Fractional quantization of Hall resistance as a consequence of mesoscopic feedback

A nonlinear single-particle model is introduced, which captures the characteristic of systems in the quantum Hall regime. The model involves the magnetic Schrödinger equation with spatially variable magnetic flux density. The distribution of flux is prescribed via the postulates of the mesoscopic mechanics (MeM) introduced in my previous articles (cf. [9, 10]). The model is found to imply exact integer and fractional quantitzation of the Hall conductance. In fact, Hall resistance is found to be R _H = (h/e ²)(M/N) at the filling factor value N/M. The assumed geometry of the Hall plate is rectangular. Special properties of the magnetic Schrödinger equation with the mesoscopic feedback loop allow us to demonstrate quantization of Hall resistance as a direct consequence of charge and flux quantization. I believe results presented here shed light at the overall status of the MeM in quantum physics, confirming its validity.     

Nonlinear wave mechanics and particulate self-focusing

A previous model for treating electromagnetic nonlinear wave systems is examined in the context of wave mechanics. It is shown that nonlinear wave mechanics implies harmonic generation of new quasiparticle wave functions, which are absent in linear systems. The phenomenon is interpreted in terms of pair (and higher order ensembles) coherence of the interacting particles. The implications are far-reaching, and the present approach might contribute toward a common basis for diverse physical phenomena involving nonlinearity. An intimate relationship connecting coherence, nonlocal interaction, and nonlinearity has been previously noticed in the physics of superconductivity. It is shown here that all these ingredients are consistently contained in the present formalism. The present theory may contribute to elucidate a controversial theory proposed by Panarella, who claims to have measured high-energy photons due to high-intensity laser radiation, which cannot be predicted on the basis of linear quantum theory. Panarella explains the new phenomena by stipulating a nonlinear intensity-dependent photon energy. It is argued here that nonlinearity, manifested in the presence of high intensity, may give rise to high- and low-energy photons, the so-called effective and tired photons, respectively. However, the present explanation does not involve ad hoc assumptions regarding the foundations of quantum theory. In analogy with the electrodynamic model, the present theory leads to particulate self-focusing in high-density streams of particles. Since such particulate beams are currently under consideration in connection with fusion reactions, this might be of future interest.On leave of absence from the Department of Electrical Engineering, Ben-Gurion University of the Negev, Beer Sheva, Israel.     

A Process Algebra Approach to Quantum Electrodynamics

The process algebra program is directed towards developing a realist model of quantum mechanics free of paradoxes, divergences and conceptual confusions. From this perspective, fundamental phenomena are viewed as emerging from primitive informational elements generated by processes. The process algebra has been shown to successfully reproduce scalar non-relativistic quantum mechanics (NRQM) without the usual paradoxes and dualities. NRQM appears as an effective theory which emerges under specific asymptotic limits. Space-time, scalar particle wave functions and the Born rule are all emergent in this framework. In this paper, the process algebra model is reviewed, extended to the relativistic setting, and then applied to the problem of electrodynamics. A semiclassical version is presented in which a Minkowski-like space-time emerges as well as a vector potential that is discrete and photon-like at small scales and near-continuous and wave-like at large scales. QED is viewed as an effective theory at small scales while Maxwell theory becomes an effective theory at large scales. The process algebra version of quantum electrodynamics is intuitive and realist, free from divergences and eliminates the distinction between particle, field and wave. Computations are carried out using the configuration space process covering map, although the connection to second quantization has not been fully explored.     

Mechanical model of vulnerable atherosclerotic plaque rupture

Atherosclerotic vascular disease is the most common cause of morbidity and mortality in the world. Until quite recently, it has been generally thought that the accretion of atherosclerotic plaque in coronary arteries progressively occluded the arterial lumen, resulting in a decrease in coronary blood flow reserve and ultimately producing myocardial ischemia, and the therapeutic aim to atherosclerosis has mainly focused on reducing the plaque. However, evidence accumulated over recent years has…     

Lattice soliton equation hierarchy and associated properties

As a new subject, soliton theory is shown to be an effective tool for describing and explaining nonlinear phenomena in nonlinear optics, super conductivity, plasma physics, magnetic fluid, etc. Thus, the study of soliton equations has always been one of the most prominent events in the field of nonlinear science during the past few years. Moreover, it is important to seek the lattice soliton equation and study its properties. In this study, firstly, we derive a discrete integrable system by using the Tu model. Then, some properties of the obtained equation hierarchies are discussed.     

