Information Transfer with Two-state Two-particle Quantum Systems

Abstract

Any future quantum information machine will contain unitary operators and entangled particle states. The Hilbert space describing the action of the quantum information machine separates into a bosonic and a fermionic sector. Because the bosonic sector is of higher dimension, it is always possible to encode more information into a multiboson state than into a multifermion state, given the same complexity, that is unitary representation, of the quantum information machine. This is explicitly studied for the case of two particles defined in two modes. There the beam splitter is a generic representation of any U(2) matrix, and it has recently been shown that one can realize any N-dimensional unitary operator by successive application of such two-dimensional operators. The two-boson two-mode Hilbert space is of dimension three, and thus one can encode log₂3 = 1·57 bits of information into such an entangled state. Finally, some explicit schemes for creating and detecting the three possible, two-photon, two-mode states spanning the bosonic Bell basis are given.     

The Statistical Properties of a Generalized Two-mode Squeezed Operator

Abstract

In this paper we have employed the generalized two-mode squeeze operator to discuss the effect of squeezing on two-mode coherent states, number states and thermal states. By using the Glauber second-order correlation function we examined the statistical properties of these various squeezed states. The statistical investigations are carried out for the quasi-probability distribution functions (Wigner function and Q function). The P representation is also considered.     

Statistical Properties of the Time Evolution Operator for Two Coupled Oscillators

Abstract

In the present work we study the effects of squeezing on coherent states, number states, and on the thermal field states related to the time evolution operator, which is the result of the Hamiltonian describing the simultaneous non-degenerate parametric amplifier with mixing of two modes a and b via a rotation of their polarization. By using the Glauber second-order correlation function we examined the statistical properties of these various squeezed states. The quasi-probabilities of the W Wigner and Q functions are calculated. The Glauber P representation for the squeezed thermal state explicitly shows the limit of its applicability.     

Analysis of Modulational Instability in Monomode Optical Fibres with High-order Nonlinearity

Abstract

The modulational instability (MI) in monomode optical fibres with fifth-order nonlinearity, fibre loss, higher-order dispersion, and the temporal variation of third-order nonlinearity is studied theoretically. The conditions for the existence of the MI and the maximal modulational growth are given and discussed in detail. The results obtained show that the key factor dominating the producing condition of the MI is the power P of the continuous wave initially launched into the optical fibres. If P falls into 3/10<P/P ₀ <1/2 where P ₀ is defined as characteristic power, the MI can be produced in the range of not only anomalous group velocity dispersion but also the normal in which the final evolution state of the modulated wave is dark soliton.     

Necessary and Sufficient Conditions for Quantum Computation

Abstract

Necessary and sufficient conditions are given for a quantummechanical system to possess a coordinate system with respect to which its behaviour at discrete times is that of a universal digital computer. The form of the diagonal representation for the unitary time evolution operator for quantum universal computers is derived; aspects of the transformation between the diagonal representation and the computational representation are shown to be uncomputable. A quantum-mechanical treatment of macroscopic, dissipative computers is given.     

Multi-Gaussian Ultrasonic Beam Modeling for Multiple Curved Interfaces—an ABCD Matrix Approach

ABSTRACT

A multi-Gaussian beam model uses a superposition of Gaussian beams to simulate the waves radiated from an ultrasonic transducer. We show that propagation and reflection/transmission laws for Gaussian beams in fluids and elastic solids can be written in the form of A , B , C , D matrices that are analogous to the A, B, C, D scalars used in Gaussian optics. This representation leads to simple expressions for a Gaussian beam even after that beam has been transmitted or reflected at multiple curved interfaces and produces a highly modular multi-Gaussian beam model that is also computationally very efficient. Some examples of the use of this model for both planar and curved interfaces are given.     

Conchoidal transform of two plane curves

The conchoid of a plane curve C is constructed using a fixed circle B in the affine plane. We generalize the classical definition so that we obtain a conchoid from any pair of curves B and C in the projective plane. We present two definitions, one purely algebraic through resultants and a more geometric one using an incidence correspondence in P ² × P ². We prove, among other things, that the conchoid of a generic curve of fixed degree is irreducible, we determine its singularities and give a formula for its degree and genus. In the final section we return to the classical case: for any given curve C we give a criterion for its conchoid to be irreducible and we give a procedure to determine when a curve is the conchoid of another.     

Damping mechanisms of Fe–Mn alloy with (γ + ɛ) dual phase structure

Abstract

The objective of the present study is to propose damping mechanisms for Fe–Mn alloys containing austenite (face centred cubic) and ? martensite (hexagonal close packed), and to analyse the individual contribution of damping mechanisms to the total damping capacity of an Fe–17 wt-%Mn alloy with respect to volume fraction of ? martensite. On the basis of substructural characteristics of γ and ? phases, it is suggested that damping mechanisms of Fe–Mn alloys with (γ + ?) dual phase structures involve stress induced movement of various boundaries such as stacking fault boundaries in austenite and ? martensite, ?martensite variant boundaries, and γ/? interphase boundaries. The damping capacity of the Fe–17Mn alloy increases with increasing ? martensite content. The quantitative analysis shows that in the as quenched state, the ? martensite phase is responsible for a major part of the damping capacity.     

