Quantum Physics

In [3], a simple quantum programming language is presented, together with both denotational and operational semantics. This language follows [24] in that it uses classical control with quantum data. Correspondence results between these semantics are stated; but not proved. We shall firstly prove these results. We shall also expand upon the dynamic logic approach given in [3] and give a full example to show how a formal verification of the Deutch-Josza algorithm can be performed in our framework.

We shall then reformulate the semantics of the language with respect to the abstract categorical quantum axiomatics in [6] and again prove the correspondence results with respect to these abstract semantics. This shall be novel in the following respects: Firstly, it shall be a language explicitly based on the recast axioms of quantum mechanics in [6]. Secondly, it shall provide operational semantics directly from the abstract category, something that is rarely seen. We shall then investigate the sense in which the original concrete semantics is a special case of the abstract semantics. The abstract semantics will use Peter Selinger’s CPM construction [23] since they will need to deal with probability distributions over states. Finally, we shall then investigate how it may be possible to develop the logical semantics at our abstract level (using subobjects to represent predicates.)

We live in a divided world dominated by a fragmentary worldview that treats the wholeness of the human family, urban environments, and social reality as inherently discrete, distanced, and disconnected. This fragmentary perspective, emerging from Greek dualism and fueled by the Newtonian mechanical view of the world with its Cartesian split of either/or understanding of reality, does not lead to wholeness. Almost all discussion of urban social policies emerges from a context of fragmented thinking. Drawing from quantum physics, this paper presents a theoretical framework, a new “context” for understanding urban environments and the implementing of programs of urban transformation, including faith-based programs. The paper examines examples of effective change agents who have made a difference in people’s lives. It culminates with an analysis of the Broken Window Theory and how the differences in approaches—fragmentation or wholeness—generate different results. The critical point is in recognizing the energy patterns and operative attractor fields from which emerge negative or positive patterns of behavior.

The accuracy reached in the past few years by Satellite Laser Ranging (SLR) allows for measuring even tiny features of the Earth's gravitational field predicted by Einstein's General Relativity by means of artificial satellites. The gravitomagnetic dragging of the orbit of a test body is currently under measurement by analyzing a suitable combination of the orbital residuals of LAGEOS and LAGEOS II. The lower bound of the error in this experiment amount to 12.92%. It is due to the mismodeling in the even zonal harmonics of the geopotential which are the most important sources of systematic error. A similar approach could be used in order to measure the relativistic gravitoelectric pericenter shift in the field of the Earth with a lower bound of the systematic relative error of 0.6% due to the even zonal harmonics as well. The inclusion of the ranging data to the Japanese passive geodetic satellite Ajisai would improve such limits to 10.78% and 0.08% respectively and would allow to improve the accuracy in the determination of the PPN parameters beta and gamma.

"We consider the recently estimated corrections
̟˙ to the Newtonian/
Einsteinian secular precessions of the longitudes of perihelia ̟ of several
planets of the Solar System in order to evaluate whether they are compatible with
the predicted precessions due to models of long-range modified gravity put forth
to account for certain features of the rotation curves of galaxies without resorting
to dark matter. In particular, we consider a logarithmic-type correction and a
f(R) inspired power-law modification of the Newtonian gravitational potential.
The results obtained by taking the ratio of the apsidal rates for different pairs
of planets show that the modifications of the Newtonian potentials examined in
this paper are not compatible with the secular extra-precessions of the perihelia
of the Solar System’s planets estimated by E.V. Pitjeva as solve-for parameters
processing almost one century of data with the latest EPM ephemerides."

We are building up a light scattering setup at the Instituto de Astrofísica de Andalucía (IAA), Granada, Spain. The design of this new setup is based on the well known apparatus currently located at the Astronomical Institute "Anton Pannekoek", University of Amsterdam, The Neteherlands [1],[2]. By using a polarization modulation technique, all scattering matrix elements as function of the scattering angle are obtained from 8 separate measurement runs. In this new setup we use an Argon-Kripton laser (483 nm, 488 nm, 514 nm, 568 nm, and 647 nm) as light source. The detectors are mounted on dove tails that allow their movement backward and forward. In addition, the detectors have been designed to minimize blockage of the laser beam at positions close to the forward and backward directions. In this way we intend to do measurements covering an angle range from 3 to 177 degrees. The alignment of the optics is automatically done and controlled from the computer reducing the measurement time.

