Wave-like Properties Research Articles

Quantum motion in complex space

Abstract This paper is dedicated to the development of a general theory unifying classical and quantum mechanics in complex space, and to the conveyance of the philosophy that what have been considered as probabilistic quantum events have a common origin from the particle’s deterministic motion in complex space. We postulate that the actual scenario of dynamic motion happens in complex space and what we customarily consider as physical reality is merely the projection of the actual scenario into the real space. The proposed theory employs complex-extended classical mechanics to describe and model quantum systems in such a way that all the particle-like properties can be reserved due to its classical nature and in the meanwhile, all the wave-like properties are manifested naturally via the multi-path behavior of complex trajectories. The proposed framework of complex mechanics makes use of classical concepts and tools to deal with particle’s quantum behavior by the introduction of a complex Hamiltonian from which complex Hamilton equations describing particle’s quantum motion are derived in a form of Newton’s second law defined in complex space. Complex mechanics is then connected with quantum mechanics by showing the equivalence between the complex Hamilton–Jacobi equation and Schrodinger equation. The solutions of the complex Hamilton equations give us the complex trajectories traced by a particle, which are found to be non-unique. It is this non-uniqueness of the complex trajectories projected into real space that produces the multi-path phenomenon and the observed wave behavior of a material particle in the real space. This conclusion seems to be consistent with that of Elnaschie e (∞) space–time [Elnaschie MS. The Feynman path intergal and E -infinity from the two-slit Geclanken experiment. Int J Nonlinear Sci Numer Simul 2005;6(4):335–42; Elnaschie MS. A review of the E -infinity theory and the mass spectrum of high energy particle physics. Chaos, Solitons & Fractals 2004;19:209–36; Elnaschie MS. Elementry number theory in superstrings, loop quantum mechanics, twisters and E -infinity high energy physics. Chaos, Solitons & Fractals 2006;27:297–330].

Fast-kz three-dimensional tailored radiofrequency pulse for reduced B1 inhomogeneity.

This article presents a small-flip-angle, three-dimensional tailored RF pulse that excites thin slices with an adjustable quadratic in-plane spatial variation. The quadratic spatial variation helps to compensate for the loss in image uniformity using a volume coil at 3 T due to the wavelike properties of the RF field. The pulse is based on a novel "fast-kz" design that uses a series of slice-select subpulses along kz and phase encoding "blips" along kx-ky. The method is demonstrated by acquiring a series of 5-mm-thick T2-weighted images of the human brain at 3 T using pulses 4.8 ms in length with a 45 degrees flip angle.

Controlling Enzymatic Reactions by Geometry in a Biomimetic Nanoscale Network

We demonstrate that a transition from a compact geometry (sphere) to a structured geometry (several spheres connected by nanoconduits) in nanotube-vesicle networks (NVNs) induces an ordinary enzyme-catalyzed reaction to display wavelike properties. The reaction dynamics can be controlled directly by the geometry of the network, and such networks can be used to generate wavelike patterns in product formation. The results have bearing for understanding catalytic reactions in biological systems as well as for designing emerging wet chemical nanotechnological devices.

Modification of the pattern informatics method for forecasting large earthquake events using complex eigenfactors

Recent studies have shown that real-valued principal component analysis can be applied to earthquake fault systems for forecasting and prediction. In addition, theoretical analysis indicates that earthquake stresses may obey a wave-like equation, having solutions with inverse frequencies for a given fault similar to those that characterize the time intervals between the largest events on the fault. It is therefore desirable to apply complex principal component analysis to develop earthquake forecast algorithms. In this paper we modify the Pattern Informatics method of earthquake forecasting to take advantage of the wave-like properties of seismic stresses and utilize the Hilbert transform to create complex eigenvectors out of measured time series. We show that Pattern Informatics analyses using complex eigenvectors create short-term forecast hot-spot maps that differ from hot-spot maps created using only real-valued data and suggest methods of analyzing the differences and calculating the information gain.

Anisotropic metal-insulator transition in epitaxial thin films.