Model for static recrystallisation critical temperature in microalloyed steels

Abstract

By means of hot torsion tests, the static recrystallisation critical temperature (SRCT) has been determined for 18 microalloyed steels classified into two groups. In one group the metallic microalloying element is vanadium, and in the other it is niobium. In both groups the microalloying element, carbon, and nitrogen contents vary from one steel to another. Tests have been carried out at various strains and strain rates, and recrystallisation–precipitation–time–temperature (RPTT) diagrams have been drawn for each steel in each condition. The SRCT is the asymptote of strain induced precipitation start P _s and end P _f curves, and its determination has permitted the construction of a model that quantifies the effects of all the external variables implicit in hot working such as strain and strain rate, and the internal variables such as austenite grain size and chemical composition of the steel. Hence, the influence of each of these variables has been quantified, and the model's prediction, comparing experimental values with calculated values, gives a correlation index of ～0.9.     

A detailed description of the Gurson–Tvergaard–Needleman model within a mixed velocity–pressure finite element formulation

In an effort to implement Gurson‐type models into a mixed velocity–pressure finite element formulation with the MINI‐element P1 ⁺ ∕ P1, the algorithm proposed by Aravas (IJNME, 1987) to integrate the pressure dependent plasticity as well as the formulations of consistent tangent moduli have been analyzed. This work firstly reviews and clarifies the mathematical basis of the formulations used by Aravas (IJNME, 1987) and demonstrates the equality of the tangent moduli formulations proposed by Govindarajan and Aravas (CNME, 1995) and Zhang (CMAME, 1995), which are widely used in the literature. A unified formulation to calculate the tangent moduli is proven, and its accuracy is also investigated by the finite difference method. The implementation of the Gurson–Tvergaard–Needleman model is then detailed for the mixed velocity–pressure finite element formulation, which employs the MINI‐element P1 ⁺ ∕ P1. Due to the particularity of this element, one needs to calculate two tangent moduli instead of one. The formulas for calculating the ‘linear tangent modulus’ and the ‘bubble tangent modulus’ are then detailed. Finally, comparison tests are carried out with ABAQUS (Dassault System, Simulia Corp., Providence, RI, USA) in order to validate the present implementation for both homogeneous and heterogeneous deformations. Copyright © 2013 John Wiley & Sons, Ltd.     

Petri‐net based integer programs for synthesizing optimal material‐transfer procedures in pipeline networks

Abstract

Transferring materials through the pipeline network is a basic operation in almost every batch chemical plant. Traditionally, the tasks for conjecturing the needed operation steps are carried out manually on an ad hoc basis. This approach is often time‐consuming for industrial processes and, furthermore, the resulting recipe may be error‐prone. The aim of this paper is thus to develop a systematic strategy to generate the optimal operating procedures with Petri‐net based integer programs. Specifically, the shortest material‐transfer routes are selected on the basis of Petri‐net representation of the path structure in pipeline network. The equipment models are then incorporated into this path model to create a complete system model. An integer program can therefore be constructed accordingly to identify the detailed operation steps. Finally, a realistic example is presented at the end of this paper to demonstrate the effectiveness and correctness of the proposed approach.     

Model simplification of stable discrete‐time systems by the squared magnitude Padé approximation

Abstract

A squared magnitude Padé approximation technique is presented for the model simplification of stable discrete‐time systems. The simplification is started from the squared magnitude function M(e^jTω ) =G(e^jTω )G(e^–jTω ), where G(z) is the z‐transfer function of a given high order discrete‐time system. The method is fully computer‐oriented and leads to a satisfactory approximation while preserving stability and minimum‐phase characteristics.     

Eigenvalues of damped structures: Vectoriteration in the original space of DOF

The equations of motion in structural dynamics as well as the corresponding eigenvalue problem are governed by 3 matrices for mass, damping and stiffness of order n which equals the number of degrees of freedom. High-performance eigenvalue-solvers are developed for only pairs A, B of matrices. Nevertheless, to benefit from these solvers, the original eigenvalue problem (λ² M+λD+K)x=0 is transformed into a linear eigenvalue representation with only two hypermatrices of double order 2n. Consequently the total numerical effort depends on this order 2n. This paper presents a vectoriteration process which actually works in the original space of order n and which needs no special actions like simultaneous iteration if complex conjugate eigenvalues λ, λˉ with identical norm have to be calculated. The theoretical foundation of this process still goes back to the pair of hypermatrices.     