The nonlinear dynamics of whistler waves in magnetized plasmas is studied. Since the plasmas and beam-plasma systems considered here are assumed to be weakly collisional, the point of reference for the analysis performed in the present paper is the system of hydrodynamic and field equations. The renormalization group method is applied to obtain dynamical equations for the slowly varying amplitudes of whistler waves. Further, it has been shown that the amplitudes of eigenmodes satisfy an infinite system of coupled nonlinear Schrödinger equations. In this sense, the whistler eigenmodes form a sort of a gas of interacting quasiparticles, while the slowly varying amplitudes can be considered as dynamical variables heralding the relevant information about the system. An important feature of the approach is that whistler waves do not perturb the initial uniform density of plasma electrons. The plasma response to the induced whistler waves consists in velocity redistribution which follows exactly the behavior of the whistlers. In addition, selection rules governing the nonlinear mode coupling have been derived, which represent another interesting peculiarity of the description presented here.

Based on the Vlasov–Maxwell equations describing self-consistent nonlinear beam dynamics and collective processes, the evolution of an intense sheet beam propagating through a periodic focusing field has been studied. It has been shown that in the case of a beam with uniform phase-space density, the Vlasov–Maxwell equations can be replaced exactly by the hydrodynamic equations with a triple adiabatic pressure law coupled with the Maxwell equations. We further demonstrate that starting from the system of hydrodynamic and Maxwell equations, a set of coupled nonlinear Schrödinger equations for the slowly varying amplitudes of density waves can be derived. In the case where a parametric resonance between a certain mode of density waves and the external focusing occurs, the slow evolution of the resonant amplitudes in the cold-beam limit is shown to be governed by a system of coupled Gross–Pitaevskii equations. Properties of the nonlinear Schrödinger equation as well as properties of the Gross–Pitaevskii equation are discussed, together with soliton and condensate formation in intense particle beams.

The present paper studies a feedback regulation problem that arises in at least two di erent biological applications. The feedback regulation problem under consideration may be interpreted as an adaptive control problem for tuning bifurcation parameters, and it has not been studied in the control literature. The goal of the paper is to formulate this problem and to present some preliminary results.

We survey recent work on non-linear recurrence equations that arise in computer science or combinatorics. We consider the examples of the height of digital trees, the QUICKSORT algorithm, height of binary search trees, and enumeration problems concerning random binary trees characterized by nodes and path lengths. In each case a singular perturbation analysis of the recurrence yields insights into the asymptotic behavior, such as limiting distributions and tail probabilities.

In this paper, we argue that members of Congress differ in their abilities to guide their sponsored and cosponsored bills through the legislative process. We discuss the prospects for generating systematic measures of effectiveness, and carry out the construction of such measures for the 106 th House of Representatives. Analysis of these measures reveals significant limitations on members of the minority party, on ideological extremists, and on women and minorities in their attempts to advance their legislative agendas. Further intriguing patterns of effectiveness at different stages of the legislative process emerge with important implications for theories of committee deference, party leadership, seniority, and the electoral connection. We discuss the prospects of extending our approach to include both houses of the 93 rd to the 110 th Congresses, to include amendment activities, and to account for the importance of bills, their referral committees, and their areas of substantive interest. Finally, we argue that these new measures can be important tools to address major questions of legislative behavior.

When browsing a digital library of research papers, it is natural to ask which authors are most influential in a particular topic. We present a probabilistic model that ranks authors based on their influence in particular areas of scientific research. This model combines several sources of information: citation information between documents as represented by PageRank scores, authorship data gathered through automatic information extraction, and the words in paper abstracts. We compare the performance of a topic model versus a smoothed language model by assessing the number of major award winners in the resulting ranked list of researchers.

