Full Numerical Calculations Research Articles

Quasinormal mode approach to modelling light-emission and propagation in nanoplasmonics

We describe a powerful and intuitive theoretical technique for modeling light–matter interactions in classical and quantum nanoplasmonics. Our approach uses a quasinormal mode (QNM) expansion of the photon Green function within a metal nanoresonator of arbitrary shape, together with a Dyson equation, to derive an expression for the spontaneous decay rate and far field propagator from dipole oscillators outside resonators. For a single QNM, at field positions outside the quasi-static coupling regime, we give a closed form solution for the Purcell factor and generalized effective mode volume. We augment this with an analytic expression for the divergent local density of optical states very near the metal surface, which allows us to derive a simple and highly accurate expression for the electric field outside the metal resonator at distances from a few nanometers to infinity. This intuitive formalism provides an enormous simplification over full numerical calculations and fixes several pending problems in QNM theory.

Determination of the transition speed in journal bearings under consideration of bearing deformation

This paper discusses the further development of an analytical model to calculate the minimum film thickness and the transition speed in journal bearings with consideration of bearing deformations. The focus of the development was on generalising an existing model to include any relative eccentricities and width/diameter ratios. Furthermore, the influence of different bearing types and the layer structure of plain bearings on the deformation are taken into account. Using two white metal journal bearings as examples, the results of the new approach are discussed and compared with previous analytical models and full numerical calculations.

Plasma current start-up experiments using a dielectric-loaded waveguide array antenna in the TST-2 spherical tokamak

Plasma current start-up and ramp-up using the lower hybrid wave (LHW) were investigated on the TST-2 spherical tokamak. The LHW was launched by a dielectric-loaded waveguide array (grill) antenna. The antenna–plasma coupling of this antenna deteriorates as the input power exceeds several kW. This deterioration is believed to be caused by the density depletion due to the ponderomotive force. This conjecture was confirmed by the measurement of density reduction and the result of a non-linear full wave numerical calculation based on the finite element method (FEM). The plasma current was started and ramped up to 10 kA using this antenna. The ability of this grill antenna to excite the LHW with different n∥ = ck∥/ω was used to identify the most favourable n∥ spectrum for plasma current ramp-up. It was found that effective current drive can be achieved by the LHW with n∥ less than 6. However, even in this case, the energetic electrons which account for a large fraction of the driven current, are lost rapidly because the poloidal field generated by this level of plasma current is not sufficient to confine high energy electrons.

Rydberg dressing: understanding of collective many-body effects and implications for experiments

The strong interaction between Rydberg atoms can be used to control the strength and character of the interatomic interaction in ultracold gases by weakly dressing the atoms with a Rydberg state. Elaborate theoretical proposals for the realization of various complex phases and applications in quantum simulation exist. Also a simple model has been already developed that describes the basic idea of Rydberg dressing in a two-atom basis. However, an experimental realization has been elusive so far. We present a model describing the ground state of a Bose–Einstein condensate dressed with a Rydberg level based on the Rydberg blockade. This approach provides an intuitive understanding of the transition from pure two-body interaction to a regime of collective interactions. Furthermore it enables us to calculate the deformation of a three-dimensional sample under realistic experimental conditions in mean-field approximation. We compare full three-dimensional numerical calculations of the ground state to an analytic expression obtained within Thomas–Fermi approximation. Finally we discuss limitations and problems arising in an experimental realization of Rydberg dressing based on our experimental results and point out possible solutions for future approaches. Our work enables the reader to straight forwardly estimate the experimental feasibility of Rydberg dressing in realistic three-dimensional atomic samples.

Consequences of geomagnetic activity on energization and loss of radiation belt electrons by oblique chorus waves

