Note on the kinetic energy inequality leading to Lieb's negative ionization upper bound

The kinetic energy inequality is alternatively proved which yields Lieb's boundN < 2Z + 1 on the maximum negative ionization of an atom with nucleus chargeZ andN electrons when the kinetic energy operator is the nonrelativistic or relativistic magnetic Schrödinger operator. It is seen to follow from the free case where the vector potential vanishes. The proof applies to the Weyl quantized relativistic magnetic Schrödinger operator as well.Research partially supported by Grant-in-Aid for Scientific Research Nos. 04640141 and 05640165, Ministry of Education, Science and Culture, Japanese Government.     

A refinement of Simon's correlation inequality

A general formulation is given of Simon's Ising model inequality: whereB is any set of spins separating from . We show that _b can be replaced by _{b A} whereA is the spin system insideB containing . An advantage of this is that a finite algorithm can be given to compute the transition temperature to any desired accuracy. The analogous inequality for plane rotors is shown to hold if a certain conjecture can be proved. This conjecture is indeed verified in the simplest case, and leads to an upper bound on the critical temperature. (The conjecture has been proved in general by Rivasseau. See notes added in proof.)Work partially supported by U.S. National Science Foundation grant PHY-7825390 A01     

General correlation functions of the Clauser-Horne-Shimony-Holt inequality for arbitrarily high-dimensional systems

We generalize the correlation functions of the Clauser-Horne-Shimony-Holt (CHSH) inequality to arbitrarily high-dimensional systems. Based on this generalization, we construct the general CHSH inequality for bipartite quantum systems of arbitrarily high dimensionality, which takes the same simple form as CHSH inequality for two dimensions. This inequality is optimal in the same sense as the CHSH inequality for two-dimensional systems, namely, the maximal amount by which the inequality is violated consists of the maximal resistance to noise. We also discuss the physical meaning and general definition of the correlation functions. Furthermore, by giving another specific set of the correlation functions with the same physical meaning, we realize the inequality presented by Collins et al. [Phys. Rev. Lett. 88, 040404 (2002)]].     

Calculation of the out of plane dynamical correlation for TMMC

The out of plane dynamical correlation function for the one dimensional easy plane antiferromagnet is calculated at low temperatures using a diagramatic expansion for the temperature dependent Green function. The calculation is applied to the compound (CH₃)₄NM _n Cl₃ (TMMC).     

Defining a reaction plane in particle-fission correlation measurements

A simple model is developed to describe the spin misalignment in particle-fission correlation measurements. Analytical expressions are derived for the spin fluctuations as a function of fission fragment emission angle. Some recent experimental results onα-fission correlations are interpreted within the framework of the model.     

一种实用成像系统像面动态散斑的空-时相关函数

本文根据傅里叶光学和统计理论,推导了一种实用的成像光学系统像面动态散斑的振幅及强度的空-时相关函数表达式,并提出利用相干场混合法提取空-时强度相关的信息.     

Lieb's Spin-Reflection-Positivity Method and Its Applications to Strongly Correlated Electron Systems

In this paper, we discuss the spin-reflection-positivity method introduced by Lieb [E. H. Lieb, Phys. Rev. Lett. 62:1201 (1989)] and its applications to strongly correlated electron systems in a pedagogical manner. We emphasize the important role played by the sign rule of the ground-state wave function in studying a many-body system. To make our explanation more readable, we shall first review some well-known one-dimensional examples and recall the Lieb–Mattis theorem on the Heisenberg localized spin models. Then, after introducing the general theory of spin-reflection positivity, we show in detail how to use it to overcome the sign problem caused by the fermion characteristics of itinerant electrons in strongly correlated models. Finally, we establish several rigorous results on the Hubbard model, the periodic Anderson model and the Kondo lattice model.     

Decision optimization for face recognition based on an alternate correlation plane quantification metric

We consider a new approach for enhancing the discrimination performance of the VanderLugt correlator. Instead of trying to optimize the correlation filter, or propose a new decision correlation peak detection criterion, we propose herein to denoise the correlation plane before applying the peak-to-correlation energy (PCE) criterion. For that purpose, we use a linear functional model to express a given correlation plane as a linear combination of the correlation peak, noise, and residual components. The correlation peak is modeled using an orthonormalized function and the singular value decomposition method. A set of training correlation planes is then selected to create the correlation noise components. Finally, an optimized correlation plane is reconstructed while discarding the noise components. Independently of the filter correlation used, this technique denoises the correlation plane by lowering the correlation noise magnitude in case of true correlation and decreases the false alarm rate when the target image does not belong to the desired class. Test results are presented, using a composite filter and a face recognition application, to verify the effectiveness of the proposed technique.     

Spatial correlation between 1.06 μm laser irradiation and emitted current for a plane target

The distribution of current generated by the irradiation of a copper target with a 4 J, 30 ns, Nd-glass laser pulse was measured at the laser-plasma interface. Current distribution was compared with the irradiation distribution.     