By comparing the properties of In and Pb quantum wells in a scanning tunneling microscopy subsurface imaging experiment, we found the existence of lateral bound states, a 2D Mott-Hubbard correlation gap, induced by transverse confinement. Its formation is attributed to spin or charge overscreening of quasi-2D excitations. The signature of the 2D confinement-deconfinement transition is also experimentally observed, with the correlation gap being pinned in the middle of the conduction band. A self-organized 2D Anderson lattice is suggested as a new ground state.

Tunable interactions in ultracold Bose gases

We have created bright matter wave solitons by using a Feshbach resonance to tune the interactions in a Bose–Einstein condensate of 7Li. The solitons are made to propagate in a one-dimensional potential formed by a focused laser beam. We observed dispersive wave-like properties for repulsive interactions and soliton-like behavior for attractive interactions. Adjacent solitons are observed to interact repulsively.

Wavelike Properties of Solar Supergranulation Detected in Doppler Shift Data

Recently, Gizon, Duvall, & Schou suggested that supergranulation has a wavelike component. In this Letter, I show that the same phenomenon can be observed using surface Doppler shift data, thereby confirming their observations, which were made using a helioseismic time-distance technique. In addition to confirming those results, I show that the wave motion is predominantly longitudinal (the fluid displacement is in the direction of propagation), and I am able to extend the results for the rotation and the meridional flow beyond ±70° latitude. The meridional flow results, which extend further than previous helioseismic measurements, appear to show no sign of a second cell.

Shelley's Poetics, Wave Dynamics, and the Telling Rhythm of Complementarity

With discovery of superstring theory, musical metaphors take on startling reality, for theory suggests that microscopic landscape is suffused with tiny strings whose pattern orchestrate evolution of cosmos. The winds of change, according superstring theory, gust through aeolian universe. Brian Greene, The Elegant Universe: Superstrings, Hidden Dimensions, and Quest for Ultimate Theory (1999) 19. It is well known that brain has periodic of activity.. entire [neural network] can operate only by large amount of cooperative, back-and-forth matching of activity at all levels ... neurons in central nervous system have rich diversity of electrical properties based on ionic conductances that endow with oscillatory Francisco Varela, et.al., The Embodied Mind: Cognitive Science & Human Experience (1993)75 Drawn from quantum cosmology and cognitive neuroscience, epigraphs capture my recollection of critical coincidence in which my thinking about Percy Shelley's theoretical poetics began. too, theorized that cosmological structure expressed itself in vibrational and that mental events manifest autorhythmic oscillatory properties. In fact, he positioned their rhythmic interactions at foundation of his poetics, which proposed a certain order or rhythm at core of all imaginative expressivity (i.e. wide range of 'texts' falling within definitions of poetry in Defense). (1) Early in A Defense of Poetry, states that rhythmic principle within human beings corresponds to impressions which excite them (481). Mind and matter, as aspects of cosmos apparent in laws, express their shared dynamics in physical sensation[s] of rhythm and therein embody, in well chosen words of Amittai Aviram, an insistent manifestation of (Telling Rhythm: Body and Meaning in Poetry [1994]200. The world expresses itself in waves of information, yet these outer waves encounter and interact with inner waves generated in brain, placing consciousness itself at/as event horizon of Being. To employ phrase current with these interactive waves form patterns of interference, and under optimal conditions, both material vehicles of rhythmic manifestation/expression (biosphere and brain) achieve what contemporary physics and neuroscience term cohesion. For images of light and water provide symbolic tracks in wavelike properties of discussed in his poetics and embody properties thematically evoked in his best poetry. New readings of Shelley's figures and theories of light: confirm De Man's belief in Shelley Disfigured, that these tropes establish extraordinarily systematic foundation for occasionally chaotic poetic events (The Rhetoric of Romanticism [1984] 110). Critical analysis has also moved beyond this restricted rhetorical sphere of semiotic play toward more materialized and theorized views (Arkady Plotinsky, All Shapes of Light: The Quantum Mechanical Shelley, Shelley: Poet and Legislator ..., eds. Bennett and Curran [1996] 263). For example, given Shelley's probing nature, recovery of such symbolic pattern in physics and mind science of his day creates widened cultural context within which his imagistic tendencies. Light and water, two principles expressed through wave dynamics, embody wavelike aspects of mind and matter evoked in his poetry. Zajonc's term in Catching Light: The Entwined History of Light and Mind (1993) also fit Shelley: the lights of nature and of mind entwine ... call forth vision, and these harmonic interactions frame emergent feature calls perfect symmetry between inner and outer phenomena (2). Shelley's ability synthesize scientific and poetic insights grows from his comprehensive and synthetical view of celestial and cerebral mechanics (David Clark,ed. …

