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Background. Quantum dots (QDs) have unique optical properties that have found wide applications in optoelectronics, biology and medicine. The problem of controlling the spectral – luminescent properties of QDs initiated studies of the mechanisms of interaction of QDs with each other and with the surrounding matrix. Such interactions, under certain conditions, can significantly modify the radiative properties of QDs, which will affect the characteristics of laser structures and biosensors based on them. The purpose of this work is to study the effect of 2D dissipative tunneling in the QDs - surrounding matrix system, as well as the paired electrostatic interaction of QDs with (А+ + е) impurity complexes, on recombination radiation associated with the optical transition of an electron from the ground state of QDs to a quasi-stationary A+ state in the external electric field. Materials and methods. The interaction of an electron in the ground state of the QDs and a hole localized at the A+ center was considered in the framework of the adiabatic approximation. The dispersion equations determining the dependence of the binding energy of a hole in an impurity complex (А+ + е) in a spherically symmetric QDs on the magnitude of the external electric field and the parameters of dissipative tunneling are obtained within the framework of the zero radius potential model, in the approximation of the effective mass. The spectral intensity of recombination radiation (SIRI) in QDs with an impurity complex (А+ + е) in an external electric field is calculated in the dipole approximation. The effect of the electric field on the ground state of the electron in the QDs was taken into account in the second order of the perturbation theory. Numerical calculations and plotting of graphs were carried out for InSb-based semiconductor quantum dots using symbolic mathematics Mathcad 14 and Wolfram Mathematica 9. The probability of 2D dissipative tunneling was calculated with exponential accuracy for a model 2D oscillatory potential at a finite temperature, taking into account linear interaction with phonon modes of the environment at one time instanton quasi-classical approximation. Results. It is shown that the field dependence of the binding energy of the quasi-stationary A+ state has an oscillating character associated with quantum beats that occur during parallel 2D tunneling transfer. It is found that the SIRI curves have a characteristic fracture corresponding to the 2D bifurcation point that occurs when the tunneling modes in the interacting QDs pair change from synchronous to asynchronous. It is established that in the vicinity of the 2D bifurcation point there are irregular oscillations in SIRI associated with the modes of quantum beats when competing trajectories of tunnel transport appear. It is found that the parameters of dissipative tunneling: temperature, frequency of the phonon mode, the constant of interaction with the contact medium, the constant of interaction of QDs, have a significant effect on the amplitude of quantum beats and the position of the 2D bifurcation point in SIRI. Conclusions. Taking into account the interaction of QDs with the surrounding matrix leads to a significant modification of SIRI, which manifests itself in the form of bifurcation points and quantum beats depending on the parameters of dissipative tunneling. Taking into account the paired interaction of QDs with each other by means of hole pushing in (А+ + е) complexes leads to the suppression of recombination radiation with an increase in the constant interaction.

Quantum dots (QDs) have unique optical properties that are widely used in optoelectronics, biology, and medicine. The problem of controlling the spectral and luminescent properties of QDs has initiated studies of the mechanisms by which QDs interact with each other and with the surrounding matrix. Such interactions can, under certain conditions, significantly modify the radiative properties of QDs, which will affect the characteristics of laser structures and biosensors based on them. The aim of this work is a theoretical study of the 2D dissipative tunneling effect in the "QD–surrounding matrix" system, as well as the pair electrostatic interaction of QDs with A++ e impurity complexes, on recombination radiation associated with the optical transition of an electron from the QD ground state to the quasi-stationary A+ state in an external electric field. The interaction of an electron, which is in the ground state of a QD, and a hole that is localized at the A+ center has been considered within the framework of the adiabatic approximation. The dispersion equations that determine dependence of the hole binding energy in the A++ e impurity complex in a spherically symmetric QD on the external electric field and dissipative tunneling parameters have been obtained within the zero range potential model, in the effective mass approximation. Calculation of the spectral intensity of recombination radiation (SIRR) in QDs with an A++e impurity complex in an external electric field has been performed in the dipole approximation. Influence of the electric field on the ground state of an electron in a QD has been taken into account in the second order of the perturbation theory. Numerical calculations and plotting were carried out for a semiconductor quantum dot based on InSb using the symbolic mathematics of Mathcad 14 and Wolfram Mathematica 9. The 2D dissipative tunneling probability has been calculated with exponential accuracy for the 2D oscillatory potential model at a finite temperature, taking into account the linear interaction with the phonon modes of the environment media (or a heat bath) in the one-instanton semiclassical approximation. It is shown that the field dependence of the binding energy for the quasi-stationary A+ state has an oscillating character, associated with quantum beats that occur during parallel 2D tunneling transfer. It is found that the SIRR curves have a characteristic kink corresponding to the 2D bifurcation point that occurs when the tunneling regimes in the interacting pair of QDs change from synchronous to asynchronous. It has been established that, in the vicinity of the 2D bifurcation point, there are irregular oscillations in the SIRR associated with the modes of quantum beats, in the course of which competing trajectories of tunneling appear. It is found that the parameters of dissipative tunneling—the temperature, frequency of the phonon mode, constant of interaction with the contact medium, constant of the QDs interaction—have a significant effect on the amplitude of quantum beats and the position of the 2D bifurcation point in the SIRR. Taking into account the interaction of the QD with the surrounding matrix leads to a significant modification of the SIRR, which manifests itself in the form of bifurcation points and quantum beats that depend on the dissipative tunneling parameters. Accounting for the pairwise interaction of QDs with each other via hole repulsion in A++ e complexes leads to suppression of recombination radiation with an increase in the interaction constant. [ABSTRACT FROM AUTHOR]

