The consistency of consistent histories: A reply to d'Espagnat

This article is a response to various assertions made by B. d'Espagnat about the consistent history approach to quantum mechanics. It is argued that the consistent history interpretation allows for counterfactual definitions, does not imply that the future influences the past, is realistic according to d'Espagnat's own definition of that term, and provides a consistent substitute for classical logic in the quantum domain.     

Similarity between the Mandelbrot set and Julia sets

The Mandelbrot setM is “self-similar” about any Misiurewicz pointc in the sense that if we examine a neighborhood ofc inM with a very powerful microscope, and then increase the magnification by a carefully chosen factor, the picture will be unchanged except for a rotation. The corresponding Julia setJ _c is also “self-similar” in the same sense, with the same magnification factor. Moreover, the two setsM andJ _c are “similar” in the sense that if we use a very powerful microscope to look atM andJ _c, both focused atc, the structures we see look like very much the same.     

A consistent formulation of the null-plane quantum field theory

It is shown in the usual framework of quantum field theory that the null-plane restriction of a field operator is not a well-defined operator-valued distribution. The cause of the trouble is the so-called P⁺ = 0 mode; in order to make it harmless, it is almost inevitable to violate Lorentz invariance. A consistent formulation of the null-plane quantization, which is supposed to be the simplest possible one, is proposed by modifying the definition of Poisson brackets. This theory is invariant under a Poincaré subalgebra containing seven generators. It is also shown that the absence of vacuum polarization is realized consistently in this formalism.     

Energy spectra of the ocean's internal wave field: theory and observations

The high-frequency limit of the Garrett and Munk spectrum of internal waves in the ocean and the observed deviations from it are shown to form a pattern consistent with the predictions of wave turbulence theory. In particular, the high-frequency limit of the Garrett and Munk spectrum constitutes an exact steady-state solution of the corresponding kinetic equation.     

Existence and renormalization of the Sine-Gordon field theory in all dimensions

The Euclidean field theory of the Sine-Gordon model (SG) is investigated by using methods of statistical physics. The SG model is shown to be the continuum limit of the ferromagnetic Harmonic Rotator model (HR) which itself is equivalent to a classical Coulomb plasma of unit charges on a lattice. Using our recent results for the latter models in all Euclidean dimensionsD we determine the existence of the SG field theory in terms of the HR parameters, temperaturet and magnetic fieldB. The following results are derived: 1. InD=1 the SG exists neart=B=0; the quantum theory in zero space dimensions is just the Mathieu equation as Schrödinger equation. 2. ForD>2 the SG field theory exists for allt nearB=0. The theory is actually constructed and is equivalent to a free massive scalar theory. 3. In the most interesting case ofD=2 the SG field theory exists for allt<t=8 nearB=0, it does not exist fortt. All necessary renormalizations are performed and all necessary subtractions are obtained in closed form which proves that the theory is superrenormalizable when it exists. We also discuss the relations between the structure of the particle spectrum of the SG, the phase transitions of the HR, and the binding properties of the classical Coulomb charges.     

Fuzzy sets in the theory of measurement of incompatible observables

The notion of fuzzy event is introduced in the theory of measurement in quantum mechanics by indicating in which sense measurements can be considered to yield fuzzy sets. The concept of probability measure on fuzzy events is defined, and its general properties are deduced from the operational meaning assigned to it. It is pointed out that such probabilities can be derived from the formalism of quantum mechanics. Any such probability on a given fuzzy set is related to the frequency of occurrence within that set of points in a random sample, where the sample points are themselves fuzzy sets obtained as outcomes of measurements of, in general, incompatible observables on replicas of the system in the same prepared state.     

