrated