Wave-particle Research Articles

Transmission coefficient in double barrier quantum tunnelling effect

At the turn of the twentieth century, the establishment of quantum theory propelled rapid advancements, particularly in the understanding of quantum tunnellinga fundamental phenomenon in quantum mechanics crucial for various physical processes. The quantum phenomenon of particle passes through potential barriers is of great importance. In classical physics, when the energy of a particle is less than the height of a double barrier structure, it is impossible for it to pass through. However, quantum mechanics allows a particle to penetrate the barrier and emerge on the other side. This paper explores the quantum tunnelling effect, focusing on the single potential barrier model in one dimension and subsequently extending to the double potential barrier model. The Schrdinger equation provides the foundational framework for elucidating the motion of microscopic particles, emphasizing wave-particle duality inherent in quantum mechanics. The analysis of the single potential barrier model involves solving the Schrdinger equation in different regions, determining wave functions and coefficients through boundary conditions. The transmission coefficient is derived, representing the probability of a particle passing through a barrier. In the case of a thick barrier, an approximate form for transmission coefficient is provided, demonstrating the exponential decrease in transmission probability with increasing barrier thickness.

Velocity-space Signatures of Resonant Energy Transfer between Whistler Waves and Electrons in the Earth’s Magnetosheath

Wave–particle interactions play a crucial role in transferring energy between electromagnetic fields and charged particles in space and astrophysical plasmas. Despite the prevalence of different electromagnetic waves in space, there is still a lack of understanding of fundamental aspects of wave–particle interactions, particularly in terms of energy flow and velocity-space characteristics. In this study, we combine a novel quasilinear model with observations from the Magnetospheric Multiscale mission to reveal the signatures of resonant interactions between electrons and whistler waves in magnetic holes, which are coherent structures often found in the Earth’s magnetosheath. We investigate the energy transfer rates and velocity-space characteristics associated with Landau and cyclotron resonances between electrons and slightly oblique propagating whistler waves. In the case of our observed magnetic hole, the loss of electron kinetic energy primarily contributes to the growth of whistler waves through the n = −1 cyclotron resonance, where n is the order of the resonance expansion in linear Vlasov–Maxwell theory. The excitation of whistler waves leads to a reduction of the temperature anisotropy and parallel heating of the electrons. Our study offers a new and self-consistent understanding of resonant energy transfer in turbulent plasmas.

Robustness of Wave-Particle Duality under Unruh Effect.

By considering a uniformly accelerated two-level system in an initial superposition state of a qubit, we investigate the loss of coherence induced by the acceleration. In addition, we investigate the impact of acceleration on the complementarity relation in a quantum interferometric circuit or quantum scattering circuit. We present an alternative approach to exploring acceleration effects through examination of quantum coherence decay and degradation in the interference pattern. Our investigations help to provide understanding of the consequences of decoherence induced by the Unruh effect on the wave-particle duality of a uniformly accelerated qubit.

Contrariety and Complementarity: Reading Spinoza’s Intersubjective Holism of Ideas with Aristotle’s Two Accounts of Motion

Do minds and ideas connect, interact, or even depend on each other, and if so, how exactly do they connect and interact? How to conceive of the mode and process of minds and ideas being in a network and connected in some way, that is, being intersubjective or social? Martin Lenz’s study Socializing Minds (2022) convincingly shows that, contrary to widespread opinion in philosophy of mind, at least some early modern philosophers, here Spinoza, Locke, and Hume, actually give a positive answer to the first question and present models that respond to the second question, thus, addressing what Lenz proposes to call ‘the contact problem’ and repudiating the idea that mentalism is necessarily bound to individualism. In this comment, I focus on a detail in Lenz’s reconstruction of Spinoza’s ‘metaphysical model’ of intersubjectivity of minds, namely the Aristotelian physical dynamism that would underlie Spinoza’s idea of the interaction of minds. While I agree that Spinoza’s model of the interaction of minds refers to the Aristotelian conception of motion, I argue that the guiding principle in natural motion is best understood not only in terms of contrariety but also in terms of complementarity. A closer reading of Aristotle’s theory of motion (kinēsis, metabolē) identifies two approaches to natural motion, one based on contrary principles, the other on complementary principles or powers (dynameis; potentiae). I suggest conceiving them as two sources for modelling natural motion and thus as two resources for a kinetic modelling of intersubjectivity and sociality. Admittedly, my proposal goes beyond Spinoza’s model of ideas in contact, and probably beyond Lenz's interpretation of that model, but it might enrich the imagination of the socialising of minds and ideas from a kinetic point of view, which, at least as I understand it, is precisely what Spinoza and Lenz thrive on.

