Social differences in women's use of personal care products: A study of magazine advertisements, 1950 - 1994

This study examined advertising for women's personal care products from 1950 through 1994 in widely read, long-lived magazines whose audience have different demographic profiles: Ladies' Home Journal, Mademoiselle, and Essence

Two-body scattering in a trap and a special periodic phenomenon sensitive to the interaction

Two-body scattering of neutral particles in a trap is studied theoretically. The control of the initial state is realized by using optical traps. The collisions inside the trap occur repeatedly; thereby the effect of interaction can be accumulated. Two periodic phenomena with a shorter and a much longer period, respectively, are found. The latter is sensitive to the interaction. Instead of measuring the differential cross section as usually does, the measurement of the longer period and the details of the periodic behavior might be a valid source of information on weak interactions among neutral particles.Comment: 5 pages, 5 figure

The Information Geometry of the Ising Model on Planar Random Graphs

It has been suggested that an information geometric view of statistical mechanics in which a metric is introduced onto the space of parameters provides an interesting alternative characterisation of the phase structure, particularly in the case where there are two such parameters -- such as the Ising model with inverse temperature $\beta$ and external field $h$. In various two parameter calculable models the scalar curvature ${\cal R}$ of the information metric has been found to diverge at the phase transition point $\beta_c$ and a plausible scaling relation postulated: ${\cal R} \sim |\beta- \beta_c|^{\alpha - 2}$. For spin models the necessity of calculating in non-zero field has limited analytic consideration to 1D, mean-field and Bethe lattice Ising models. In this letter we use the solution in field of the Ising model on an ensemble of planar random graphs (where $\alpha=-1, \beta=1/2, \gamma=2$) to evaluate the scaling behaviour of the scalar curvature, and find ${\cal R} \sim | \beta- \beta_c |^{-2}$. The apparent discrepancy is traced back to the effect of a negative $\alpha$.Comment: Version accepted for publication in PRE, revtex

Adapt Or Die: Polynomial Lower Bounds For Non-Adaptive Dynamic Data Structures

In this paper, we study the role non-adaptivity plays in maintaining dynamic data structures. Roughly speaking, a data structure is non-adaptive if the memory locations it reads and/or writes when processing a query or update depend only on the query or update and not on the contents of previously read cells. We study such non-adaptive data structures in the cell probe model. The cell probe model is one of the least restrictive lower bound models and in particular, cell probe lower bounds apply to data structures developed in the popular word-RAM model. Unfortunately, this generality comes at a high cost: the highest lower bound proved for any data structure problem is only polylogarithmic (if allowed adaptivity). Our main result is to demonstrate that one can in fact obtain polynomial cell probe lower bounds for non-adaptive data structures. To shed more light on the seemingly inherent polylogarithmic lower bound barrier, we study several different notions of non-adaptivity and identify key properties that must be dealt with if we are to prove polynomial lower bounds without restrictions on the data structures. Finally, our results also unveil an interesting connection between data structures and depth-2 circuits. This allows us to translate conjectured hard data structure problems into good candidates for high circuit lower bounds; in particular, in the area of linear circuits for linear operators. Building on lower bound proofs for data structures in slightly more restrictive models, we also present a number of properties of linear operators which we believe are worth investigating in the realm of circuit lower bounds

Complex Extension of Quantum Mechanics

It is shown that the standard formulation of quantum mechanics in terms of Hermitian Hamiltonians is overly restrictive. A consistent physical theory of quantum mechanics can be built on a complex Hamiltonian that is not Hermitian but satisfies the less restrictive and more physical condition of space-time reflection symmetry (PT symmetry). Thus, there are infinitely many new Hamiltonians that one can construct to explain experimental data. One might expect that a quantum theory based on a non-Hermitian Hamiltonian would violate unitarity. However, if PT symmetry is not spontaneously broken, it is possible to construct a previously unnoticed physical symmetry C of the Hamiltonian. Using C, an inner product is constructed whose associated norm is positive definite. This construction is completely general and works for any PT-symmetric Hamiltonian. Observables exhibit CPT symmetry, and the dynamics is governed by unitary time evolution. This work is not in conflict with conventional quantum mechanics but is rather a complex generalisation of it.Comment: 4 Pages, Version to appear in PR