When browsing a digital library of research papers, it is natural to ask which authors are most influential in a particular topic. We present a probabilistic model that ranks authors based on their influence in particular areas of scientific research. This model combines several sources of information: citation information between documents as represented by PageRank scores, authorship data gathered through automatic information extraction, and the words in paper abstracts. We compare the performance of a topic model versus a smoothed language model by assessing the number of major award winners in the resulting ranked list of researchers.

ABSTRACT: The guided, single-mode propagation of ultrashort optical pulses is commonly described by a well studied and understood generalized nonlinear Schrödinger equation. Here we present and discuss an extended version for multimode optical fibers and waveguides including polarization effects, high-order dispersion, Kerr and Raman nonlinearities, self-steepening effects, as well as wavelength-dependent mode coupling and nonlinear coefficients. We then investigate the symmetry properties of the nonlinear coupling coefficients for the cases of step-index and circularly symmetric conventional fibers and for microstructured fibers with hexagonal symmetry. Finally, we study the computational complexity of the proposed algorithm.

Log-periodic precursors have been identified before most and perhaps all financial crashes of the Twentieth Century, but efforts to statistically validate the leading model of log-periodicity, the Johansen-Ledoit-Sornette (JLS) model, have generally failed. The main feature of this model is that log-harmonic fluctuations in financial prices are driven by similar fluctuations in expected daily returns.

For the class of cylindrically symmetric velocity fields U(r, z, t) = {u(r, t), v(r, t), zγ (r, t)}, two infinite energy exact solutions of the three-dimensional incompressible Euler equations are exhibited that blow up at every point in space in finite time. The first solution is embedded within the second as a special case and in both cases v = 0. Both solutions represent three-dimensional vortices which take the form of hollow cylinders for which the vorticity vector is ω = (0, ω θ , 0). An analysis on characteristics shows how more general solutions can be constructed and analysed.

Implicit surface techniques provide useful tools for modeling and rendering smooth surfaces. Deriving implicit formulations for fractal representations extends the scope of implicit surface techniques to rough surfaces. Linear fractals modeled by recurrent iterated function systems may be defined implicitly using either geometric distance or escape time. Random fractals modeled using Perlin's noise function are already defined implicitly when described as ''hypertexture.''

Chinese checkers is a game played on a hexagonal grid. This regular hexagonal tesselation is an artifact of Euclidean geometry that provides a fair playing eld only for games of two, three, four or six players. Hyperbolic geometry allows tessallations of the plane by regular polygons with any number of sides. Hyperbolic versions of the chinese checkers board permit fair games with ve, seven and even more players.

Morse theory describes the relationship between a function's critical points and the homotopy t ype of the function's domain. The theorems of Morse theory were developed speci cally for functions on a manifold. This work adapts these theorems for use with parameterized families of implicit surfaces in computer graphics. The result is a theoretical basis for the determination of the global topology of an implicit surface, and supports the interactive modeling of implicit surfaces by direct manipulation of a topologically-correct triangulated representation.

Since a Lie group, G, is a smooth manifold, we can endow G with a Riemannian metric. Among all the Riemannian metrics on a Lie groups, those for which the left translations (or the right translations) are isometries are of particular interest because they take the group structure of G into account. As a consequence, it is possible to find explicit formulae for the Levi-Civita connection and the various curvatures, especially in the case of metrics which are both left and right-invariant. This chapter makes extensive use of results from a beautiful paper of Milnor .