A mathematical model of Bloch NMR equations for quantitative analysis of blood flow in blood vessels of changing cross-section—PART II

Unlike most medical imaging modalities, magnetic resonance imaging (MRI) is based on effects that cross multiple biological levels: contrast depends on interactions between the local chemistry, water mobility, microscopic magnetic environment at the subcellular, cellular or vascular level, cellular integrity, etc. These interactions potentially allow for imaging functional changes in the same reference frame as the anatomic information. However, to tap this potential, we need methodologies that robustly incorporate the best models of the underlying physics interactions in order to extract the best possible interaction obtainable on flow velocity and rates. Due to the fundamental role the Bloch NMR equations play in the analysis of the properties of magnetic resonance imaging, this presentation will focus on mathematical modeling of the Bloch NMR flow equations into the harmonic differential equation. This simplification allows us to explain qualitatively, the effects of coriolis force on the motion of flowing fluid. The Transverse magnetization M y, is introduced as a stream function. Our choice of conditions has led to a linear equation for M y. We derived the stream function as a form of solution which contains the linearity property demanded by conditions at x=0. The resulting flow reveals some interesting wave-like properties which were examined directly. The existence of the waves is associated with the non-uniformity of the Coriolis parameter, and it is not difficult to see the general mechanism. The quantum mechanical models of Bloch NMR equations describe dynamical states of particles in flowing fluid. We introduce the basic background for understanding some of the applications of quantum mechanics to NMR and explain their significance and potentials. It also describes the behavior of the rF B 1 field when the fluid particles flow under physiological and some modeled pathological conditions. The wave function is explored to determine the minimum energy, a function of the rF B 1 field for the fluid particle to be located in the non-classical region. These models can be invaluable to understand the basic Physics of extracting the relevant flow parameters by which velocity quantification can be made in Blood vessels with changing cross-section.

Nonunitary higher derivative gravity classically equivalent to Einstein gravity and its Newtonian limit

Runaway solutions can be avoided in fourth order gravity by a doubling of the matter operator algebra with a symmetry constraint with respect to the exchange of observable and hidden degrees of freedom together with the change in sign of the ghost and the dilaton fields. The theory is classically equivalent to Einstein gravity, while its non-unitary Newtonian limit is shown to lead to a sharp transition, around $10^{11}$ proton masses, from the wavelike properties of microscopic particles to the classical behavior of macroscopic bodies, as well as to a trans-Planckian regularization of collapse singularities. A unified reading of ordinary and black hole entropy emerges as entanglement entropy with hidden degrees of freedom. The emergent picture gives a substantial agreement with B-H entropy and Hawking temperature.

The development of light fastness testing and light fastness standards

The development of the theories of light has taken place over many centuries. Theories were being proposed more than 2500 years ago, possibly by Pythagoras, or the Atomists a century later, that light consists of particles emitted by objects that are collected by the eye. Conversely, Euclid proposed that the eye sends out rays that detect objects and produce the sensation of sight [1]. Throughout the centuries that followed, the properties of light were widely investigated, particularly the phenomena of reflection and refraction. One of the more important discoveries was that made by Newton, using a prism to split white light into the colours of the rainbow. His experiments demonstrated the wave-like behaviour of light. It was universally accepted at the time that waves could only travel through a propagating medium, as demonstrated by sound and water waves. This led scientists at the time to introduce the concept of luminiferous ether that fills all space, including vacua, and thus allows light waves to be propagated. An important discovery of Maxwell was the theory of electromagnetic radiation. This shows that a change in a magnetic field will induce a changing electric field and vice versa. This electric field will, in turn, exhibit wave-like properties. The electromagnetic field can be considered as a potential, which will act