Research on nonlinear optical materials: an assessment. IV. Photorefractive and liquid crystal materials

This panel considered two separate subject areas: photorefractive materials used for nonlinear optics and liquid crystal materials used in light valves. Two related subjects were not considered due to lack of expertise on the panel: photorefractive materials used in light valves and liquid crystal materials used in nonlinear optics. Although the inclusion of a discussion of light valves by a panel on nonlinear optical materials at first seems odd, it is logical because light valves and photorefractive materials perform common functions

Martingale Models for Quantum State Reduction

Stochastic models for quantum state reduction give rise to statistical laws that are in most respects in agreement with those of quantum measurement theory. Here we examine the correspondence of the two theories in detail, making a systematic use of the methods of martingale theory. An analysis is carried out to determine the magnitude of the fluctuations experienced by the expectation of the observable during the course of the reduction process and an upper bound is established for the ensemble average of the greatest fluctuations incurred. We consider the general projection postulate of L\"uders applicable in the case of a possibly degenerate eigenvalue spectrum, and derive this result rigorously from the underlying stochastic dynamics for state reduction in the case of both a pure and a mixed initial state. We also analyse the associated Lindblad equation for the evolution of the density matrix, and obtain an exact time-dependent solution for the state reduction that explicitly exhibits the transition from a general initial density matrix to the L\"uders density matrix. Finally, we apply Girsanov's theorem to derive a set of simple formulae for the dynamics of the state in terms of a family of geometric Brownian motions, thereby constructing an explicit unravelling of the Lindblad equation.Comment: 30 pages LaTeX. Submitted to Journal of Physics

Classical Tensors and Quantum Entanglement I: Pure States

The geometrical description of a Hilbert space asociated with a quantum system considers a Hermitian tensor to describe the scalar inner product of vectors which are now described by vector fields. The real part of this tensor represents a flat Riemannian metric tensor while the imaginary part represents a symplectic two-form. The immersion of classical manifolds in the complex projective space associated with the Hilbert space allows to pull-back tensor fields related to previous ones, via the immersion map. This makes available, on these selected manifolds of states, methods of usual Riemannian and symplectic geometry. Here we consider these pulled-back tensor fields when the immersed submanifold contains separable states or entangled states. Geometrical tensors are shown to encode some properties of these states. These results are not unrelated with criteria already available in the literature. We explicitly deal with some of these relations.Comment: 16 pages, 1 figure, to appear in Int. J. Geom. Meth. Mod. Phy

Efficient generation of random multipartite entangled states using time optimal unitary operations

We review the generation of random pure states using a protocol of repeated two qubit gates. We study the dependence of the convergence to states with Haar multipartite entanglement distribution. We investigate the optimal generation of such states in terms of the physical (real) time needed to apply the protocol, instead of the gate complexity point of view used in other works. This physical time can be obtained, for a given Hamiltonian, within the theoretical framework offered by the quantum brachistochrone formalism. Using an anisotropic Heisenberg Hamiltonian as an example, we find that different optimal quantum gates arise according to the optimality point of view used in each case. We also study how the convergence to random entangled states depends on different entanglement measures.Comment: 5 pages, 2 figures. New title, improved explanation of the algorithm. To appear in Phys. Rev.

The quantum brachistochrone problem for non-Hermitian Hamiltonians

Recently Bender, Brody, Jones and Meister found that in the quantum brachistochrone problem the passage time needed for the evolution of certain initial states into specified final states can be made arbitrarily small, when the time-evolution operator is taken to be non-Hermitian but PT-symmetric. Here we demonstrate that such phenomena can also be obtained for non-Hermitian Hamiltonians for which PT-symmetry is completely broken, i.e. dissipative systems. We observe that the effect of a tunable passage time can be achieved by projecting between orthogonal eigenstates by means of a time-evolution operator associated with a non-Hermitian Hamiltonian. It is not essential that this Hamiltonian is PT-symmetric