In Chapter 2 we defined the notion of a manifold embedded in some ambient space, R N . In order to maximize the range of applications of the theory of manifolds it is necessary to generalize the concept of a manifold to spaces that are not a priori embedded in some R N . The basic idea is still that, whatever a manifold is, it is a topological space that can be covered by a collection of open subsets, U α , where each U α is isomorphic to some "standard model", e.g., some open subset of Euclidean space, R n . Of course, manifolds would be very dull without functions defined on them and between them. This is a general fact learned from experience: Geometry arises not just from spaces but from spaces and interesting classes of functions between them. In particular, we still would like to "do calculus" on our manifold and have good notions of curves, tangent vectors, differential forms, etc. The small drawback with the more general approach is that the definition of a tangent vector is more abstract. We can still define the notion of a curve on a manifold, but such a curve does not live in any given R n , so it it not possible to define tangent vectors in a simple-minded way using derivatives. Instead, we have to resort to the notion of chart. This is not such a strange idea. For example, a geography atlas gives a set of maps of various portions of the earth and this provides a very good description of what the earth is, without actually imagining the earth embedded in 3-space. The material of this chapter borrows from many sources, including Warner [111], Berger and Gostiaux [13], O'Neill [90], Do Carmo [36, 35], Gallot, Hulin and Lafontaine [44], Lang [72], Schwartz [103], Hirsch [56], Sharpe [107], Guillemin and Pollack [49], Lafontaine [69], Dubrovin, Fomenko and Novikov [38] and Boothby [14]. A nice (not very technical) exposition is given in Morita [85] (Chapter 1). The recent book by Tu [110] is also highly recommended for its clarity. Among the many texts on manifolds and differential geometry, the book by Choquet-Bruhat, DeWitt-Morette and Dillard-Bleick [29] stands apart because it is one of the clearest and most comprehensive (many proofs are omitted, but this can be an advantage!) Being written for (theoretical) physicists, it contains more examples and applications than most other sources.

Since a Lie group, G, is a smooth manifold, we can endow G with a Riemannian metric. Among all the Riemannian metrics on a Lie groups, those for which the left translations (or the right translations) are isometries are of particular interest because they take the group structure of G into account. As a consequence, it is possible to find explicit formulae for the Levi-Civita connection and the various curvatures, especially in the case of metrics which are both left and right-invariant. This chapter makes extensive use of results from a beautiful paper of Milnor .

A key challenge that will face nanotechnologies will be controlling the uncertainty introduced by stochastic selfassembly. In this paper we explore architectural and manufacturing strategies to cope with this uncertainty when assembling nanoarrays, crossbars composed of two orthogonal sets of coded parallel nanowires. Because the encodings of nanowires that are assembled into a nanoarray cannot be predicted in advance, a discovery process is needed and specialized decoding circuitry must be employed. We have developed a probabilistic method of analysis so that various design strategies can be evaluated.

Works that measure the substantive representation of minority interests based solely on roll call data have been criticized for ignoring more behind-the-scenes activities that legislators might perform on behalf of their constituents. We thus focus in this paper on cosponsorship as a proxy for the degree to which members maneuver to create coalitions that will advance the substantive policy goals of the minority community. We find, consistent with previous work, that minority legislators tend to provide more of these types of activities than do other types of legislators, but maximizing cosponsorship benefits for bills that pass Congress involves creating districts of about 45% black voting age population.

Using large-scale network analysis I map the cosponsorship networks of all 280,000 pieces of legislation proposed in the U.S. House and Senate from 1973 to 2004. In these networks, a directional link can be drawn from each cosponsor of a piece of legislation to its sponsor. I use a number of statistics to describe these networks such as the quantity of legislation sponsored and cosponsored by each legislator, the number of legislators cosponsoring each piece of legislation, the total number of legislators who have cosponsored bills written by a given legislator, and network measures of closeness, betweenness, and eigenvector centrality. I then introduce a new measure I call "connectedness" which uses information about the frequency of cosponsorship and the number of cosponsors on each bill to make inferences about the social distance between legislators. Connectedness predicts which members will pass more amendments on the floor, a measure that is commonly used as a proxy for legislative influence. It also predicts roll call vote choice even after controlling for ideology and partisanship.

