Table of contents

We model recent experiments on living sulphur bacteria interacting with quantised light, using the Dicke model. Our analysis shows that the strong coupling between the bacteria and the light, when both are treated quantum-mechanically, indicates that in those experiments there is entanglement between the bacteria (modelled as dipoles) and the quantised light (modelled as a single quantum harmonic oscillator). The existence of lower polariton branch due to the vacuum Rabi splitting, measured in those experiments for a range of different parameters, ensures the negativity of energy (with respect to the lowest energy of separable states), thus acting as an entanglement witness.

To deal with the behaviour of wire structures subjected to electromagnetic waves with the finite-difference time-domain (FDTD) method, it is necessary to establish the external electromagnetic excitation in time-domain. For a homogeneous lossy half-space problem, the Fresnel reflection coefficients for arbitrary polarization plane wave are usually multiplied by the pulse spectrum in the frequency domain and the result is transformed into the time-domain. In this paper, an accurate method based on the Padé approximation theory in conjunction with the partial fraction expansion is used, and leads to expressions of the field above a homogeneous lossy earth that can analytically be transformed into the time-domain. The influence of the common degree of the numerator and denominator of the Padé approximant on the accuracy of the proposed method is discussed.

A low-frequency gravitational-wave background (GWB) from the cosmic merger history of supermassive black holes is expected to be detected in the next few years by pulsar timing arrays. A GWB induces distinctive correlations in the pulsar residuals—the expected arrival time of the pulse less its actual arrival time. Simplifying assumptions are made in order to write an analytic expression for this correlation function, called the Hellings and Downs curve for an isotropic GWB, which depends on the angular separation of the pulsar pairs, the gravitational-wave frequency considered, and the distance to the pulsars. This is called the short-wavelength approximation, which we prove here rigorously and analytically for the first time.

Simple experimental method was developed to examine magnetic self-assembly of macroscopic magnetic spheres of 3mm and 5mm diameters in the lack of external magnetic field. Magnetic force driven aggregation was followed up by video recording and was analysed in detail to identify the processes that lead to the creation of clusters (chains, pairs, circles, etc). Self-aggregation of randomly distributed single spheres, pairs and triplets were examined with this method as well. Applying several liquid media with different viscosity helped to characterize the aggregation processes regarding the kinetic energy of collisions. The results were compared with results of previous experimental works and computer simulations of aggregation of magnetic nanoparticles and magnetic-dipolar systems. Besides to earlier described rings and chains that represent the lowest potential energy of the system of ideal magnetic dipoles in two dimensions, we observed several other structures during the experiments. The most frequently appearing clusters were investigated by direct minimization of the potential energy function of these structures.

A detailed analysis of micro- and nanoantennas is crucial for enhancing the performance of photodetectors in the mid- and far-infrared (IR) region. In contrast to the rapid progress in IR detectors based on nanodevices, the local nanoscale properties of antennas for the purpose of near-field coupling with these detectors have not been well investigated. In this work, we fabricated and studied a logarithm-spiral (log-spiral) antenna with an arm termination, which was designed as a low-loss, wide-band antenna for highly efficient near-field interaction with nanoscale IR detectors. By using a scattering-type near-field optical microscope (s-SNOM) combined with a highly stable quantum cascade laser, we observed a nanoscale spatial distribution of amplitudes generated via IR illumination on the antenna surface. Experimental and simulated results revealed a clear dependence on IR-light polarization corresponding to the rotationally symmetric structure of the spiral antenna. Furthermore, phase mapping measurements indicated a π reversal of the out-of-plane phase between two adjacent antenna probes regardless of polarization direction, providing a possibility of efficient near-field coupling with nanoscale detectors. These results demonstrate that s-SNOM imaging offers a powerful tool for gaining useful information regarding mutual coupling between optical antennas and nanostructures.

First-principles calculation has become an indispensable methodology in revealing the working principles of nanoscale electronic devices, but ultra-large supercells are usually required in modeling the devices with critical metal/dielectric interfaces. Traditional density functional theory within the generalized gradient approximation (GGA) suffers from the inaccurate band gap problem when metal oxides are present, but they serve as the core component in resistive random access memory (RRAM), which is a promising path for novel high speed non-volatile memories. To obtain improved oxide band gaps, we applied the efficient GGA-1/2 method for self-energy correction, whose computational load is at the same level as standard GGA. In particular, we have investigated the influence of exchange-correlation functional flavors on the GGA-1/2 band structures, taking four important binary oxide RRAM materials (α-Al₂O₃, r-TiO₂, m-ZrO₂ and m-HfO₂) as benchmark examples. Five GGA functionals (PBE, PBEsol, PW91, revPBE and AM05) were considered and their band structures were compared in detail. We have found that the performance of GGA-1/2 is comparable to state-of-the-art GW and generally superior to the HSE06 hybrid functional. Among the five GGA functionals, PBEsol yields the best results in general. In addition, the applicability of a single self-energy potential for various GGA-1/2 flavors is discussed. Our work provides a guide to the GGA flavor selection, when applying the GGA-1/2 method to metal oxides.