Thinking about physics

Physical scientists are problem solvers. They are comfortable doing science: they find problems, solve them, and explain their solutions. Roger Newton believes that his fellow physicists might be too comfortable with their roles as solvers of problems. He argues that physicists should spend more time thinking about physics. If they did, he believes, they would become even more skilled at solving problems and doing science. As Newton points out in this thought-provoking book, problem solving is always influenced by the theoretical assumptions of the problem solver. Too often, though, he believes, physicists haven't subjected their assumptions to thorough scrutiny. Newton's goal is to provide a framework within which the fundamental theories of modern physics can be explored, interpreted, and understood. Surely physics is more than a collection of experimental results, assembled to satisfy the curiosity of appreciative experts, Newton writes. Physics, according to Newton, has moved beyond the describing and naming of curious phenomena, which is the goal of some other branches of science. Physicists have spent a great part of the twentieth century searching for explanations of experimental findings. Newton agrees that experimental facts are vital to the study of physics, but only because they lead to the development of a theory that can explain them. Facts, he argues, should undergird theory. Newton's explanatory sweep is both broad and deep. He covers such topics as quantum mechanics, classical mechanics, field theory, thermodynamics, the role of mathematics in physics, and the concepts of probability and causality. For Newton the fundamental entity in quantum theory is the field, from which physicists can explain the particle-like and wave-like properties that are observed in experiments. He grounds his explanations in the quantum field. Although this is not designed as a stand-alone textbook, it is essential reading for advanced undergraduate students, graduate students, professors, and researchers. This is a clear, concise, up-to-date book about the concepts and theories that underlie the study of contemporary physics. Readers will find that they will become better-informed physicists and, therefore, better thinkers and problem solvers too.

Peak structure with a quadrupole mass filter operated in the third stability region

Peak structure for a quadrupole operated in the third stability region with Mathieu parameters ( a, q) ≈ (3, 3) has been studied experimentally and modeled theoretically. It is shown that the structure is due to the imaging properties of the quadrupole field which are caused by the wavelike properties of the ion trajectories. Ions enter the quadrupole through a small inlet aperture on axis. When ions are focused on the center of the exit aperture the transmission is a maximum. Conversely when ions have trajectories that place them near the rods at the exit aperture the transmission is a minimum and a dip appears on a peak. The positions of dips on a peak can be assigned to lines in the stability diagram. These lines follow iso-β lines, where β is the parameter that determines the frequencies of ion motion. The positions of the lines are controlled by the number of rf cycles, which ions spend in the quadrupole field. At high resolution (>300) and low ion axial energy (<20 eV) the peak splitting is minimal or absent.

Modern Physics, 3rd edn

The number of broadly based physics texts written at a level corresponding to second year and above of UK physics degrees is limited. This is such a book thoroughly updated in a third edition, the first edition having been published 20 years ago. The book is unusual in that the reader is referred to the Freeman website www.whfreeman.com/physics for some additional sections. It will be interesting to see whether this proves to be an attractive feature. The coverage reflects the US emphasis on topics and contains both theoretical and experimental details. It should not be regarded as an introductory text although it is clearly written. Thus the first two chapters take the reader straight into relativity, concentrating mainly on special relativity but going on to general relativity. From here the reader is led to ideas of quantization of charge, light and energy, followed by an exploration of the nuclear atom, wavelike properties of particles and Schr�dinger's equation. Solution of this equation for the hydrogen atom introduces a section on spectroscopy. The next chapter on statistical physics includes Fermi-Dirac and Bose-Einstein statistics and brings to a close Part 1, which concentrates on the theoretical groundwork. Consistent with its title, the book does not cover traditional aspects of thermodynamics and electromagnetic theory. Part 2 is entitled `Applications' and begins with a chapter on molecular structure and spectra. Lasers and masers are included here but geometrical, physical and nonlinear optics get limited or no coverage. Solid state physics follows but, despite the title of the book, there is little on modern devices, although the section on superconductivity mentions high temperature materials. The chapters on nuclear physics, fission, fusion reactors and medical applications and a chapter on particle physics are comprehensive. Finally a chapter on astrophysics and cosmology is referred to, but the reader must find this at the website. As this is an attractive chapter it is a pity that it is not printed within the book. Although viewing the chapter on the Web gives the benefit of full colour, it is not easy to read the textual information off the screen. Within the printed material, there are good diagrams with the addition of a single colour, burgundy, a colour that is wasted on those of us who are red-green colour-blind! Each chapter is provided with an impressive number of graded problems (it is not easy to provide such a comprehensive range of problems at this level) and numerical answers are given in the back for every third problem. There is a student solution manual available for these problems and a complete instructor's solution manual has also been produced. It is therefore a useful book for both students and lecturers.

