Wavefunction localization in a binary alloy

The nature (localized or extended) of the eigenstates of a large disordered system is studied by evaluating the imaginary part of the local Green's function at the specific eigenvalues over various atomic sites. The latter is obtained from the recursion method of Haydock-Heine-Kelly. An explicit calculation on an 841-atom cluster of random binary alloy in a square lattice ensures us that this approach is able to provide the relevant answers in even larger systems. In addition to confirming the usual conjectures about localization in a random binary alloy, several interesting points show up in the result of the model calculation. For example, the localized states in the minority band are correlated to certain clustering of the minority atoms. Their specific eigenvalues, which are not easily identified from the peaks in the d.o.s., are accurately found through the |ζ|² vs. energy plots at the specific sites.     

The behaviour of the gold 5d band in Gold-Palladium alloys

The change of bandwidth and effective spin-orbit splitting of Gold 5d bands in a number of alloy systems has been found to be dependent only on the concentration of Gold and not on the second alloy constituent. Theoretically, this has been described as the split band limit where the Gold 5d electrons interact only weakly with electrons on the other component. The binding energy shifts are found to be dependent on this interaction. In this paper we report ultraviolet photoelectron spectra from a number of Gold-Palladium alloys and compare the d-band behaviour with that in previously reported spectra. In spite of the overlapping Gold and Palladium d bands the dominant interaction is that between like atoms. We also discuss the final state of dilute Gold in the Palladium matrix.     

Questions and answers

The aim of this paper is twofold. First, we shall derive the Fermi-Dirac (FD) and Bose-Einstein (BE) distributions from the classical Maxwell-Boltzmann (MB) distribution by introducing into the classical system the consequences of quantum mechanical indistinguishability in a direct and simple manner. Next, we go through a brief introduction to feedback systems and see how the FD and BE systems may be viewed as classical systems with appropriate feedback. We shall see that the resemblance to feedback systems is more than formal and that a feedback mechanism does exist in systems obeying quantum statistical mechanics.     

Magneto optics and time resolved terahertz spectrocopy

Exploring, manipulating, and understanding new exotic quantum phenomena in condensed-matter systems have generated great interest in the scientific community. Static and time resolved optical spectroscopies after photoexcitations are important experimental tools for probing charge dynamics and quasiparticle excitations in quantum materials. In Synergetic Extreme Condition User Facility(SECUF), we shall construct magneto-infrared and terahertz measurement systems and develop a number of ultrafast femtosecond laser based systems, including intense near to mid-infrared pump terahertz probe. In this article, we shall describe several systems to be constructed and developed in the facilities, then present some examples explaining the application of magneto optics and time resolved spectroscopy techniques.     

Random waves and more: Eigenfunctions in chaotic and mixed systems

The structure of wavefunctions strongly depends on the underlying classical dynamics. We illustrate this with several numerical examples and relate them to conjectures and mathematical results. In particular we focus on the random wave model and its implications for chaotic systems and its extension to systems with a mixed phase space.     

Rigorous Results for the Distribution of Money on Connected Graphs

This paper is concerned with general spatially explicit versions of three stochastic models for the dynamics of money that have been introduced and studied numerically by statistical physicists: the uniform reshuffling model, the immediate exchange model and the model with saving propensity. All three models consist of systems of economical agents that consecutively engage in pairwise monetary transactions. Computer simulations performed in the physics literature suggest that, when the number of agents and the average amount of money per agent are large, the limiting distribution of money as time goes to infinity approaches the exponential distribution for the first model, the gamma distribution with shape parameter two for the second model and a distribution similar but not exactly equal to a gamma distribution whose shape parameter depends on the saving propensity for the third model. The main objective of this paper is to give rigorous proofs of these conjectures and also extend these conjectures to generalizations of the first two models and a variant of the third model that include local rather than global interactions, i.e., instead of choosing the two interacting agents uniformly at random from the system, the agents are located on the vertex set of a general connected graph and can only interact with their neighbors.     

Discovery of closed orbits of dynamical systems with the use of computers

In this paper we derive a general criterion which can be used for the discovery with the use of a computer of closed orbits of systems of ordinary differential equations. We apply this criterion to the Lorenz model and show rigorously the existence of a closed orbit for the case under consideration. In a subsequent paper we shall show how the stable manifold of this orbit determines the boundary of the stochastic attractor.     

