Pentagrams and Paradoxes

Klyachko and coworkers consider an orthogonality graph in the form of a pentagram, and in this way derive a Kochen-Specker inequality for spin 1 systems. In some low-dimensional situations Hilbert spaces are naturally organised, by a magical choice of basis, into SO(N) orbits. Combining these ideas some very elegant results emerge. We give a careful discussion of the pentagram operator, and then show how the pentagram underlies a number of other quantum “paradoxes”, such as that of Hardy.     

Quantum Mechanical Effect of Path-polarization Contextuality for a Single Photon

Using measurements pertaining to a suitable Mach-Zehnder (MZ) type setup, a curious quantum mechanical effect of contextuality between the path and the polarization degrees of freedom of a polarized photon is demonstrated, without using any notion of realism or hidden variables—an effect that holds good for the product as well as the entangled states. This form of experimental context-dependence is manifested in a way such that at either of the two exit channels of the MZ setup used, the empirically verifiable subensemble statistical properties obtained by an arbitrary polarization measurement depend upon the choice of a commuting (comeasurable) path observable, while this effect disappears for the whole ensemble of photons emerging from the two exit channels of the MZ setup.     

Nature's natural numbers: relativistic quantum theory over the ring of complex quaternions

The 2×2 complex matrix formulation of relativity and the two-component spin-1/2 formalism are merged with the complex quaternion algebra to yield a concise, manifestly covariant formalism of relativistic quantum mechanics. Along with reproducing all the old results of quantum theory, this complex quaternion formulation extends naturally the concept of scalar mass by adding to it orientation- and velocity-dependent parts giving a hyper-mass. The hyper-mass spin-1/2 equation, with the scalar part of the mass set equal to zero, gives a subtle variation on the two-component neutrino theory with very unsubtle consequences, such as an invariant mass parameter which could distinguishv _eandv and elimination of the superposition principle.     

Foundations of the Quaternion Quantum Mechanics

We show that quaternion quantum mechanics has well-founded mathematical roots and can be derived from the model of the elastic continuum by French mathematician Augustin Cauchy, i.e., it can be regarded as representing the physical reality of elastic continuum. Starting from the Cauchy theory (classical balance equations for isotropic Cauchy-elastic material) and using the Hamilton quaternion algebra, we present a rigorous derivation of the quaternion form of the non- and relativistic wave equations. The family of the wave equations and the Poisson equation are a straightforward consequence of the quaternion representation of the Cauchy model of the elastic continuum. This is the most general kind of quantum mechanics possessing the same kind of calculus of assertions as conventional quantum mechanics. The problem of the Schrödinger equation, where imaginary ‘i’ should emerge, is solved. This interpretation is a serious attempt to describe the ontology of quantum mechanics, and demonstrates that, besides Bohmian mechanics, the complete ontological interpretations of quantum theory exists. The model can be generalized and falsified. To ensure this theory to be true, we specified problems, allowing exposing its falsity.     

Differential and Twistor Geometry of the Quantum Hopf Fibration

We study a quantum version of the SU(2) Hopf fibration and its associated twistor geometry. Our quantum sphere arises as the unit sphere inside a q-deformed quaternion space . The resulting four-sphere is a quantum analogue of the quaternionic projective space . The quantum fibration is endowed with compatible non-universal differential calculi. By investigating the quantum symmetries of the fibration, we obtain the geometry of the corresponding twistor space and use it to study a system of anti-self-duality equations on , for which we find an ‘instanton’ solution coming from the natural projection defining the tautological bundle over .     

Universality of the local eigenvalue statistics for a class of unitary invariant random matrix ensembles

This paper is devoted to the rigorous proof of the universality conjecture of random matrix theory, according to which the limiting eigenvalue statistics ofn×n random matrices within spectral intervals ofO(n ^–1) is determined by the type of matrix (real symmetric, Hermitian, or quaternion real) and by the density of states. We prove this conjecture for a certain class of the Hermitian matrix ensembles that arise in the quantum field theory and have the unitary invariant distribution defined by a certain function (the potential in the quantum field theory) satisfying some regularity conditions.     

变值测量结构及其可视化统计分布

利用测量计算模型和系统化参量统计方法模拟双态量子交互作用系统,在多种交互作用模式下模拟双路量子干涉测量的统计分布效应.从量子交互作用出发,对Einstein受激发射,Mach-Zehnder干涉仪和Stern-Gerlach自旋测量等测量模式形成测量四元组.利用多变量逻辑函数和变值原理,在N元0-1输入/输出序对上形成变值测量四元组,建立变值双路模拟模型.变值模型根据:概率、同步/异步、对称/反对称等不同组合条件特征输出统计分布结果,形成2组8个统计直方图.     