In this work, considering a simplified model we estimate the magnetic moment m associated to two neodymium magnets with different geometries. We investigated how the effect of temperature modifies magnetic properties, such as the intensity of the magnetic field evaluated at the extreme of these magnets, based on these results we present a fictitious anomaly as an didactic purpose inspired by the discussion built throughout the work, which allows illustrating a current problem in the scenario of high energy physics, known as the muon (g-2) anomaly. [ABSTRACT FROM AUTHOR]

The magnetic polarization tensor has a promising capability of determining the geometry and material properties of metallic samples. In this paper, a novel computation method is proposed to estimate the magnetic polarization tensors for the metallic samples using the boundary element method. In this method, the metallic sample is placed in a uniformly distributed magnetic field. Based on assumptions that the excitation frequency and/or the conductivity of the sample is very high, the metallic sample is regarded as a perfect electrical conductor (PEC). Therefore, the scattered field at a certain distance can be simulated. By utilising the boundary element method, the magnetic polarization tensor can be derived from the simulated scattered field. The theoretical calculation is presented and simulations and experiments have been carried out to validate the proposed method. The results from the simulation are matched with the analytical solution for the case of sphere samples. Moreover, there is a good agreement between the simulation results and the experimental results for the copper cylindrical samples.

Subsurface geoelectric structures and resources can be detected based on the propagation of the electromagnetic field. Near‐source electromagnetic methods have recently become the most popular survey mode. However, calculation of the electromagnetic field in the near‐source region with artificial sources has always been performed based on far‐source dipole approximation. Owing to the introduction of artificial sources in the near‐source region, it is challenging to obtain accurate solution of the electromagnetic field based on the relationship between the observation point and the source, thereby affecting the detection accuracy. Specifically, the main problem lies in the position vector of the transmitting source, which is generally neglected in the response calculation based on the plane‐wave theory. Moreover, only far‐source data can be observed in the plane‐wave theory. However, near‐source data have been collected in a near‐source survey, with the dipole approximation resulting in a large error. We introduce a point charge element to decrease or eliminate the error caused by the dipole approximation. The non‐homogeneous Helmholtz equation is first solved using the Green's function. Then, the response expression of the real source, including the source position vector, is obtained by integrating the response of the harmonic point charge element. The substitution of the dipole elements with the point‐charge elements not only reduces the dipole approximation errors but also displays the electromagnetic characteristics of the entire zone, which are verified by the forward modeling and field survey results. The near‐source (offset is 0.8 of the target depth) survey can be realized based on the point charge element. Key Points: A point charge element is introduced to decrease or eliminate the error caused by dipole approximationThe response expression of the real source, including the source position vector, is derivedThe electromagnetic characteristics of the entire zone are displayed [ABSTRACT FROM AUTHOR]

We investigate the control landscapes of closed n-level quantum systems beyond the dipole approximation by including a polarizability term in the Hamiltonian. The latter term is quadratic in the control field. Theoretical analysis of singular controls is presented, which are candidates for producing landscape traps. The results for considering the presence of singular controls are compared to their counterparts in the dipole approximation (i.e., without polarizability). A numerical analysis of the existence of traps in control landscapes for generating unitary transformations beyond the dipole approximation is made upon including the polarizability term. An extensive exploration of these control landscapes is achieved by creating many random Hamiltonians which include terms linear and quadratic in a single control field. The discovered singular controls are all found not to be local optima. This result extends a great body of recent work on typical landscapes of quantum systems where the dipole approximation is made. We further investigate the relationship between the magnitude of the polarizability and the fluence of the control resulting from optimization. It is also shown that including a polarizability term in an otherwise uncontrollable dipole coupled system removes traps from the corresponding control landscape by restoring controllability. We numerically assess the effect of a polarizability term on a known example of a particular three-level Λ-system with a second order trap in its control landscape. It is found that the addition of the polarizability removes the trap from the landscape. The general practical control implications of these simulations are discussed.

