Comparison of experimental microwave tunneling data with calculations based on Maxwell's equations

We compare microwave tunneling experiments using three types of potentials with calculations describing these systems, using only Maxwell's equations. The values obtained are identical within a very narrow error limit. Thus, microwave tunneling through evanescent waveguide regions, including superluminal tunneling velocities, is described by Maxwell's equations. The dispersion relation yields purely imaginary, complex, or real k-values. As an analogy, microwave tunneling presents an ideal tool for studying quantum mechanical tunneling.     

Light-matter interactions within the Ehrenfest–Maxwell–Pauli–Kohn–Sham framework: fundamentals,implementation, and nano-optical applications

In recent years significant experimental advances in nano-scale fabrication techniques and in available light sources have opened the possibility to study a vast set of novel light-matter interaction scenarios, including strong coupling cases. In many situations nowadays, classical electromagnetic modeling is insufficient as quantum effects, both in matter and light, start to play an important role. Instead, a fully self-consistent and microscopic coupling of light and matter becomes necessary. We provide here a critical review of current approaches for electromagnetic modeling, highlighting their limitations. We show how to overcome these limitations by introducing the theoretical foundations and the implementation details of a density-functional approach for coupled photons, electrons, and effective nuclei in non-relativistic quantum electrodynamics. Starting point of the formalism is a generalization of the Pauli–Fierz field theory for which we establish a one-to-one correspondence between external fields and internal variables. Based on this correspondence, we introduce a Kohn-Sham construction which provides a computationally feasible approach for ab-initio light-matter interactions. In the mean-field limit, the formalism reduces to coupled Ehrenfest–Maxwell–Pauli–Kohn–Sham equations. We present an implementation of the approach in the real-space real-time code Octopus using the Riemann–Silberstein formulation of classical electrodynamics to rewrite Maxwell's equations in Schrödinger form. This allows us to use existing very efficient time-evolution algorithms developed for quantum-mechanical systems also for Maxwell's equations. We show how to couple the time-evolution of the electromagnetic fields self-consistently with the quantum time-evolution of the electrons and nuclei. This approach is ideally suited for applications in nano-optics, nano-plasmonics, (photo) electrocatalysis, light-matter coupling in 2D materials, cases where laser pulses carry orbital angular momentum, or light-tailored chemical reactions in optical cavities just to name but a few.     

Posteriori Error Estimation for an Interior Penalty Discontinuous Galerkin Method for Maxwell's Equations in Cold Plasma

In this paper, we develop a residual-based a posteriori error estimator for the time-dependent Maxwell's equations in the cold plasma. Here we consider a semi-discrete interior penalty discontinuous Galerkin (DG) method for solving the governing equations. We provide both the upper bound and lower bound analysis for the error estimator. This is the first posteriori error analysis carried out for the Maxwell's equations in dispersive media.     

Wave coupling theory of the quadratic electro-optic effect in a linear absorbent medium

Starting from Maxwell's equations and considering the quadratic electro-optic effect as a perturbation, we present a generalized wave coupling theory of quadratic electro-optic effect in linear absorbent centrosymmetric medium. We use a KLTN crystal as an example for studying the influences of linear absorption on the amplitudes and phases of the two electromagnetic wave components of electro-optic modulation.     

Systolic processor designs using single-electron digital circuits

The possibility of using single-electron digital circuits (SEDCs) to achieve ultra-high performance digital signal processing is explored. SEDCs are highly-scalable Coulomb blockade-based circuits that operate in the discrete limit where bits are represented by single electrons. Such circuits are well-suited to implementing bit-level systolic processing algorithms because the local connectivity of systolic arrays translates into locally-interconnected hardware. By relieving interconnect bandwidth limitations this enables circuits that can fully exploit the extreme scaling possible with the single-electron devices. Errors associated with co-tunneling, thermal fluctuations, etc. are an important issue in single-electron circuits, especially for a digital application. The systolic arrays are, however, amenable to simple error-correction techniques which may make computing with these unreliable components possible. Nevertheless, it must be emphasized that realization of these complex circuits depends on tremendous advances in fabrication technology, particularly to meet their stringent uniformity requirements.     

Maxwell's demon assisted thermodynamic cycle in superconducting quantum circuits

We study a new quantum heat engine (QHE), which is assisted by a Maxwell's demon. The QHE requires three steps: thermalization, quantum measurement, and quantum feedback controlled by the Maxwell demon. We derive the positive-work condition and operation efficiency of this composite QHE. Using controllable superconducting quantum circuits as an example, we show how to construct our QHE. The essential role of the demon is explicitly demonstrated in this macroscopic QHE.     