Quaternion Octonion Reformulation of Quantum Chromodynamics

We have made an attempt to develop the quaternionic formulation of Yang–Mill’s field equations and octonion reformulation of quantum chromo dynamics (QCD). Starting with the Lagrangian density, we have discussed the field equations of SU(2) and SU(3) gauge fields for both cases of global and local gauge symmetries. It has been shown that the three quaternion units explain the structure of Yang–Mill’s field while the seven octonion units provide the consistent structure of SU(3) _C gauge symmetry of quantum chromo dynamics.     

A Quantum-Like Description of the Planetary Systems

The Titius–Bode law for planetary distances is reviewed. A model describing the basic features of this rule in the “quantum-like” language of a wave equation is proposed. Some considerations about the ’t Hooft idea on the quantum behavior of deterministic systems with dissipation are discussed.     

Microplasma generated at solid–solid interface and its application to nanostructure formation

The dynamics of the microplasmas created at a transparent solid–solid interface were investigated extensively. Microplasmas were generated at an interface between a carbon (C) or a germanium (Ge) target and a SiO₂ substrate by irradiating a KrF excimer laser beam onto the target, and the dynamics of the plasmas were investigated with the aid of optical emission spectroscopy. Although the emission spectra that contained the characteristic emission lines and the absorption bands originated from C and Ge species were observed from the C and Ge plasmas without the SiO₂ substrate, identical spectra were obtained from both the plasmas created at the C–SiO₂ and Ge–SiO₂ interfaces. Furthermore, the target and the Si substrate surfaces were examined with a scanning electron microscope. The SiO₂ substrate was smoothly etched and a nanostructure of a chain-like morphology was also observed in the deposits on the SiO₂ substrate.     

四元数在量子力学中的应用

把双四元数推广到了二级双四元数，并设计了一种态函数的四元数表示法，从而用四元数表述了相对论量子力学，使四元数物理学形成了系统，用四元数表示的算符和状态，对于导出算符间的对易关系和状态的洛伦兹变换性质是方便的。     

Quantum tricriticality in transverse Ising-like systems

The quantum tricriticality of d-dimensional transverse Ising-like systems is studied by means of a perturbative renormalization group approach focusing on static susceptibility. This allows us to obtain the phase diagram for 3 ≤ d < 4, with a clear location of the critical lines ending in the conventional quantum critical points and in the quantum tricritical one, and of the tricritical line for temperature T ≥ 0. We determine also the critical and the tricritical shift exponents close to the corresponding ground state instabilities. Remarkably, we find a tricritical shift exponent identical to that found in the conventional quantum criticality and, by approaching the quantum tricritical point increasing the non-thermal control parameter r, a crossover of the quantum critical shift exponents from the conventional value φ = 1/(d − 1) to the new one φ = 1/2(d − 1). Besides, the projection in the (r,T)-plane of the phase boundary ending in the quantum tricritical point and crossovers in the quantum tricritical region appear quite similar to those found close to an usual quantum critical point. Another feature of experimental interest is that the amplitude of the Wilsonian classical critical region around this peculiar critical line is sensibly smaller than that expected in the quantum critical scenario. This suggests that the quantum tricriticality is essentially governed by mean-field critical exponents, renormalized by the shift exponent φ = 1/2(d − 1) in the quantum tricritical region.     

The Theory of (Exclusively) Local Beables

It is shown how, starting with the de Broglie–Bohm pilot-wave theory, one can construct a new theory of the sort envisioned by several of QM’s founders: a Theory of Exclusively Local Beables (TELB). In particular, the usual quantum mechanical wave function (a function on a high-dimensional configuration space) is not among the beables posited by the new theory. Instead, each particle has an associated “pilot-wave” field (living in physical space). A number of additional fields (also fields on physical space) maintain what is described, in ordinary quantum theory, as “entanglement.” The theory allows some interesting new perspective on the kind of causation involved in pilot-wave theories in general. And it provides also a concrete example of an empirically viable quantum theory in whose formulation the wave function (on configuration space) does not appear—i.e., it is a theory according to which nothing corresponding to the configuration space wave function need actually exist. That is the theory’s raison d’etre and perhaps its only virtue. Its vices include the fact that it only reproduces the empirical predictions of the ordinary pilot-wave theory (equivalent, of course, to the predictions of ordinary quantum theory) for spinless non-relativistic particles, and only then for wave functions that are everywhere analytic. The goal is thus not to recommend the TELB proposed here as a replacement for ordinary pilot-wave theory (or ordinary quantum theory), but is rather to illustrate (with a crude first stab) that it might be possible to construct a plausible, empirically viable TELB, and to recommend this as an interesting and perhaps-fruitful program for future research.     