Koopman‐von Neumann formulation of classical Yang‐Mills theories: I

In this paper we present the Koopman‐von Neumann (KvN) formulation of classical non‐Abelian gauge field theories. In particular we shall explore the functional (or classical path integral) counterpart of the KvN method. In the quantum path integral quantization of Yang‐Mills theories concepts like gauge‐fixing and Faddeev‐Popov determinant appear in a quite natural way. We will prove that these same objects are needed also in this classical path integral formulation for Yang‐Mills theories. We shall also explore the classical path integral counterpart of the BFV formalism and build all the associated universal and gauge charges. These last are quite different from the analog quantum ones and we shall show the relation between the two. This paper lays the foundation of this formalism which, due to the many auxiliary fields present, is rather heavy. Applications to specific topics outlined in the paper will appear in later publications.     

Lattices and their continuum limits

We address the problem of the continuum limit for a system of Hausdorff lattices (namely lattices of isolated points) approximating a topological space M. The correct framework is that of projective systems. The projective limit is a universal space from which M can be recovered as a quotient. We dualize the construction to approximate the algebra C(M) of continuous functions on M. In a companion paper we shall extend this analysis to systems of noncommutative lattices (non-Hausdorff lattices).     

Effects of Compressibility on the Rayleigh-Taylor Instability in Z-pinch Implosions

In this paper we shall consider the effect of compressibility on the RT instability in Z-pinch implosions, importance is the comparing growth rates of the RT instability for two systems of the compressible and incompressible MHD plasma. For which reason, we shall use as simple model as possible. Obviously, slab geometry is the most simple. For example, in the case of annular plasma implosion, during the linear growth phase of the RT instability there are vacuums at both sides of the annular plasma shell and its thickness is sufficiently smaller than the pinch radius, allowing us to use slab geometry instead of the annular one. For simplicity, we do not consider the effects of the finite Larmor radius and the sheared axial flow which are the important physical mechanisms to compress the RT instabilities.     

Study of the crystallization morphology of VT3-1 alloy during VAR

In this paper, we consider the crystallization morphology formation of VT3-1 titanium alloy in the process of vacuum arc remelting (VAR). Based on experimental data obtained by the method of autoradiography, we numerically determine remelting parameters such as the temperature gradient G at the solidification front and its velocity V. Since practically all kinds of morphology of the crystallization microstructure of metal systems are present in an ingot (planar front, cellular, cellular-dendritic, and dendritic structures), we consider two simple models of transition from one structure to another. The models greatly depend on the parameters G and V. In this paper, the liquidus curve slopes for the alloying elements of VT3-1 alloy are determined and a morphology map is constructed. Also, the results are compared with those obtained earlier by other authors.     

Zur Definition der Drehimpulseigenfunktionen in der Vektormesontheorie

There are three possibilities for the introduction of angular momentum eigenfunctions in the vector-meson-theory: 1. Multipole fields, 2. orbital angular momentum eigenfunctions, 3. helicity eigenfunctions. We shall define these functions by eigenvalue equations and present their mutual relationship. In analogy to the usual momentum quantization we may quantize the field with respect to each of the three systems of angular momentum eigenfunctions.     

Level spacing statistics for two-dimensional massless Dirac billiards

Classical-quantum correspondence has been an intriguing issue ever since quantum theory was proposed. The searching for signatures of classically nonintegrable dynamics in quantum systems comprises the interesting field of quantum chaos. In this short review, we shall go over recent efforts of extending the understanding of quantum chaos to relativistic cases. We shall focus on the level spacing statistics for two-dimensional massless Dirac billiards, i.e., particles confined in a closed region. We shall discuss the works for both the particle described by the massless Dirac equation(or Weyl equation)and the quasiparticle from graphene. Although the equations are the same, the boundary conditions are typically different,rendering distinct level spacing statistics.     

On the Validations of the Asymptotic Matching Conjectures

In this paper we review the asymptotic matching conjectures for r-regular bipartite graphs, and their connections in estimating the monomer-dimer entropies in d-dimensional integer lattice and Bethe lattices. We prove new rigorous upper and lower bounds for the monomer-dimer entropies, which support these conjectures. We describe a general construction of infinite families of r-regular tori graphs and give algorithms for computing the monomer-dimer entropy of density p, for any p∈[0,1], for these graphs. Finally we use tori graphs to test the asymptotic matching conjectures for certain infinite r-regular bipartite graphs.     

Generalized mechanical systems. A mathematical exposition of non-smooth classical Lagrangian mechanics

In this note we shall give a generalization of classical mechanical systems.     

团簇物理的新进展(Ⅱ)——关于原子团簇和原子核的相似点和不同点

本文重点讨论金属原子团簇和原子核两费米子体系之间相似之处,如饱和性、壳结构、集体振荡、Ｊａｈｎ－Ｔｅｌｅｒ效应,裂变和聚合反应等,以及由于两者凝聚力的本质差别所造成的不同点。