Applied Bohmian mechanics

Bohmian mechanics provides an explanation of quantum phenomena in terms of point-like particles guided by wave functions. This review focuses on the use of nonrelativistic Bohmian mechanics to address practical problems, rather than on its interpretation. Although the Bohmian and standard quantum theories have different formalisms, both give exactly the same predictions for all phenomena. Fifteen years ago, the quantum chemistry community began to study the practical usefulness of Bohmian mechanics. Since then, the scientific community has mainly applied it to study the (unitary) evolution of single-particle wave functions, either by developing efficient quantum trajectory algorithms or by providing a trajectory-based explanation of complicated quantum phenomena. Here we present a large list of examples showing how the Bohmian formalism provides a useful solution in different forefront research fields for this kind of problems (where the Bohmian and the quantum hydrodynamic formalisms coincide). In addition, this work also emphasizes that the Bohmian formalism can be a useful tool in other types of (nonunitary and nonlinear) quantum problems where the influence of the environment or the nonsimulated degrees of freedom are relevant. This review contains also examples on the use of the Bohmian formalism for the many-body problem, decoherence and measurement processes. The ability of the Bohmian formalism to analyze this last type of problems for (open) quantum systems remains mainly unexplored by the scientific community. The authors of this review are convinced that the final status of the Bohmian theory among the scientific community will be greatly influenced by its potential success in those types of problems that present nonunitary and/or nonlinear quantum evolutions. A brief introduction of the Bohmian formalism and some of its extensions are presented in the last part of this review.     

Nonlinear quantum mechanics,the superposition principle,and the quantum measurement problem

There are four reasons why our present knowledge and understanding of quantum mechanics can be regarded as incomplete. (1) The principle of linear superposition has not been experimentally tested for position eigenstates of objects having more than about a thousand atoms. (2) There is no universally agreed upon explanation for the process of quantum measurement. (3) There is no universally agreed upon explanation for the observed fact that macroscopic objects are not found in superposition of position eigenstates. (4) Most importantly, the concept of time is classical and hence external to quantum mechanics: there should exist an equivalent reformulation of the theory which does not refer to an external classical time. In this paper we argue that such a reformulation is the limiting case of a nonlinear quantum theory, with the nonlinearity becoming important at the Planck mass scale. Such a nonlinearity can provide insights into the aforesaid problems. We use a physically motivated model for a nonlinear Schr?dinger equation to show that nonlinearity can help in understanding quantum measurement. We also show that while the principle of linear superposition holds to a very high accuracy for atomic systems, the lifetime of a quantum superposition becomes progressively smaller, as one goes from microscopic to macroscopic objects. This can explain the observed absence of position superpositions in macroscopic objects (lifetime is too small). It also suggests that ongoing laboratory experiments may be able to detect the finite superposition lifetime for mesoscopic objects in the near future.     

Auditory physics. Physical principles in hearing theory. II

In the first part of this series of papers [Phys. Reports 62 (1980) 87–174] several physical problems are described that are relevant for the study of the auditory system. The present paper extends this treatment, it describes more facts upon which auditory theory is to be based and it delves considerably deeper into the mechanics of the cochlea (inner ear). The first two chapters treat nonlinear phenomena that are found in physiological and mechanical responses of the cochlea and in psychophysical experiments (listening tests carried out in human subjects). The main part of the paper is devoted to the mechanics of the cochlea. This part is preceded by an overview of the results of mechanical measurements on the cochlea. As it turns out, the newest experimental data present a specific challenge for cochlear mechanics.The central three chapters of the paper describe the development of a linear three-dimensional model of the cochlea. The main intention is to describe this model in a step-by-step fashion (hence the chapter headings borrowed from the field of architecture). Even in this simplified case, the solution for the response of the cochlear model is far from easy. Therefore, a few excursions are made into fields of physics and engineering in which related problems are worked out in analytical form. Just as in Part I of this series of papers, this extended treatment considerably deepens insight into the physical factors involved. Confrontation of the requirements for modelling described in the first few chapters with what has been achieved in the final part reveals how much study in the field of auditory physics remains to be done.     