We prove a local variant of Einstein's formula for the effective viscosity of dilute suspensions, that is, µ' = µ(1 + 5/2Φ + o(Φ)), where Φ is the volume fraction of the suspended particles. Up to now rigorous justifications have only been obtained for dissipation functionals of the flow field. We prove that the formula holds on the level of the Stokes equation (with variable viscosity). We consider a regime where the number N of particles suspended in the fluid goes to infinity while their size R and the volume fraction Φ = NR³ approach zero. We establish L∞ and Lp estimates for the difference of the microscopic solution to the solution of the homogenized equation. Here we assume that the particles are contained in a bounded region and are well separated in the sense that the minimal distance is comparable to the average one. The main tools for the proof are a dipole approximation of the flow field of the suspension together with the so-called method of reflections and a coarse graining of the volume density. [ABSTRACT FROM AUTHOR]

In this article, we study the optical force exerted on nanorods. In recent years, the capture of micro-nanoparticles has been a frontier topic in optics. A Photonic Jet (PJ) is an emerging subwavelength beam with excellent application prospects. This paper studies the optical force exerted by photonic jets generated by a plane wave illuminating a Generalized Luneburg Lens (GLLs) on nanorods. In the framework of the dipole approximation, the optical force on the nanorods is studied. The electric field of the photonic jet is calculated by the open-source software package DDSCAT developed based on the Discrete Dipole Approximation (DDA). In this paper, the effects of the nanorods’ orientation and dielectric constant on the transverse force Fx and longitudinal force Fy are analyzed. Numerical results show that the maximum value of the positive force and the negative force are equal and appear alternately at the position of the photonic jet. Therefore, to capture anisotropic nanoscale-geometries (nanorods), it is necessary to adjust the position of GLLs continuously. It is worth emphasizing that manipulations with nanorods will make it possible to create new materials at the nanoscale.

Collective dynamics in lithographically-defined artificial spin ices offer profound insights into emergent correlations and phase transitions of geometrically-frustrated Ising spin systems. Their temporal and spatial evolution are often simulated using kinetic Monte Carlo (kMC) simulations, which rely on the precise knowledge of the switching barriers to obtain predictive results in agreement with experimental observations. In many cases, however, the barriers are derived from simplified assumptions only, and do not take into account the full physical picture of nanomagnetic switching. Here we describe how the immediate magnetic square- or kagome-ice environment of a nanomagnet reversing via quasi-coherent rotation can induce clockwise and counter-clockwise switching channels with different barrier energies. This energy splitting for chiral reversal channels can be sizeable and, as string-method micromagnetic simulations show, is relevant for artificial spin ice systems made of both exchange- as well as magnetostatically-dominated units. Due to the barrier splitting and further reductions due to non-uniform reversal, transition rates can be exponentially enhanced by several orders of magnitude compared to mean-field predictions, especially in the limit of rare switching events where thermal excitation is less likely. This leads to significantly faster relaxation time scales and modified spatial correlations. Our findings are thus of integral importance to achieve realistic kMC simulations of emergent correlations in artificial spin systems, magnonic crystals, or the evolution of nanomagnetic logic circuits.

Motivated by problems arising in magnetic drug targeting, we propose to generate an almost constant Kelvin (magnetic) force in a target subdomain, moving along a prescribed trajectory. This is carried out by solving a minimization problem with a tracking type cost functional. The magnetic sources are assumed to be dipoles and the control variables are the magnetic field intensity, the source location and the magnetic field direction. The resulting magnetic field is shown to effectively steer the drug concentration, governed by a drift-diffusion PDE, from an initial to a desired location with limited spreading. [ABSTRACT FROM AUTHOR]

The radiation absorption cross section of indium-tin oxide (ITO) semiconductor nanoparticles of various sizes placed in various media is calculated in the region of plasmon resonance. The photoabsorption cross sections calculated within the framework of the Mie theory and in the dipole approximation are compared with each other and with the available experimental data. The limits of applicability of the dipole approximation are determined. The prospects of using these nanoparticles as an active material in optical plasmon sensors are assessed. [ABSTRACT FROM AUTHOR]

In this article we consider one of the approaches aimed at reducing time of calculation of aerodynamic characteristics of the studied objects using discrete vortex method. Also, accuracy assessment of calculation of aerodynamic characteristics was performed.

The dipole approximation is employed to describe interactions between atoms and radiation. It essentially consists of neglecting the spatial variation of the external field over the atom. Heuristically, this is justified by arguing that the wavelength is considerably larger than the atomic length scale, which holds under usual experimental conditions. We prove the dipole approximation in the limit of infinite wavelengths compared to the atomic length scale and estimate the rate of convergence. Our results include N-body Coulomb potentials and experimentally relevant electromagnetic fields such as plane waves and laser pulses. [ABSTRACT FROM AUTHOR]

Recently there has been a large interest in achieving metasurface resonances with large quality factors. In this article, we examine metasurfaces that comprised a finite number of magnetic dipoles oriented parallel or orthogonal to the plane of the metasurface and determine analytic formulas for their resonances' quality factors. These conditions are experimentally achievable in finite-size metasurfaces made of dielectric cubic resonators at the magnetic dipole resonance. Our results show that finite metasurfaces made of parallel (to the plane) magnetic dipoles exhibit low quality factor resonances with a quality factor that is independent of the number of resonators. More importantly, finite metasurfaces made of orthogonal (to the plane) magnetic dipoles lead to resonances with large quality factors, which ultimately depend on the number of resonators comprising the metasurface. In particular, by properly modulating the array of dipole moments by having a distribution of resonator polarizabilities, one can potentially increase the quality factor of metasurface resonances even further. These results provide design guidelines to achieve a sought quality factor applicable to any resonator geometry for the development of new devices such as photodetectors, modulators, and sensors. [ABSTRACT FROM AUTHOR]