Evaluation of the coefficient of lateral stress at rest of granular materials under repetitive loading conditions

Although the internal stress state of soils can be affected by repetitive loading, there are few studies evaluating the lateral stress (or K0) of soils under repetitive loading. This study investigates the changes in K0 and directional shear wave velocity (Vs) in samples of two granular materials with different particle shapes during repetitive loading. A modified oedometer cell equipped with bender elements and a diaphragm transducer was developed to measure the variations in the lateral stress and the shear wave velocity, under repetitive loading on the loading and unloading paths. The study produced the following results: (1) Repetitive loading on the loading path resulted in an increase in the K0 of test samples as a function of cyclic loading number (i), and (2) Repetitive loading on the unloading path resulted in a decrease in K0 according to i. The shear wave velocity ratio (i.e. Vs(HH)/Vs(VH), where the first and second letters in parentheses corresponds to the directions of wave propagation and particle motion, respectively, and V and H corresponds to the vertical and horizontal directions, respectively) according to i supports the experimental observations of this study. However, when the tested material was in lightly over-consolidated state, there was an increase in K0 during repetitive loading, indicating that it was the initial K0, rather than the loading path, which is responsible for the change in K0. The power model can capture the variation in the K0 of samples according to i. Notably, the K0 = 1 line acts as the boundary between the increase and decrease in K0 under repetitive loading.

Whence Nonlocality? Removing Spooky Action-at-a-Distance from the de Broglie Bohm Pilot-Wave Theory Using a Time-Symmetric Version of the de Broglie Double Solution

In this work, we review and extend a version of the old attempt made by Louis de Broglie for interpreting quantum mechanics in realistic terms, namely, the double solution. In this theory, quantum particles are localized waves, i.e., solitons, that are solutions of relativistic nonlinear field equations. The theory that we present here is the natural extension of this old work and relies on a strong time-symmetry requiring the presence of advanced and retarded waves converging on particles. Using this method, we are able to justify wave–particle duality and to explain the violations of Bell’s inequalities. Moreover, the theory recovers the predictions of the pilot-wave theory of de Broglie and Bohm, often known as Bohmian mechanics. As a direct consequence, we reinterpret the nonlocal action-at-a-distance in the pilot-wave theory. In the double solution developed here, there is fundamentally no action-at-a-distance but the theory requires a form of superdeterminism driven by time-symmetry.

On the distinction between corpuscular and wave processes and the arbitrariness in the basis of special relativity theory

This article is devoted to the criticism of the wave-particle dualism and the provisions of the special theory of relativity (SRT). The fallacy of accepting the extended principle of relativity and identifying particles and waves is shown. The substantiation is given that the own fields of physical objects, which are material substances and spatially connect physical objects with each other, are the medium of propagation of light waves. The causal and visual picture of the propagation of light waves is considered, and the features of the mechanism of their propagation in comparison with other types of waves are described. On the basis of an alternative method for obtaining the relativistic law of velocities addition, the inconsistency of the principle of invariance of the interval adopted in the framework of SRT is shown. The inconsistency of the SRT positions and conclusions regarding the so-called relativistic effects—time dilation, mass increase, length decrease, as well as the energy of relativistic particles is shown. The presence of the clock paradox is shown by a simple example. The conclusion is made about the incorrectness of using mathematical transformations of Lorentz and the four-dimensional continuum in the physical representation.

Super‐Resolution Imaging via Lenses with Angular Magnification

AbstractThe far‐field resolution of traditional optical imaging systems is restricted by the Abbe diffraction limit, a direct result of the wave nature of light. To break this limit, one applicable approach is to reduce the effective size of the point‐spread‐function (PSF). In the past decades, great endeavors have been made to produce an effective super‐resolution PSF by exploiting different mechanisms, including optical nonlinearities and structured light illumination. However, it is difficult to apply these methods to objects at far distance miles away. Here, the study proposes a new approach to achieving super‐resolution imaging for far‐distance objects by utilizing angular magnification. To this end, a new class of metalenses with angular magnification is first theoretically and experimentally validated and demonstrated. Both theoretical and experimental results have demonstrated a more than twofold enhancement beyond the traditional angular‐resolution limit. The proposed approach is of promising potential in the applications of super‐resolution telescopes and remote sensing.

Optomechanical effects caused by non-zero field quantities in multiple evanescent waves.