基于钴和坡莫合金纳磁体的全自旋逻辑器件开关特性研究

基于纳磁体动力学和自旋传输机理, 建立了全自旋逻辑(ASL)器件的自旋传输-磁动力学模型. 基于该模型分别研究了钴纳磁体构成的全自旋逻辑(CoASL)器件和坡莫合金纳磁体构成的全自旋逻辑(PyASL)器件在不同沟道长度和电源电压下的开关特性. 结果显示PyASL器件在开关延迟时间和功耗上要小于CoASL器件, 且能可靠工作的最大沟道长度要大于CoASL器件. 另外, 两种ASL器件的开关延迟时间可通过减小沟道长度或增加电源电压来减小; 而功耗可通过减小沟道长度或电源电压来减小. 同时, 减小沟道长度能有效抑制热噪声对开关延迟时间和功耗的影响, 但增大电源电压只能抑制热噪声对开关延迟时间的影响. 上述研究结果将为优化ASL器件磁性材料和器件结构提供重要的参数选择依据.     

Scaled particle theory: Solution to the complete set of scaled particle theory conditions: Applications to surface structure and dilute mixtures

We present, so far as we know, the first solution to thecomplete set of conditions developed by scaled particle theory under the usual approximation that G(λ) can be expressed as a Laurent series for 1/2 <λ < ∞. The theory leads to a fourth virial coefficient accurate to 0.6% and fair values for the first derivative of the radial distribution function?(1). The results are used to calculate both boundary tension and boundary adsorption in the hard sphere fluid, as well as the pressure of a dilute hard sphere mixture. It is probable that the nearly linear function we calculate deviates only slightly from the true G(λ) at fluid densities. Some discussion of this point is presented.     

Some aspects of phase transitions described by the self consistent current relaxation theory

A mathematical model for a nonlinear equation of motion for correlation functions is considered which describes the essential features of the self consistent current relaxation theory for a system experiencing some interaction with a static random field in addition to some quadratic self interaction. It is shown that the plane spanned by the two coupling parameters is separated into a region of ergodic motion and another region where the motion is nonergodic. At the separation line of the two phases all correlation functions can be discussed in terms of scaling laws. The critical exponents vary along the separation line continuously and they can be evaluated explicitely. The separation line consists of two pieces. Transitions across the first piece are characterized by a polarization catastrophy, by a vanishing of the transport coefficient and by a diverging low frequency spectrum ruled by one critical frequency scale. Transitions across the second piece do not exhibit a polarization divergence but show also a power law decrease to zero of the transport coefficient. The low frequency spectrum is the sum of two diverging parts. Each part is described by a scaling law, but the scaling frequencies and the scaling functions are quite different.     

Local internal supersymmetry of the free Maxwell theory

The free Maxwell theory is shown to possess an extended gauge invariance consisting of local internal supersymmetry transformations in addition to the usual local phase transformations. The Maxwell lagrangian is derived as a particular gauge choice in the extended theory.     

On the theory of internal photoemission in heterojunctions

The theory of internal photoemission in semiconductor heterojunctions has been reviewed and the existing model has been extended by incorporating the effects of the difference in the effective masses in the active region and the substrate, nonspherical-nonparabolic bands, and the energy loss per collisions. This complete model has been applied to describe the experimental results obtained from Si_1−xGe_x/Si heterojunction infrared photodetectors. The barrier heights (correspondingly the cut-off wavelengths) of SiGe/Si samples have been determined from their internal photoemission spectra by using the extended model which has the wavelength and doping concentration dependent free carrier absorption parameters. Fowler analysis showed that the model is in good agreement with the experiments for the entire spectrum.     

The experimental localization of Aubry-Mather sets using regularization techniques inspired by viscosity theory

We provide a new method for the localization of Aubry-Mather sets in quasi-integrable two-dimensional twist maps. Inspired by viscosity theories, we introduce regularization techniques based on the new concept of "relative viscosity and friction," which allows one to obtain regularized parametrizations of invariant sets with irrational rotation number. Such regularized parametrizations allow one to compute a curve in the phase-space that passes near the Aubry-Mather set, and an invariant measure whose density allows one to locate the gaps on the curve. We show applications to the "golden" cantorus of the standard map as well as to a more general case.