The interdependence between long range correlations and topological signatures in fermionic arrays is examined. End-to-end correlations, in particular those accounting for the hopping between the chain edges, maintain a characteristic pattern in the presence of delocalized excitations. This feature can be used as an operational criterion to identify Majorana fermions in one-dimensional systems. The study discusses how to obtain the chain eigenstates in tensor-state representation as well as the correlations. Outstandingly, the final result can be written as a simple analytical expression that underlines the link with the system's topological phases.

A simulation model for second mode positive streamers in dielectric liquids is presented. Initiation and propagation is modeled by an electron-avalanche mechanism and the Townsend–Meek criterion. The electric breakdown is simulated in a point-plane gap, using cyclohexane as a model liquid. Electrons move in a Laplacian electric field arising from the electrodes and streamer structure, and turn into electron avalanches in high-field regions. The Townsend–Meek criterion determines when an avalanche is regarded as a part of the streamer structure. The results show that an avalanche-driven breakdown is possible, however, the inception voltage is relatively high. Parameter variations are included to investigate how the parameter values affect the model.

This paper reports the significances of the negative real part of ac permeability and the transition of real part of ac permittivity. The paper also identifies the μ negative media and double negative media in the frequency range 3–120 MHz. The eddy current loss calculated from the measured complex permeability is found to diminish with increasing frequency which is an important factor to be considered for high frequency applications of these materials.

Separation of variables is one of the oldest techniques for solving certain classes of partial differential equations (PDEs). As is the case with many other solution techniques for differential equations, separation of variables may be codified within the broader framework of symmetry analysis. Though the separation of variables technique is frequently used in the nuclear engineering context with various equations describing neutron transport, its connection to the symmetries of those equations has not yet been thoroughly established. It is thus the purpose of this work to establish that connection using neutron diffusion as both an initial step toward analysis of more generally applicable equations, and as a connection to previous results in related problems. Using Lie group analysis, it is found that the traditional space-time separable solution of the neutron diffusion equation (featuring a single α-eigenvalue) corresponds to time translation and flux scaling symmetries. Additional solutions of this equation are also constructed using its broader symmetry set.

An arch bridge structure, comprising of a semiring cavity resonator coupled with bus waveguide, has been investigated numerically and theoretically. Due to the interaction of broad bright state and the narrow dark state caused by the semiring cavity and bus waveguide, respectively, fano resonance can be accrued in transmission spectra which possess a sheer asymmetrical profile that can be adjusted by changing the parameters of the structure with the finite-difference time-domain (FDTD) method. A plasmonic nanosensor is devised based on fano resonance in a metal-insulator-metal (MIM) waveguide system, which has a sensitivity of 1500 nm/RIU as well as a figure of merit (FOM) of 5500. Our findings can provide the guidance for fundermental research of nanosensor in highly integrated optical circuits.

The Fermi surface pockets that lie at the corner of the two-iron Brillouin zone in heavily electron-doped iron selenide superconductors are accounted for by an extended Hubbard model over the square lattice of iron atoms that includes the principal 3d_xz and 3d_yz orbitals. At half filling, and in the absence of intra-orbital next-nearest neighbor hopping, perfect nesting between electron-type and hole-type Fermi surfaces at the the center and at the corner of the one-iron Brillouin zone is revealed. It results in hidden magnetic order in the presence of magnetic frustration within mean field theory. An Eliashberg-type calculation that includes spin-fluctuation exchange finds that the Fermi surfaces undergo a Lifshitz transition to electron/hole Fermi surface pockets centered at the corner of the two-iron Brillouin zone as on-site repulsion grows strong. In agreement with angle-resolved photoemission spectroscopy on iron selenide high-temperature superconductors, only the two electron-type Fermi surface pockets remain after a rigid shift in energy of the renormalized band structure by strong enough electron doping. At the limit of strong on-site repulsion, a spin-wave analysis of the hidden-magnetic-order state finds a 'floating ring' of low-energy spin excitations centered at the checkerboard wavenumber $(\pi ,\pi )$. This prediction compares favorably with recent observations of low-energy spin resonances around (π, π) in intercalated iron selenide by inelastic neutron scattering.

We investigate the electronic transport properties of semiconducting (m, n) carbon nanotubes (CNTs) on the mesoscopic length scale with arbitrarily distributed realistic defects. The study is done by performing quantum transport calculations based on recursive Green's function techniques and an underlying density-functional-based tight-binding model for the description of the electronic structure. Zigzag CNTs as well as chiral CNTs of different diameter are considered. Different defects are exemplarily represented by monovacancies and divacancies. We show the energy-dependent transmission and the temperature-dependent conductance as a function of the number of defects. In the limit of many defetcs, the transport is described by strong localization. Corresponding localization lengths are calculated (energy dependent and temperature dependent) and systematically compared for a large number of CNTs. It is shown, that a distinction by (m − n)mod 3 has to be drawn in order to classify CNTs with different bandgaps. Besides this, the localization length for a given defect probability per unit cell depends linearly on the CNT diameter, but not on the CNT chirality. Finally, elastic mean free paths in the diffusive regime are computed for the limit of few defects, yielding qualitatively same statements.