Evanescent waves, with their high energy density, intricate local momentum, and spatial distribution of spins, have been the subject of extensive recent study. These waves offer promising applications in near-field particle manipulation. Consequently, it becomes imperative to gain a deeper understanding of the impacts of scattering and gradient forces on particles in evanescent waves to enhance and refine the manipulation capabilities. In this study, we employ the multipole expansion theory to present analytical expressions for the scattering and gradient forces exerted on an isotropic sphere of any size and composition in multiple evanescent waves. The investigation of these forces reveals several unusual optomechanical phenomena. It is well known that the scattering force does not exist in counter-propagating homogeneous plane waves. Surprisingly, in multiple pairs of counter-propagating evanescent waves, the scattering force can arise due to the nonzero orbital momentum (OM) density and/or the curl part of the imaginary Poynting momentum (IPM) density. More importantly, it is found that the optical scattering force can be switched on and off by simply tuning the polarization. Furthermore, optical forces typically vary with spatial position in an interference field. However, in the interference field generated by evanescent waves, the gradient force becomes a spatial constant in the propagating plane as the particle's radius increases. This is attributed to the decisive role of the non-interference term of the electromagnetic energy density gradient. Our study establishes a comprehensive and rigorous theoretical foundation, propelling the advancement and optimization of optical manipulation techniques harnessed through multiple evanescent waves. Specifically, these insights hold promise in elevating trapping efficiency through precise control and manipulation of optical scattering and gradient forces, stimulating further explorations.

A novel flux splitting based on wave-particle splitting for ideal magnetohydrodynamics

A novel flux splitting method based on wave-particle splitting is developed for one-dimensional ideal magnetohydrodynamics. While ideal magnetohydrodynamics (MHD) equations are non-convex with non-homogeneous flux as opposed to their hydrodynamic counterparts, the present flux splitting methods cannot develop Riemann solver. The proposed approach based on wave-particle method referred as Advection Magnetic-direction Wave Particle Splitting (AMWPS) scheme splits the flux into four parts: the wave-like total pressure part, the wave-like normal magnetic part, the particle-like advection part and the particle-like tangential magnetic part. The particle-like parts can be solved by the scheme developed by Toro and Vazquez-Cendon (TV scheme) and we propose a novel approach to the solution of Riemann problem formed by the wave-like parts including total pressure sub-flux and normal magnetic sub-flux. As for the ordered wave foliation in MHD and other limitations in wave structure, we also analyze the relation between plasma β and specific heat ratio γ. The advantage of AMWPS is that it can sharply capture isolated, stationary Alfven wave discontinuity. Several one-dimensional and two-dimensional MHD problems have been tested to highlight the accuracy, positivity preservation and robustness of AMWPS scheme and comparative studies show that AMWPS significantly outperforms the Riemann solver named Harten, Lax and Leer for contact wave (HLLC) in most cases.

An Intriguing Interpretation of 1D and 2D Non-Diffracting Modes in Cosine Profile

We provide a simple analysis based on ray optics and Dirac notation for 1D (one-dimensional) and 2D (two-dimensional) non-diffracting modes in the cosine profile, which are often called Cosine beams. We explore various kinds of structured modes formed by the superposition of two 1D Cosine beams. We then went on to understand the properties of the Bessel beams in terms of Cosine beams. For the first time, we report on the generation of three-dimensional tunable needle structures based on the interference of 1D Cosine beams. These size-tunable optical needles can have multiple advantages in material processing. Also, we report, for the first time, on the Talbot effect in Cosine beams. Straightforward mathematical calculations are used to derive analytical expressions for Cosine beams. The present method of demonstrating Cosine beams may be utilized to understand other structured modes. The Dirac notation-based interference explanation used here can provide new researchers with an easy way to understand the wave nature of light in a fundamental aspect of interferometric experiments as well as in advanced-level experiments such as beam engineering technology, imaging, particle manipulation, light sheet microscopy, and light–matter interaction. We also provide an in-depth analysis of similarities among Cosine, Bessel, and Hermite–Gaussian beams.

Exact analytical quasibound states of a scalar particle around a Reissner-Nordström black hole

In this paper, we investigate behavior of massive and massless scalar particle around a static spherically symmetric charged black hole—so called Reissner-Nordström black hole in 3+1 dimension. We successfully discover a novel exact analytical quasibound states' wave functions and energy levels by solving the covariant Klein-Gordon wave equation. The quasibound state has complex-valued energy E=ER+iEI where the real part ER can be interpreted as the scalar particle's energy while the imaginary part represents the decay. We also discuss the Hawking radiation from the apparent horizon of Reissner-Nordström black hole which can be calculated using the scalar particle's wave function. In principle, this study could provide the possibility for laboratory testing of effects whose nature is absolutely related with quantum effects in gravity.