Vibration response of misaligned rotors

Misalignment is one of the common faults observed in rotors. Effect of misalignment on vibration response of coupled rotors is investigated in the present study. The coupled rotor system is modelled using Timoshenko beam elements with all six dof. An experimental approach is proposed for the first time for determination of magnitude and harmonic nature of the misalignment excitation. Misalignment effect at coupling location of rotor FE model is simulated using nodal force vector. The force vector is found using misalignment coupling stiffness matrix, derived from experimental data and applied misalignment between the two rotors. Steady-state vibration response is studied for sub-critical speeds. Effect of the types of misalignment (parallel and angular) on the vibration behaviour of the coupled rotor is examined. Along with lateral vibrations, axial and torsional vibrations are also investigated and nature of the vibration response is also examined. It has been found that the misalignment couples vibrations in bending, longitudinal and torsional modes. Some diagnostic features in the fast Fourier transform (FFT) of torsional and longitudinal response related to parallel and angular misalignment have been revealed. Full spectra and orbit plots are effectively used to reveal the unique nature of misalignment fault leading to reliable misalignment diagnostic information, not clearly brought out by earlier studies.     

An inequality for trace ideals

We prove an inequality for trace ideals which relates the difference of two positive operators to the difference of their square roots. Inequalities involving operator-monotone functions more general than the square root, are considered as well.     

An inequality for Hilbert-Schmidt norm

For the absolute value |C|=(C*C)^1/2 and the Hilbert-Schmidt norm ∥C∥_HS=(trC*C)^1/2 of an operatorC, the following inequality is proved for any bounded linear operatorsA andB on a Hilbert space $$|| |A|---|B| ||_{HS} \leqq 2^{1/2} ||A - B||_{HS} $$ . The corresponding inequality for two normal state ? and ψ of a von Neumann algebraM is also proved in the following form: $$d(\varphi ,\psi ) \leqq ||\xi (\varphi ) - \xi (\psi )|| \leqq 2^{1/2} d(\varphi ,\psi )$$ . Here ξ(χ) denotes the unique vector representative of a state χ in a natural positive coneP ^? forM, andd(?, ψ) denotes the Bures distance defined as the infimum (which is also the minimum) of the distance of vector representatives of ? and ψ. In particular, $$||\xi (\varphi _1 ) - \xi (\varphi _2 )|| \leqq 2^{1/2} ||\xi _1 - \xi _2 ||$$ for any vector representatives ξ _j of ? _j ,j=1, 2.     

A continuous vibration theory for rotors with an open edge crack

In this paper a new continuous model for flexural vibration of rotors with an open edge crack has been developed. The cracked rotor is considered in the rotating coordinate system attached to it. Therefore, the rotor bending can be decomposed in two perpendicular directions. Two quasi-linear displacement fields are assumed for these two directions and the strain and stress fields are calculated in each direction. Then the final displacement and stress fields are obtained by composing the displacement and stress fields in the two directions. The governing equation of motion for the rotor has been obtained using the Hamilton principle and solved using a modified Galerkin method. The free vibration has been analyzed and the critical speeds have been calculated. Results are compared with the finite element results and an excellent agreement is observed.     

Absence of symmetry breaking for systems of rotors with random interactions

We prove that Gibbs states for the Hamiltonian , with thes _x varying on theN-dimensional unit sphere, obtained with nonrandom boundary conditions (in a suitable sense), are almost surely rotationally invariant if withJ _xy i.i.d. bounded random variables with zero average, 1 in one dimension, and 2 in two dimensions.     

Non-linear dynamics of flexible multi-bearing rotors

A general analysis has been developed to computer simulate steady state and transient vibration phenomena of complex rotor-bearing-support systems. A central feature of this analysis is a proper handling of various highly non-linear effects (most notably journal bearings) which dominate the dynamic phenoména encountered during large amplitude rotor-bearing vibrations. There are a number of potential causes of large amplitude rotor vibration, such as high rotor imbalance (e.g., loss of turbine blades at running speed), critical speed operation, journal bearing dynamic instability (oil whip), earthquakes, and shock. Failure mode analysis requires the evaluation and understanding of such potentially large dynamic forces and displacements. The paper presents development of the analysis, comparison with experiment and examples of its use in industrial applications.     

A spectral isoperimetric inequality for cones

In this note, we investigate three-dimensional Schrödinger operators with \(\delta \)-interactions supported on \(C^2\)-smooth cones, both finite and infinite. Our main results concern a Faber–Krahn-type inequality for the principal eigenvalue of these operators. The proofs rely on the Birman-Schwinger principle and on the fact that circles are unique minimizers for a class of energy functionals. The main novel idea consists in the way of constructing test functions for the Birman-Schwinger principle.     

Angular-momentum--mass inequality for axisymmetric black holes

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