Experimental evidence of enhancement in the anticipation time by cascading

We have studied and verified experimentally the enhancement in the anticipation time by cascading Chua's circuits. The experiments have been carried out in a one dimensional array of Chua's circuits (2 to 8) coupled unidirectionally, such that each one acts as a master for the next one. By doing so, it has been observed that the anticipation time increases with an increase in the array size. Moreover, the numerical simulations of an array of eighty Chua's circuits verify the experimental observations.     

Mathematical study of the two-dimensional lasing problem for the whispering-gallery modes in a circular dielectric microcavity

Microdisk lasers are investigated for their thresholds characteristics. We present a novel approach for studying the threshold gains of the whispering-gallery (WG) and other modes based on solving the boundary value problem for the Maxwell's equations. The novelty is that we consider the real-value pairs of frequencies and material gains as eigenvalues. In the two-dimensional (2D) approximation this problem is reduced to the set of independent transcendental equations. A Newton's method is further used to calculate the thresholds and natural frequencies numerically.     

Experimental evidence for amplitude death induced by a time-varying interaction

In this paper, we study the time-varying interaction in coupled oscillatory systems. For this purpose, we have designed a novel time-varying resistive network using an analog switch and inverter circuits. We have applied this time-varying resistive network to mutually coupled identical Chua's oscillators. When the resistances are varied in time, we find that amplitude death arises in coupled identical oscillators. This has been observed numerically as well as verified through hardware experiments.     

Numerical Simulation of a Multi-Frequency Resistivity Logging-While-Drilling Tool Using a Highly Accurate and Adaptive Higher-Order Finite Element Method

A novel, highly efficient and accurate adaptive higher-order finite element method ($hp$-FEM) is used to simulate a multi-frequency resistivity logging-while-drilling (LWD) tool response in a borehole environment. Presented in this study are the vector expression of Maxwell's equations, three kinds of boundary conditions, stability weak formulation of Maxwell's equations, and automatic $hp$-adaptivity strategy. The new $hp$-FEM can select optimal refinement and calculation strategies based on the practical formation model and error estimation. Numerical experiments show that the new $hp$-FEM has an exponential convergence rate in terms of relative error in a user-prescribed quantity of interest against the degrees of freedom, which provides more accurate results than those obtained using the adaptive $h$-FEM. The numerical results illustrate the high efficiency and accuracy of the method at a given LWD tool structure and parameters in different physical models, which further confirm the accuracy of the results using the Hermes library (http://hpfem.org/hermes) with a multi-frequency resistivity LWD tool response in a borehole environment.     

Multi-Symplectic Wavelet Collocation Method for Maxwell's Equations

In this paper, we develop a multi-symplectic wavelet collocation method for three-dimensional (3-D) Maxwell's equations. For the multi-symplectic formulation of the equations, wavelet collocation method based on autocorrelation functions is applied for spatial discretization and appropriate symplectic scheme is employed for time integration. Theoretical analysis shows that the proposed method is multi-symplectic, unconditionally stable and energy-preserving under periodic boundary conditions. The numerical dispersion relation is investigated. Combined with splitting scheme, an explicit splitting symplectic wavelet collocation method is also constructed. Numerical experiments illustrate that the proposed methods are efficient, have high spatial accuracy and can preserve energy conservation laws exactly.     

Electromagnetic and Force Field Equations

In classical physics the electromagnetic equations are described by Maxwell's equations. Maxwell's equations proved to be invariant under gauge, or Lorentz transformations. Also, Einstein's equations of the special theory of relativity are invariant under Lorentz transformations. On the other hand classical mechanics and quantum mechanics laws are invariant under Galilean transformations. This means that, there are two different dynamical structures describing our universe. Einstein's unified field theory failled in putting our universe in one dynamical structure. New electromagnetic and force field equations are going to be derived. They have the same shape like Maxwell's equations, but with different dynamical structure. Those equations are invariant under Galilean transformations and in the density matrix formalism of quantum mechanics.     

Mechanical systems in the quantum regime

Mechanical systems are ideal candidates for studying quantum behavior of macroscopic objects. To this end, a mechanical resonator has to be cooled to its ground state and its position has to be measured with great accuracy. Currently, various routes to reach these goals are being explored. In this review, we discuss different techniques for sensitive position detection and we give an overview of the cooling techniques that are being employed. The latter includes sideband cooling and active feedback cooling. The basic concepts that are important when measuring on mechanical systems with high accuracy and/or at very low temperatures, such as thermal and quantum noise, linear response theory, and backaction, are explained. From this, the quantum limit on linear position detection is obtained and the sensitivities that have been achieved in recent opto- and nanoelectromechanical experiments are compared to this limit. The mechanical resonators that are used in the experiments range from meter-sized gravitational wave detectors to nanomechanical systems that can only be read out using mesoscopic devices such as single-electron transistors or superconducting quantum interference devices. A special class of nanomechanical systems is bottom-up fabricated carbon-based devices, which have very high frequencies and yet a large zero-point motion, making them ideal for reaching the quantum regime. The mechanics of some of the different mechanical systems at the nanoscale is studied. We conclude this review with an outlook of how state-of-the-art mechanical resonators can be improved to study quantum mechanics.     