Traveling wave thermoacoustic refrigeration with variable phase-coordinated boundary conditions.

Thermoacoustic refrigerators exploit the thermodynamic interaction between oscillating gas particles and a porous solid to generate a temperature gradient that provides a cooling effect. In this work, we present a resonator with dual enclosed driver end-caps and show that the temperature gradient across a ceramic thermoacoustic element placed in the cavity could be controlled by modifying the phase difference of the drivers, thus enabling precise control of the refrigeration capability via the temperature difference. Through deltaec simulation results, the response of the temperature gradient to various dynamic boundary conditions that alter the time-phasing and wave dynamics in the resonator are demonstrated. An experimental apparatus is constructed with two moving-coil speakers and a ceramic stack, which is shown to exhibit a temperature gradient along its length, based on the traveling-wave-like nature of the acoustic wave excited by the speakers. By adjusting the relative phase lag between the two speakers, the temperature gradient across the stack is made to increase, decrease, or flip sign. Finally, a desired temperature difference that changes in time is achieved. The results presented in this work represent a key conceptual advancement of thermoacoustic-based temperature control devices that can better serve in extreme environments and precision applications.

On the relation between nodal structures in quantum wave functions and particle correlation

We study the influence of nodal structures in two-dimensional quantum mechanical densities on wave packet entanglement. This is motivated by our recent study [Entropy, 25, 970 (2023)], which showed that the mutual information derived from the momentum-space probability density of a coupled two-particle system exhibits an unusual time dependence, which is not encountered if the position-space density is employed in the calculation. In studying a model density, here, we identify cases where the mutual information increases with the number of nodes in the wave function and approaches a finite value, whereas in this limit, the linear correlation vanishes. The results of the analytical model are then applied to interpret the correlation measures for coupled electron-nuclear dynamics, which are treated by numerically solving the time-dependent Schrödinger equation.

Solar Electron Beam—Langmuir Wave Interactions and How They Modify Solar Electron Beam Spectra: Solar Orbiter Observations of a Match Made in the Heliosphere

Solar Orbiter's four in situ instruments have recorded numerous energetic electron events at heliocentric distances between 0.5 and 1 au. We analyze energetic electron fluxes, spectra, pitch-angle distributions, associated Langmuir waves, and type III solar radio bursts for three events to understand what causes modifications in the electron flux and identify the origin and characteristics of features observed in the electron spectrum. We investigate what electron beam properties and solar wind conditions are associated with Langmuir wave growth and spectral breaks in the electron peak flux as a function of energy. We observe velocity dispersion and quasilinear relaxation in the electron flux caused by the resonant wave–particle interactions in the deca-keV range, at the energies at which we observe breaks in the electron spectrum, cotemporal with the local generation of Langmuir waves. We show, via the evolution of the electron flux at the time of the event, that these interactions are responsible for the spectral signatures observed around 10 and 50 keV, confirming the results of simulations by Kontar and Reid. These signatures are independent of pitch-angle scattering. Our findings highlight the importance of using overlapping FOVs when working with data from different sensors. In this work, we exploit observations from all in situ instruments to address, for the first time, how the energetic electron flux is modified by the beam–plasma interactions and results in specific feature appearing in the local spectrum. Our results, corroborated with numerical simulations, can be extended to a wider range of heliocentric distances.

Electron resonant interaction with whistler-mode waves around the Earth's bow shock I: The probabilistic approach

Adiabatic heating of solar wind electrons at the Earth's bow shock and its foreshock region produces transversely anisotropic hot electrons that, in turn, generate intense high-frequency whistler-mode waves. These waves are often detected by spacecraft as narrow-band, electromagnetic emissions in the frequency range of [0.1, 0.5] of the local electron gyrofrequency. Resonant interactions between these waves and electrons may cause electron acceleration and pitch-angle scattering, which can be important for creating the electron population that seeds shock drift acceleration. The high intensity and coherence of the observed whistler-mode waves prohibit the use of quasi-linear theory to describe their interaction with electrons. In this paper, we aim to develop a new theoretical approach to describe this interaction, which incorporates nonlinear resonant interactions, gradients of the background density and magnetic field, and the fine structure of the waveforms that usually consist of short, intense wave-packet trains. This is the first of two accompanying papers. It outlines a probabilistic approach to describe the wave–particle interaction. We demonstrate how the wave-packet size affects electron nonlinear resonance at the bow shock and foreshock regions, and how to evaluate electron distribution dynamics in such a system that is frequented by short, intense whistler-mode wave-packets. In the Paper II, this probabilistic approach is merged with a mapping technique, which allows us to model systems containing short and long wave-packets.