Secondary electron emission from highly charged carbon grains

Surfaces in contact with a plasma can influence its characteristics and, on the other hand, the impact of plasma particles can change surface properties of materials immersed in a plasma. Carbon is often present in plasma systems either as a building material or a product of technological processes, thus its behavior is an important factor of these applications. The paper deals with investigations of secondary emission of 1–6 μm spherical grains from amorphous carbon under the electric field of the order of 10⁸ V/m. We have found that the secondary emission yield increases with the electric field at the sample surface nearly linearly and does not depend on the grain diameter. Long-lasting (hours) electron irradiation of the sample surface leads to a significant decrease of the yield that was attributed to the removal of an absorbed layer from the grain surface. This conclusion is supported by the fact that a similar effect was achieved after several minutes of simultaneous electron and ion treatments.     

Correction to: Dynamic Mach–Zehnder interferometer based on a Michelson configuration and a cube beam splitter system

Optical Review - The article Dynamic Mach–Zehnder interferometer based on&nbsp;a&nbsp;Michelson configuration and&nbsp;a&nbsp;cube beam splitter system written by A. Montes...     

Mechanical spectroscopy of laser deposited polymers

Pulsed laser deposition (PLD) at 248 nm in ultra high vacuum was used to produce thin poly(methyl methacrylate) (PMMA) and poly(ethyl methacrylate) (PEMA) films. The ablation and deposition mechanisms were found to be similar in both systems. Having the same backbone, these polymers differ in the size of their polar side groups leading to changes in their dynamics. Studies of the relaxation processes were performed using mechanical torsion and bending spectroscopy by means of a double-paddle oscillator (DPO) and an in-situ plasma plume excited reed (PPXR), respectively. A strong increase of the mechanical damping was observed during annealing of the polymer films well above the glass transition temperature T _g, while in-situ X-ray measurements did not reveal any structural changes. For PEMA, the glass transition temperature T _g=335 K and the main absorption maximum appear at lower temperatures compared to PMMA (T _g=380 K), allowing one to measure the mechanical properties in a much wider range above T _g.     

A novel fabrication of superhydrophobic surfaces for universal applicability

The present work reports a novel and facile approach to fabricate stable superhydrophobic surfaces for universal applicability in practice. Poly(furfuryl alcohol)/copper composite coatings were prepared on substrates via a brush-painting method; after being immersed in a stearic acid solution, the superhydrophobic surfaces were obtained due to the formation of copper stearate on the substrates. These products were characterized by field-emission scanning electron microscopy, Fourier transform infrared spectrometry, X-ray powder diffraction and the X-ray photoelectron spectrum. Results demonstrate that the superhydrophobic surfaces formed originally on copper substrates can also be generated on other substrates without the copper element. Furthermore, this work will provide a simple and universal method to create large-scale superhydrophobic surfaces on various substrates.     

Fabrication of fluorescent nanoparticles of dendronized perylenediimide by laser ablation in water

Highly fluorescent organic nanoparticles with size of about 300 nm were prepared by nanosecond laser ablation of micrometer-sized powder of dendronized perylenediimide dispersed in water. The nanoparticle colloidal solution provided a fluorescence quantum yield of 0.58. The absorption and emission spectral studies demonstrated that the bulky dendron groups at the side bays of perylenediimide chromophore efficiently suppress the interchromophoric interactions in the nanoparticles. Fluorescence measurement on several single nanoparticles underlines that the prepared nanoparticles are bright and photo-stable enough to be a useful probe for single particle fluorescence investigation.     

Electron diffraction study of various lattice defects in a Bi<Subscript>4</Subscript>Ge<Subscript>3</Subscript>O<Subscript>12</Subscript> crystal

Lattice defects in a scintillation detector made of Bi₄Ge₃O₁₂ (BGO) could severely impact detector efficiency via non-radiative transfer of electron excitation, thus making thorough investigations of these defects highly important. Here we present a combined experimental and theoretical study of two- and three-dimensional defects in a Czochralski-grown BGO crystal. Upon examination by transmission electron microscopy the selected-area electron diffraction (SAED) patterns in two neighboring parts of the specimen reveal different kinds of two- and three-dimensional defects. Three sub-grains misoriented at 2.47° with reference to each other and probable presence of stacking faults lying in {011} planes were observed in the first examined local area. The SAED image taken from an area in the close neighborhood is much more complicated and is explained in terms of the superposition of reflections from: (i) a partially textured GeO₂ second-phase inclusion; (ii) the basic lattice of BGO and (iii) a superlattice-like structure based on the BGO lattice. The atomic structure of such a superlattice-like structure was theoretically modeled and the corresponding simulated SAED patterns were found to be in good agreement with the experimentally observed one.