Dynamics of a single peak of the Rosensweig instability in a magnetic fluid

To describe the dynamics of a single peak of the Rosensweig instability a model is proposed which approximates the peak by a half-ellipsoid atop a layer of magnetic fluid. The resulting nonlinear equation for the height of the peak leads to the correct subcritical character of the bifurcation for static induction. For a time-dependent induction the effects of inertia and damping are incorporated. The results of the model show qualitative agreement with the experimental findings, as in the appearance of period doubling, trebling, and higher multiples of the driving period. Furthermore, a quantitative agreement is also found for the parameter ranges of frequency and induction in which these phenomena occur.     

Parametric generation of soliton-like spin wave pulses in ferromagnetic thin-film ring resonators

Intense soliton-like spin wave pulses were parametrically generated in ferromagnetic thin-film ring resonators under the action of periodic parallel magnetic pulse pumping. Various types of nonlinear pulse sequences were observed depending on the pump pulse repetition period and the position of the pulse carrier frequency with respect to the ring resonator frequency spectrum. A theoretical model is suggested and calculations are performed that give a detailed explanation of the observed phenomena.     

磁记忆检测的力磁耦合型磁偶极子理论及解析解

磁偶极子理论在缺陷漏磁场解释中被成功广泛使用.由于磁荷密度等参数不易定量,磁偶极子理论在应用中常常进行归一化处理,被认为不适用于对应力相关的磁记忆信号做量化分析.本文通过建立力磁耦合型磁偶极子理论模型,以适用于分析磁记忆检测中应力对磁信号的影响.基于铁磁学理论确定应力和磁场联合作用下的等效场强度,基于弱磁化状态的一阶近似,获得了各向同性铁磁材料微弱环境磁场下的应力磁化解析解.结合磁信号二维问题中矩形和V形磁荷分布假定,建立了光滑与破坏试件表面磁信号、矩形和V形表面缺陷所诱导磁信号的力磁耦合型磁偶极子理论分析模型,并获得其解析解.基于力磁耦合型磁偶极子理论的解析解,对拉伸实验中试件破坏前后的信号差异、矩形和V形表面缺陷诱导磁信号,以及磁信号的影响因素和规律等进行了详细分析.理论研究表明,基于本文理论模型的解析解可实现对磁记忆检测中的一些基本实验现象和规律的解释.     

高速跟驰交通流动力学模型研究

为研究道路交通中的高速跟驰物理现象,针对高速跟驰车辆特点,综合考虑了驾驶员换道决策行为以及随机慢化等因素,结合前景理论等方法,提出了一种用于模拟道路交通流中高速跟驰物理现象的动力学模型(简称HCCA模型).通过计算机数值模拟,研究了高速跟驰交通流物理现象演化机理及高速跟驰特性.结果表明:与对称的双车道元胞自动机动力学模型相比,本文建立的HCCA动力学模型能够再现道路高速跟驰物理现象,并得到了道路小间距高速跟驰率超过7%的结果与实测结果相符合,最后模拟得到了丰富的交通物理现象,再现了自由流、同步流及运动阻塞等复杂交通物理现象.     

贝利相与非线性输运

电子输运现象包含一系列很重要的材料性质,并可以用来提供关于载体物理系统的很多信息。在 最近的二三十年,人们逐渐认识到除了电子能谱之外,电子在布里渊区的几何性质,比如贝利曲率和 轨道磁矩,会在电子输运中起到关键性的作用。在线性输运现象中的此种关联已引起广泛的兴趣并得 到深入的研究。然而,在非线性输运现象中的电子几何性质的作用的研究最近才逐渐起步。此种关联 可以大大加深对各种非线性输运现象的认识,并对如何从材料控制上调节非线性现象的强度提供有价 值的研究视角和指导原则。基于此背景,本文试图引入研究输运现象的半经典理论框架,并在几种输 运现象中举例说明贝利相的作用。     