Control of Open Quantum Systems

Spontaneous emission in atomic tunneling has been virtually unexplored before our recent work [1]. Since tunneling is a distinct manifestation of wave-like properties, it is important to raise the basic questions: can spontaneous decay of internal excitations in tunneling atoms be viewed as a decoherence process that is analogous to its counterpart in diffracted atoms? and if so, how would such decoherence manifest itself? We have put forward a theory of spontaneous emission from a two-level atom as it tunnels through a square potential barrier [1]. Our theory demonstrates that the emission process is describable as loss of coherence between interfering classical trajectories in space-time, which constitute the atom tunneling motion. The emitted photon at each frequency is correlated to particular atomic classical trajectories, in a way which makes them measurably distinguishable. This distinguishability destroys their interference [2], as does which-way (Welcher-Weg) information, which is obtainable from spontaneous emission in diffracted atoms [3, 4]. The ensuing analysis rests on two observations. (i) The overall duration of the decay process is much longer than the inverse transition frequency ω (see below). This allows us to resort to the rotating wave approximation (RWA), which is used in the Wigner—Weisskopf (WW) treatment of spontaneous emission [5]. (ii) Nearly all of the cavity-enhanced spontaneous emission is funneled into the continuum of nearly resonant modes with wave-vectors q (ω/c)ź, which are aligned with the cavity axis z, perpendicular to the atomic incidence axis x. This allows us to use the dipole approximation, since q . x 0, and neglect off-axis photon recoil effects on the atomic wave packet. Hence, the RWA interaction Hamiltonian of the atom with the cavity-mode continuum becomes effectively one-dimensional,

Finite-velocity diffusion

The phenomenon of diffusion modelled as Brownian motion or in terms of the diffusion equation is deficient in that it permits an infinite speed of signal propagation. The simplest diffusion-like equation with a bounded speed of signal propagation is the so-called telegrapher's equation which implicitly contains a type of momentum. We discuss some properties, solutions and problems related to this equation. These are generally more complicated in form than corresponding ones for the diffusion equation, exhibiting wave-like properties at short times and diffusion-like properties in the long-time limit.Resumen. El fenómeno de la difusión, modelado tanto como movimiento Browniano como mediante la ecuación de difusión, es deficiente en el sentido que permite una velocidad de propagación infinita. La denominada ecuación del telegrafista es una de las ecuaciones más simples con una velocidad de propagación acotada y que contiene de forma implícita un cierto tipo momento. En este trabajo se discuten algunas propiedades, soluciones y cuestiones relacionadas con esta ecuación. Estas propiedades y soluciones son generalmente más complicadas que las correspondientes a la ecuación de difusión ordinaria, presentando, a tiempos cortos, propiedades de tipo ondulatorio y propiedades difusivas en el límite asintótico.

Edge-flame-holding

Nonpremixed flame sheets often have edges, which we call edge flames. Edge flames have wave-like properties in the sense that stationary structures can exist that travel at a well-defined speed relative to the flow on the reaction-free side of the edge. Edge speeds can be positive or negative. Recently, a one-dimensional model of edge flames was proposed by Buckmaster, and here we apply this model to an edge flame that is located in an accelerating flow and fixed by diffusive interaction with a burner rim. Blow-off occurs if an assigned Damkohler number is too small, and for values of this number greater than some minimum there are two solutions. A stability analysis shows, as expected, that the solution branch for which the stand-off distance increases with Damkohler number is unstable. These results are familiar, but have not been previously deduced in the context of a simple model with exact, albeit asymptotic, solutions.