The nonlinear evolution of whistler-mode chorus: modulation instability as the source of tones

We review the modulation stability of parallel-propagating/field-aligned whistler-mode chorus (WMC) waves propagating in a warm plasma from a formal perspective with a focus on wave–particle interactions via ponderomotive forces. The modulation instability criteria are characterised by the group velocity dispersion,$d c_g/dk$, for whistler-mode waves and a condition on the ratio between the group velocity$c_g$and the electron sound speed$c_{s,e}$. We also demonstrate that in order to investigate the spatiotemporal evolution of the envelope and the formation of packets (according to this mechanism), one necessarily needs to account for the motion of ions within the system, leading to an ionic influence on the modulation instability threshold determined by the ion fraction of the plasma. Finally, we demonstrate that chirping may be captured when higher-order effects are included within the spatiotemporal evolution of the amplitude. This yields not only an explicit expression for the sweep rate but also identifies a possible origin for the power band gap that occurs at half the electron gyrofrequency. Numerical validation demonstrates that the interaction between wave packets is a source for the emergence of tones observed within mission data, and such interactions may be a major source of the electron energisation which WMC are responsible for.

Deciphering the physical basis of the intermediate-scale instability

We study the underlying physics of cosmic ray (CR)-driven instabilities that play a crucial role for CR transport across a wide range of scales, from interstellar to galaxy cluster environments. By examining the linear dispersion relation of CR-driven instabilities in a magnetised electron–ion background plasma, we establish that both the intermediate and gyroscale instabilities have a resonant origin, and show that these resonances can be understood via a simple graphical interpretation. These instabilities destabilise wave modes parallel to the large-scale background magnetic field at significantly distinct scales and with very different phase speeds. Furthermore, we show that approximating the electron–ion background plasma with either magnetohydrodynamics (MHD) or Hall-MHD fails to capture the fastest-growing instability in the linear regime, namely the intermediate-scale instability. This finding highlights the importance of accurately characterising the background plasma for resolving the most unstable wave modes. Finally, we discuss the implications of the different phase speeds of unstable modes on particle–wave scattering. Further work is needed to investigate the relative importance of these two instabilities in the nonlinear, saturated regime and to develop a physical understanding of the effective CR transport coefficients in large-scale CR hydrodynamics theories.

Sub-Diffraction Photon Trapping: The Possible Optical Energy Eigenstates within a Tiny Circular Aperture with a Finite Depth

One of the challenging riddles that is set by light is: do photons have wavefunctions like other elementary particles do? Wave–particle duality has been a prevailing fact since the beginning of quantum theory thought; in electromagnetism, light is already a kind of undulation, so what about the waves of probability then? Well, Quantum Field Theory (QFT) has a rigorous explanation and supports the idea when they are considered as fields of particles via second quantization; they do have wavefunctions of probability, and it does not have anything to do with the regular oscillations. They can be related to the energy and momentum signatures of harmonic oscillations, resembling an imitation of the behavior of a classical harmonic oscillator, which then has a wavefunction to solve the corresponding time-independent Schrödinger equation. For the last half century, electrical engineering has owned the best out of these implications of Quantum Electrodynamics (QED) and QFT by engineering better semiconductor techniques with finely miniaturized transistors and composite devices for digital electronics and optoelectronics fields. More importantly, these engineering applications have also greatly evolved into combined fields like quantum computing that have introduced a completely new and extraordinary world to electronics applications. The study takes advantage of the power of QFT to mathematically reveal the bosonic modes (Laguerre–Gaussian) that appear in a sub-diffraction cylindrical aperture. In this way, this may lead to the construction of the techniques and characteristics of room-temperature photonic quantum gates which can isolate photon modes under a diffraction limit.

A Bare and Gravitationally Dressed Electron Formed from Kerr–Newman Black Hole

The Kerr–Newman (KN) electron model, based on the classical KN black hole solution, is modified by adding a “mirror” sheet of KN metric corresponding to a positron, that creates a heavy electron-positron vacuum core dressed by gravity, and allows us to consider the bare and dressed electron separately. The bare electron is formed as a massless relativistic ring string and is responsible for the wave properties of the electron, while the heavy supersymmetric vacuum core receives the additional mass-energy from two Wilson loops dragged by the KN gravitational field, thus creating a magnetically coupled monopole-antimonopole pair. As a result, the KN electron becomes consistent with wave nature of quantum electron and its gravitational interaction increases dramatically from Planck to Compton scale.