贝利相与非线性输运

电子输运现象包含一系列很重要的材料性质,并可以用来提供关于载体物理系统的很多信息。在 最近的二三十年,人们逐渐认识到除了电子能谱之外,电子在布里渊区的几何性质,比如贝利曲率和 轨道磁矩,会在电子输运中起到关键性的作用。在线性输运现象中的此种关联已引起广泛的兴趣并得 到深入的研究。然而,在非线性输运现象中的电子几何性质的作用的研究最近才逐渐起步。此种关联 可以大大加深对各种非线性输运现象的认识,并对如何从材料控制上调节非线性现象的强度提供有价 值的研究视角和指导原则。基于此背景,本文试图引入研究输运现象的半经典理论框架,并在几种输 运现象中举例说明贝利相的作用。     

磁性斯格明子晶格的磁弹现象与机理

近年来,人们在一些具有手性相互作用的磁性体材料及薄膜中成功观测到具有非平凡拓扑性质的二维自旋结构,称作磁性斯格明子.在大部分情况下,磁性斯格明子自发地聚集成一种晶格结构,称作斯格明子晶格.孤立的斯格明子由于其奇特的拓扑性质以及优异的电流驱动性质等"局域化特征"受到人们的广泛关注.与此相对,斯格明子晶格作为一种新颖的宏观磁性相,可能与材料固有的多场耦合性质发生相互作用进而引发许多奇特的宏观物理现象乃至新性质.在此范畴内,人们发现由于手征磁体内禀的磁弹耦合,斯格明子晶格不但对材料的力学性质产生影响,而且在外力作用下自身具备"层展的弹性性质".本文对相关现象进行梳理,并基于一种针对B20族手征磁体磁弹耦合效应普遍适用的热力学唯象模型,逐一简述对于不同类型的磁弹现象如何建模分析,进而给出其中一部分现象的实验与理论结果比对.最后,对这一领域的发展提出几个可供进一步探索的方向.     

Universality in solar flare, magnetic storm and earthquake dynamics using Tsallis statistical mechanics

The universal character of the dynamics of various extreme phenomena is an outstanding scientific challenge. We show that X-ray flux and D_st time series during powerful solar flares and intense magnetic storms, respectively, obey a nonextensive energy distribution function for earthquake dynamics with similar values for the Tsallis entropic index q. Thus, evidence for universality in solar flares, magnetic storms and earthquakes arise naturally in the framework of Tsallis statistical mechanics. The observed similarity suggests a common approach to the interpretation of these diverse phenomena in terms of driving physical mechanisms that have the same character.     

Formation of envelope solitons of spin-wave packets propagating in thin-film magnon crystals

The formation of light envelope solitons has been experimentally observed under the pulsed excitation and propagation of radio-frequency spin-wave packets in a magnon crystal, a periodic magnetic film structure. The magnon crystal has been fabricated from a thin single-crystal yttrium iron garnet (YIG) film. The envelope solitons have been excited at frequencies corresponding to the edges of the Bragg-resonance-induced band gaps of the spin-wave spectrum of the magnon crystal. A theoretical explanation of the observed phenomenon has been proposed with the use of the numerical simulation of the formation of solitons based on the nonlinear Schrödinger equation.     

Outline of a Generalization and a Reinterpretation of Quantum Mechanics Recovering Objectivity

The ESR model has been recently proposed in several papers to offer a possible solution to the problems raising from the nonobjectivity of physical properties in quantum mechanics (QM) (mainly the objectification problem of the quantum theory of measurement). This solution is obtained by embodying the mathematical formalism of QM into a broader mathematical framework and reinterpreting quantum probabilities as conditional on detection rather than absolute. We provide a new and more general formulation of the ESR model and discuss time evolution according to it, pointing out in particular that both linear and nonlinear evolution may occur, depending on the physical environment.     

Ferroelectric Phase Transition of first Order in BaTiO3

A microscopic model of BaTiO₃ is treated to describe static phenomena near the ferroelectric phase transition. In addition to the polarization, changes of the lattice constant at fixed pressure are also considered. That leads to a new explanation of the first order character of the transition, which is carried out not only qualitatively but also quantitatively. We investigate the dependence on pressure and external field. Agreement with the experiment through the adjustment of the parameters of the theory is obtained.