Multiple Factors Govern Intraretinal Axon Guidance: A Time-Lapse Study

In this study, the multiple factors that govern the unidirectional path of intraretinal axons, as well as the cellular movements prior to and during early axonogenesis, were investigated using time-lapse videomicroscopy. For several hours prior to overt axon elongation, young retinal ganglion cells send out transient minor processes in all directions at the pial surface. Time-lapse analysis of the chondroitin sulfate (CS)-containing matrix that has been suggested to play an important role in regulating this early differentiative event revealed the dynamic, wavelike properties of this extracellular matrix component. As the CS matrix dissipates across the immature ganglion cells, only one minor process, away from the highest concentration of CS peripherally and in the direction of the optic fissure centrally, is retained and becomes the mature axon. Focal concentrations of L1 appear at points of neurite contact with previously established axons, suggesting that this growth-promoting molecule is also involved with establishing the precise, unidirectional outgrowth pattern of retinal ganglion cell axons. NCAM was diffusely distributed on neural elements and on the neuroepithelial endfeet in the central and peripheral retina and, thus, may not be an essential unidirectional axon growth cue. Growth cones mechanically deflected 180° from the optic fissure after the CS wave had receded from the central retina had morphologies and rates of elongation similar to those oriented in the proper direction. Growth cones deflected obliquely toward the ventral retinal periphery entered a territory of increasing CS-containing proteoglycan matrix and neurons with minor processes. As these deflected axons entered more deeply into this region they slowed down and sent out long transient branchlike processes. These observations illustrate the complex organization of the changing cell surface and matrix components within the retina during axonogenesis and axon outgrowth. The results also elucidate the potential importance of a cell state where immature neurons probe their environment via minor processes. These specialized neurites may provide the neuron with a way to sample a full 360° of terrain around them. This method of exploring the environment could afford the cell a mechanism with which to sample, summate, and respond to physical structures as well as simultaneously occurring negative and positive molecular influences that are distributed unequally on either side of the cell body.

Mechanics of a particle in a gauge field

Classical motion of a charged particle in an electromagnetic field is described by the Lorentz equation in terms of the field components. The field is defined by the infinitesimal gauge group elements associated with closed curves. The Lorentz equation may be derived from the action principle with an appropriate Lagrangian. The Lagrangian may also be used to associate group elements with curves in the space-time manifold. The action principle is shown here to be an equivalence relation between the infinitesimal elements so defined for a collection of closed curves and the identity element. This suggests a natural extension to require the equivalence of global elements with the identity and by considering all curves. The resulting equation, in addition to providing an extension of the Lorentz equation, also admits a straightforward generalization to non-Abelian gauge fields. The extended equation has an infinite number of trajectories as solutions. The properties of these paths are shown to impart wavelike properties to the particles in motion. In view of these results, the motion of a particle is formulated within the framework of the path integral formalism that yields a generalized Schrödinger type equation in a general gauge field. As a further implication of the properties of the trajectories assigned to a particle, this equation is shown to reduce to a set of equations, one of them being the Klein–Gordon equation.

Linear Wave Propagation in Mildly Relativistic Thermal Pair Plasmas

view Abstract Citations (1) References (30) Co-Reads Similar Papers Volume Content Graphics Metrics Export Citation NASA/ADS Linear Wave Propagation in Mildly Relativistic Thermal Pair Plasmas Pietrini, Paola ; Krolik, Julian H. Abstract We present dispersion relations and eigenmodes for linear waves propagating in fluid-like mildly relativistic thermal pair plasmas For any given wavevector, four modes are possible: two with sound wave-like properties, and two that are isobaric and essentially non-propagating. One of the isobaric modes strongly perturbs the pair balance, while the other does so much more weakly. Short-wavelength sound waves propagate non-dispersively with a speed which is not a monotonic function of temperature. All sound waves are damped in a time short compared to a wave crossing time; the isobaric modes are generally damped in a time short compared to a light crossing time. At low temperatures (corresponding to high pair content), long-wavelength sound waves are so strongly damped that they do not propagate. On this basis we predict that pressure perturbations should be very weak in thermal pair plasmas, and that even subsonic projectile motion should create pressure jumps. Publication: The Astrophysical Journal Pub Date: March 1994 DOI: 10.1086/173848 Bibcode: 1994ApJ...423..693P Keywords: PLASMAS; WAVES full text sources ADS |