Shear free solutions of Maxwell's equations

A twisting shear free solution of Maxwell's equations is obtained by transforming to a complex coordinate system in which the corresponding solution is complex but twist free. The equations in this system are easily solved, and, by transforming back to the original coordinates, a twisting shear free solution of Maxwell's equations is obtained.     

Analysis of numerical dispersion properties of SFDTD and MRTD schemes

In this paper, the Maxwell's equations are written as Hamilton canonical equations by using Hamilton functional variation method. Maxwell's equations can be discretized with symplectic propagation technique combined with high-order difference schemes approximations to construct symplectic finite difference time domain (SFDTD) method. The high-order dispersion equations of the scheme for space is deduced. The numerical dispersion analysis is included, and it is compared with the multiresolution time-domain (MRTD) method based on the Daubechies scaling functions. Numerical results show high efficiency and accuracy of the SFDTD method.     

Free‐Electron Gas Spectrum Uniqueness in the Mixture of Noble Gases

Gas mixtures can reach the Maxwell's specter shape in case of low‐ionized mono‐atomic mixtures in the weak electric field. The parameters pertaining to the Maxwell spectrum of free electrons' gas straightforwardly settle on the insulating characteristics of the examined gas mixture at the fundamental level. In this paper, a condition for breakdown has been accomplished taking as a starting point the ionization coefficients derived accordingly, as well as the conditions for breakdown in keeping with the Townsend mechanism. The dc breakdown voltage value of noble gases mixture has been measured in the experimental part of the paper. The hypothesis that the free‐electron gas spectrum is unique in the noble gas mixture and is of Maxwell's type has been verified. (© 2016 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Quantized current in a quantum dot turnstile

We have performed RF experiments on a lateral quantum dot defined in the two dimensional electron gas (2DEG) of a GaAs/AlGaAs heterostructure. The small capacitance of the quantum dot gives rise to single-electron charging effects, which we employed to realize a quantum dot turnstile device. By modulating the tunnel barriers between the quantum dot and the 2DEG leads with two phase-shifted RF signals, we pass an integer number of electrons through the quantum dot per RF cycle. This is demonstrated by the observation of quantized current plateaus at multiples ofef in current-voltage characteristics, wheref is the frequency of the RF signals. When an asymmetry is induced by applying unequal RF voltages, our quantum dot turnstile operates as a single-electron pump producing a quantized current at zero bias voltage.     

A simulator for single-electron tunnel devices and circuits based on simulated annealing

Simulated annealing is proposed as a simulation method for single-electron tunnel devices and circuits. Tunnel junctions, voltage sources and capacitors are used as elements for the construction of single-electron circuits. The simulator is applied successfully to the two-stage tunnel junction inverter circuit. The computation time is practically acceptable when cooling schedule and cooling parameters are appropriately chosen.     

A Spectral Time-Domain Method for Computational Electrodynamics

Ever since its introduction by Kane Yee over forty years ago, the finite-difference time-domain (FDTD) method has been a widely-used technique for solving the time-dependent Maxwell's equations that has also inspired many other methods. This paper presents an alternative approach to these equations in the case of spatially-varying electric permittivity and/or magnetic permeability, based on Krylov subspace spectral (KSS) methods. These methods have previously been applied to the variable-coefficient heat equation and wave equation, and have demonstrated high-order accuracy, as well as stability characteristic of implicit time-stepping schemes, even though KSS methods are explicit. KSS methods for scalar equations compute each Fourier coefficient of the solution using techniques developed by Golub and Meurant for approximating elements of functions of matrices by Gaussian quadrature in the spectral, rather than physical, domain. We show how they can be generalized to coupled systems of equations, such as Maxwell's equations, by choosing appropriate basis functions that, while induced by this coupling, still allow efficient and robust computation of the Fourier coefficients of each spatial component of the electric and magnetic fields. We also discuss the application of block KSS methods to problems involving non-self-adjoint spatial differential operators, which requires a generalization of the block Lanczos algorithm of Golub and Underwood to unsymmetric matrices.