We examine the fundamental concept of Popper's falsifiability within an economic model in which a tester hires a potential expert to produce a theory. Payments are made contingent on the performance of the theory vis-a-vis future realizations of the data. We show that if experts are strategic, then falsifiability has no power to distinguish legitimate scientific theories from worthless theories. We also show that even if experts are strategic there are alternative criteria that can distinguish legitimate from worthless theories. * We are grateful to Eddie Dekel, Yossi Feinberg, Nabil Al-Najjar, Sandeep Baliga, Roger Myerson, and Rakesh Vohra for comments and conversations. We also thank workshop participants at Brown,

In this paper we propose a 3D image reconstruction algorithm for a 3D Compton camera being developed at the University of Michigan. We present a mathematical model of the transition matrix of the camera which exploits symmetries by using an adapted spatial sampling pattern in the object domain. For each projection angle, the sampling pattern is uniform over a set of equispaced nested hemispheres. By using this sampling pattern the system matrix is reduced to a product of a (approximately) block circulant matrix and a sparse interpolation matrix. This representation reduces the very high storage and computation requirement inherent to 3D reconstruction using transition matrix inversion methods. We geometrically optimize our hemispherical sampling and propose a 3D volumetric interpolation. Finally, we present a 3D image reconstruction method which uses the Gauss-Seidel algorithm to minimize a penalized least square objective.

In this paper we propose a 3D image reconstruction algorithm for a 3D Compton camera being developed at the University of Michigan. We present a mathematical model of the transition matrix of the camera which exploits symmetries by using an adapted spatial sampling pattern in the object domain. For each projection angle, the sampling pattern is uniform over a set of equispaced nested hemispheres. By using this sampling pattern the system matrix is reduced to a product of a (approximately) block circulant matrix and a sparse interpolation matrix. This representation reduces the very high storage and computation requirement inherent to 3D reconstruction using transition matrix inversion methods. We geometrically optimize our hemispherical sampling and propose a 3D volumetric interpolation. Finally, we present a 3D image reconstruction method which uses the Gauss-Seidel algorithm to minimize a penalized least square objective.

This paper presents a new representation and corresponding set of genetic operators for a scheme to evolve quantum circuits with various properties. The scheme is a variant on the techniques of genetic programming and genetic algorithms, having components borrowed from each. By recognising the foundation of a quantum circuit as being a collection of gates, each operating on various categories of qubits and each taking parameters, the scheme can successfully search for most circuits. The algorithm is applied to the problem of entanglement production.

This paper presents the most general solutions to the two dimensional elliptic and hyperbolic Liouville equations using elementary techniques. It is demonstrated how previously known general solutions are special cases of these most general solutions.

We discuss some basic issues that arise when one attempts to model quantum mechanical systems on a computer, and we describe the mathematical structure of the resulting discretized cannonical commutation relations. The C *algebras associated with the discretized CCRs are the non-commutative spheres of Bratteli, Elliott, Evans and Kishimoto.

In probability theory all nonatomic probability measures look the same. That is because any two nonatomic separable measure algebras are isomorphic. Quantum probability theory is different: two normal states of B(H) are conjugate only when the eigenvalue lists of their density operators are the same. Suppose now that one is given an increasing sequence M 1 ⊆ M 2 ⊆ . . . of type I subfactors of B(H) whose union is weak * -dense in B(H). Common sense suggests that if one restricts a normal state ρ of B(H) to M n and considers its eigenvalue list Λ n for large n, then Λ n should be close to the eigenvalue list of ρ when n is large.

Let X = {λ1, . . . , λN } be a finite set of complex numbers and let A be a normal operator with spectrum X that acts on a separable Hilbert space H. Relative to a fixed orthonormal basis e1, e2, . . . for H, A gives rise to a matrix whose diagonal is a sequence d = (d1, d2, . . . ) with the property that each of its terms dn belongs to the convex hull of X. Not all sequences with that property can arise as the diagonal of a normal operator with spectrum X.

Normal endomorphisms of von Neumann algebras need not be extendable to automorphisms of a larger von Neumann algebra, but they always have asymptotic lifts. We describe the structure of endomorphisms and their asymptotic lifts in some detail, and apply those results to complete the identification of asymptotic lifts of unital completely positive linear maps on von Neumann algebras in terms of their minimal dilations to endomorphisms.