Improved Multiple Comparisons With a Control in Response Surface Analysis

Quadratic response surface methodology often focuses on finding the levels of some (coded) predictor variables x = (x ₁, x ₂,…, x _k) that optimize the expected value of a response variable y. Typically the experimenter starts from some best guess or “control” combination of the predictors (usually coded to x = 0) and performs an experiment varying them in a region around this center point. The question of interest addressed here is whether any x in the experimental region provides a long-run mean response E(y) preferable to that of the control, and if so, by what amount? This article approaches this question via simultaneous confidence intervals for δ(x) = E(y|x) = E(y|0) for all x within a specified distance of 0. A new method for two or more predictors is introduced that gives sharper intervals than the Scheffé method and also the Sa and Edwards adaptation of the Casella and Strawderman method. The new method does not require a rotatable design and allows for one-sided simultaneous bounds for δ(x). Approximate sample-size savings of the improved method over the Sa and Edwards adaptation of the Casella and Strawderman method ranged from 12%–45% for two-sided intervals and 19%–40% for one-sided intervals for designs with two or three predictors. Approximate sample-size savings of the improved method over the Scheffe method ranged from 14%–47% for two-sided intervals and 22%–62% for one-sided intervals.     

Preparation information and optimal decompositions for mixed quantum states

Abstract

Consider a joint quantum state of a system and its environment. A measurement on the environment induces a decomposition of the system state. Using algorithmic information theory, we define the preparation information of a pure or mixed state in a given decomposition. We then define an optimal decomposition as a decomposition for which the average preparation information is minimal. The average preparation information for an optimal decomposition characterizes the system–environment correlations. We discuss properties and applications of the concepts introduced above and give several examples.     

Phase relationships involving TiC and Ti3AlC (P phase) in Ti–Al–C system

Abstract

Titanium rich alloys of the Ti–Al–C system have been investigated to determine the constitution in the range 1250–750°C with particular reference to phase equilibria and transformations involving TiC and Ti₃AlC (P phase). Alloys with varying aluminium and carbon concentrations up to 15 at.-%Al and 15 at.-%C have been studied using scanning and transmission electron microscopy and X-ray diffraction. The isothermal sections at 1250, 1050, 1000, and 750°C reported by previous workers are reviewed. Equilibria involving the phases β-Ti, α-Ti, Ti₃Al (α ₂), TiC, and Ti₃AlC (P phase) have been investigated and partial isothermal sections at 1050 and 750°C are presented. A revision of the previously established Ti–Al–C isothermal section at 750°C is shown involving equilibria of α+α ₂+P and α+P+TiC. The orientation relationship between the P phase and Ti–Al (α/α ₂) matrix has been found to be (0001)_{α/α 2} ∥{111}_P and 〈12¯10〉_{α/α 2} ∥〈110〉_P.     

Effect of notch root radius on fracture toughness of Ti–18Al–8Nb alloy

Abstract

The effect of notch root radius on the mode I fracture toughness of Ti–18Al–8Nb alloy in beta solution treated and water quenched condition was investigated. The apparent fracture toughness K _IA was found to be independent of the notch root radius below a critical notch root radius ρ ₀ and subsequently increase linearly with the square root of notch root radius ρ^1/2 beyond ρ ₀. The critical notch root radius in this alloy was found to be ～50 μm. The results were explained on the basis of strain controlled fracture model.     

Synthesis and Structure of U(VI), Np(VI), and Pu(VI) 2-Fluorobenzoates

The compounds NH₄[AnO₂(C₆H₄FCOO₃], where An = U (I), Np (II), or Pu (III), CgH₄COO^? is the 2-fluorobenzoate anion, were synthesized and studied by single crystal X-ray diffraction. Compounds I–III are isostructural and crystallize in the cubic system, space group P2₁3, Z = 4. The main structural units of I–III are mononuclear complexes [AnO₂(C₆H₄COO)₃]^? belonging to crystal-chemical group AB₃¹ (A = AnO₂²⁺, B⁰¹ = C₆H₄FCOO^?). The actinide contraction in the structures of I–III is manifested in a regular decrease in the lengths of the An=0 bonds in the AnO₂²⁺ cations and in the volumes of the Voronoi-Dirichlet polyhedra (VDPs) of the An atoms in the series U-Np-Pu. The intermolecular interactions in crystal structures of I–III were analyzed by the method of molecular VDPs.

     

The design and use of nuclear orientation thermometers employing54Mn and60Co nuclei in ferromagnetic hosts

The magnetic dipole interaction between the nuclear magnetic momentu and the hyperfine fieldH _hf in ferromagnetic metals leads to well-defined, evenly spaced nuclear energy levels which are accurately measurable by NMR techniques. When this is combined with the well-established anisotropic -ray emission properties of radioactive nuclei an excellent basis for absolute temperature measurement between 1 and 30 mK is obtained. Practical applications, however, require consideration of several experimental aspects. These are discussed in detail and graphs and tables are given in such a form that the data can be easily utilized. Experience gained with a nuclear orientation thermometer system employed in a nuclear refrigeration cryostat is discussed. A calibration of a pulsed copper NMR thermometer against a⁵⁴MnNi nuclear orientation thermometer is presented.