New exact solution class of Born—Infeld type nonlinear scalar field model is obtained. The variational principle of this model has a specific form which is characteristic for extremal four-dimensional hypersurface or hyper-film in five-dimensional space-time. Obtained solutions are singular solitons propagating with speed of light and having energy, momentum, and angular momentum which can be calculated for explicit conditions. Such solitons will be called the lightlike ones. The soliton singularity has a form of moving two-dimensional surface or shell. The lightlike soliton can have a set of tubelike singular shells with the appropriate cavities. A twisted lightlike soliton is considered. It is notable that its energy is proportional to its angular momentum in high-frequency approximation. A case with one tubelike cavity is considered. In this case the soliton shell is diffeomorphic to a cylindrical surface with threads by multifilar helix. The shell transverse size of the appropriate finite energy soliton can be converging to zero at infinity. The ideal gas of such lightlike solitons with minimal twist parameter is considered in a finite volume. Explicit conditions provide that the angular momentum of each soliton in the volume equals Planck constant. The equilibrium energy spectral density for the solitons is obtained. It has the form of Planck distribution in some approximation. A beam of the twisted lightlike solitons is considered. The representation of arbitrary polarization for the beam with the twisted lightlike solitons is discussed. It is shown that the effect of mechanical angular momentum transfer to absorbent by the circularly polarized beam can be provided. This effect is well known for photon beam. Thus the soliton solution which have determinate likeness with photon is obtained in particular.

It has been shown repeatedly over a period of 50 years that the use of relativistic classical physics and the inclusion of classical electromagnetic zero-point radiation leads to the Planck blackbody spectrum for classical radiation equilibrium. However, none of this work involves scattering calculations. In contrast to this work, currently accepted physical theory connects classical physics to only the Rayleigh-Jeans spectrum. Indeed, in the past, it has been shown that a nonlinear classical oscillator (which is necessarily a nonrelativistic scattering system) achieves equilibrium only for the Rayleigh-Jeans spectrum where the random radiation present at the frequency of the second harmonic of the oscillator motion has the same energy per normal mode as the radiation present at the fundamental frequency. Here we continue work emphasizing the importance of relativistic versus nonrelativistic analysis. We consider the scattering of random classical radiation by a charged harmonic oscillator of small but non-zero oscillatory amplitude (which can be considered as a relativistic scattering system) and show that detailed radiation balance holds not only at the fundamental frequency of the oscillator but through the first harmonic corresponding to quadrupole scattering, provided that the radiation energy per normal mode at the first harmonic is double the radiation energy per normal mode at the fundamental frequency. This condition corresponds exactly to the zero-point radiation spectrum which is linear in frequency. It is suggested that for this relativistic scattering system, the detailed balance for zero-point radiation holds not only for the fundamental and first harmonic but extends to all harmonics. Here we have the first example of an explicit relativistic classical scattering calculation; equilibrium corresponds not to the Rayleigh-Jeans spectrum, but rather corresponds to the Lorentz-invariant zero-point radiation spectrum.

A weakly interacting Bose gas on a simple cubic lattice is considered. We prove the existence of the standard or zero-mode Bose condensation at sufficiently low temperature. This result is valid for sufficiently small interaction potential and small values of chemical potential. Our method exploits infra-red bound for the suitable two-point Bogolyubov's inner product. We do not use the reflection positivity or some expansion methods.

An electrical line is one of the transmission media used worldwide for the transmission of signals. This is for the fact that it is less expensive and easy to manufacture than the other transmission media. In linear domain, the electrical lines transmit sinusoidal signals whose amplitude decreases exponentially and loss a lot of energy. It is therefore necessary to valorize electrical lines by enabling them to transmit solitary waves which are more stable and do not dissipate energy. This will be possible if the media of transmission line are dispersive and nonlinear. We define the analytical expressions that the charges of capacitors must obey so that the Noguchi electrical line with crosslink capacitor accepts to propagate a coupled solitary wave of the need type. The application of those definitions and Kirchhoff laws to the networks of a modified Noguchi electrical line with crosslink capacitor have enable to obtain new set of higher-order nonlinear partial differential equations which govern the dynamics of a coupled solitary wave in the said line. The construction of coupled solitary waves solutions of those set of equations by direct and effective mathematical methods notably that of Bogning-Djeumen Tchaho-Kofane [16–22] has permitted to discover that, solitary waves of type (Kink; Kink) and type (Pulse; Pulse) are easily propagated in that line when certain conditions we have elaborated are respected. The Noguchi electrical line with crosslink capacitor that we have studied is advantageous for the fact that it permits simultaneously the propagation of a set of two solitary waves contrary to a non-coupled Noguchi electrical line which only enables the propagation of one solitary wave when the signal considered is the voltage; the more we will multiply the crosslink in the line, the more we will multiply the simultaneous propagation of solitary wave in the line.