We consider an example of strongly non-local interaction in incompressible magnetohydrodynamic (MHD) turbulence which corresponds to the case where the Alfvén waves travelling in the opposite directions have essentially different characteristic wavelengths. We use two approaches to the dynamics of turbulent Alfvénic wavepackets: the first is a geometrical WKB theory [Phys. Lett. A 165 (1992) 330] and the second one is a three-wave kinetic equation derived for weakly turbulent waves [J. Plasma Phys., in press]. We show that these theories have a common limit of weak turbulence with scale separation in which they both predict the same Fokker-Planck equation for the wave power spectrum. In both cases the packet wavenumbers (and therefore the Lagrangian field-line separations) are allowed to experience order 1 changes. The WKB theory developed here formalises an intuitive geometrical argument of Goldreich and Sridhar [ApJ 485 (1997) 680] and allows one to see where such an intuition leads to a wrong conclusion about the inapplicability of the three-wave kinetic equation for order 1 wavepacket distortions. We show that the exponent of the constant flux non-local spectrum matches the value previously found for local turbulence at the boundary of the locality interval. The relationship between the WKB theory and the weak turbulence theory found in this paper for an ensemble of Alfvén waves seems to be general for three-wave systems.

This Letter demonstrates that the kinetic equations for wave turbulence, the long time statistical behavior of a sea of weakly coupled, dispersive waves, will almost always develop solutions for which the theory fails due to strongly nonlinear and intermittent events either at small or large scales.  (A.C. Newell). 0375-9601/01/$ -see front matter  2001 Elsevier Science B.V. All rights reserved. PII: S 0 3 7 5 -9 6 0 1 ( 0 1 ) 0 0 0 1 6 -0

We report a numerical study of turbulence and Bose-Einstein condensation within the two-dimensional Gross-Pitaevsky model with repulsive interaction. In the presence of weak forcing localized around some wave number in the Fourier space, we observe three qualitatively different evolution stages. At the initial stage a thermodynamic energy equipartition spectrum forms at both smaller and larger scales with respect to the forcing scale. This agrees with predictions of the four-wave kinetic equation of the Wave Turbulence (WT) theory. At the second stage, WT breaks down at large scales and the interactions become strongly nonlinear. Here, we observe formation of a gas of quantum vortices whose number decreases due to an annihilation process helped by the acoustic component. This process leads to formation of a coherent-phase Bose-Einstein condensate. After such a coherent-phase condensate forms, evolution enters a third stage characterised by three-wave interactions of acoustic waves that can be described again using the WT theory.

We present a brief review of the application of boundary integral methods in two dimensions to multicomponent fluid flows and multiphase problems in materials science. We focus on the recent development and outcomes of methods which accurately and efficiently include surface tension. In fluid flows, we examine the effects of surface tension on the Kelvin-Helmholtz and Rayleigh-Taylor instabilities in inviscid fluids, the generation of capillary waves on the free surface, and problems in Hele-Shaw flows involving pattern formation through the Saffman-Taylor instability, pattern selection, and singularity formation. In materials science, we discuss microstructure evolution in diffusional phase transformations, and the effects of the competition between surface and elastic energies on microstructure morphology. A common link between these different physical phenomena is the utility of an analysis of the appropriate equations of motion at small spatial scales to develop accurate and efficient time-stepping methods.

If ψ is a bijection from C n onto a complex manifold M, which conjugates every holomorphic map in C n to an endomorphism in M, then we prove that ψ is necessarily biholomorphic or antibiholomorphic. This extends a result of A. Hinkkanen to higher dimensions. As a corollary, we prove that if there is an epimorphism from the semigroup of all holomorphic endomorphisms of C n to the semigroup of holomorphic endomorphisms in M, or an epimorphism in the opposite direction for a doubly-transitive M, then it is given by conjugation by some biholomorphic or antibiholomorphic map. We show also that there are two unbounded domains in C n with isomorphic endomorphism semigroups but which are neither biholomorphically nor antibiholomorphically equivalent.

This is one in a series of papers devoted to the foundations of Symplectic Field Theory sketched in [EGH]. We prove compactness results for moduli spaces of holomorphic curves arising in Symplectic Field Theory. The theorems generalize Gromov's compactness theorem in [Gr] as well as compactness theorems in Floer homology theory, [F1, F2], and in contact geometry, .