Statistics of amplitudes and obliquity of lower band chorus whistler mode waves have been obtained from Cluster measurements in Earth's outer radiation belt and fitted as functions of L, latitude, magnetic local time, and three geomagnetic activity ranges for Dst∈[+10,−80] nT. Very oblique chorus waves have generally a much smaller average intensity than quasi‐parallel waves, especially on the nightside. Nevertheless, analytical estimates and full numerical calculations of quasi‐linear diffusion rates show that dayside very oblique waves (θ>60°) dominate pitch angle scattering of energetic electrons during moderately disturbed periods. As geomagnetic activity increases, leading to higher wave amplitudes, electron lifetimes are only slightly reduced, due to a decrease of the wave obliquity probably related to Landau damping by stronger incoming fluxes from the plasma sheet. As a result, electron energization by chorus waves for Dst>−80 nT generally occurs in a loss‐dominated regime in which energization increases at lower L. However, at L≥6 the most disturbed periods (Dst<−40 nT) produce a stronger energization independent of losses. Double‐belt structures may therefore arise when Dst<−40 nT, with two peaks of energization located just outside the plasmapause and at L∼6. The variability of lower band chorus wave obliquity with geomagnetic activity could actually account for some part of the observed variability of energization and loss in the outer belt. It is also suggested that quasi‐linear pitch angle diffusion by very oblique waves together with energy diffusion by parallel waves might contribute to the steep wave growth observed in the day sector between the equator and 25°.

Angular-resolved electron energy loss spectroscopy on a split-ring resonator

We investigate the plasmonic near field of a lithographically defined split-ring resonator with angular-resolved electron energy loss spectroscopy in a scanning transmission electron microscope. By tilting the sample, different electric field components of the plasmonic modes can be probed with the electron beam. The electron energy loss spectra recorded under oblique incidence can feature plasmonic resonances that are not observable under normal incidence. Our experimental findings are supported by full numerical calculations based on the discontinuous Galerkin time-domain method.

Optical cloaking using alternate Raman gain and free-space media in the presence of spatially distributed pump fields

We discuss an optical ``cloaking'' scheme using three-level active Raman gain media in tandem in the presence of a spatially distributed pump field. Using eikonal approximation we first derive analytically the deflection angle and show that the trajectory of light can be controlled dynamically using a spatially distributed pump. We further show an excellent agreement of analytical results with a full numerical calculation of the Maxwell equation for the probe field propagating across regions where an object is embedded. Our results show that the probe light travels around the object under detection, achieving the desired spatial cloaking of the object.

Storm‐induced energization of radiation belt electrons: Effect of wave obliquity

New Cluster statistics allow us to determine for the first time the variations of both the obliquity and intensity of lower‐band chorus waves as functions of latitude and geomagnetic activity near L∼5. The portion of wave power in very oblique waves decreases during highly disturbed periods, consistent with increased Landau damping by inward‐penetrating suprathermal electrons. Simple analytical considerations as well as full numerical calculations of quasi‐linear diffusion rates demonstrate that early‐time electron acceleration occurs in a regime of loss‐limited energization. In this regime, the average wave obliquity plays a critical role in mitigating lifetime reduction as wave intensity increases with geomagnetic activity, suggesting that much larger energization levels should be reached during the early recovery phase of storms than during quiet time or moderate disturbances, the latter corresponding to stronger losses. These new effects should be included in realistic radiation belt simulations.

Effective-mass theory of metal-semiconductor contact resistivity

We have calculated the contact resistivity for a metal-silicon interface, using an accurate application of effective-mass theory that includes tunneling and quantum reflection. We found that earlier treatments missed an increase in resistivity of a factor of ten due to the mismatch of the wavefunctions at the interface, not included in the WKB approximation. This arises in effective-mass theory for all metal-semiconductor interfaces. We carried out full numerical calculations of the interface resistivity and describe approximations which lead to explicit formulae for the current flow, allowing one to see the dependence of the resistivity on doping, Schottky-barrier height, temperature, crystal orientation, and choice of metal. Finally, we see how the number and energy distribution of transmitted carriers changes as a function of doping density.

Multipolar effects on the dipolar polarizability of magneto-electric antennas

We show the important role played by the multipolar coupling between the illuminating field and magneto-electric scatterers even in the small particle limit (λ/10). A general multipolar method is presented which, for the case of planar non centrosymmetric particles, generates a simple expression for the polarizability tensor that directly links the dipolar moment to the incident field. The relevancy of this approach is demonstrated by comparing thoroughly the dipolar moments predicted by the method with full numerical calculations.

Topological phases of quasi-one-dimensional fermionic atoms with a synthetic gauge field

We theoretically investigate the effect of intertube tunneling in topological superfluid phases of a quasi-one-dimensional Fermi gas with a Rashba-type spin–orbit interaction. It is shown that the effective Hamiltonian is analogous to that of a nanowire topological superconductor with multibands. Using a hidden mirror symmetry in the system, we introduce a new topological number that ensures the existence of non-Abelian Majorana zero modes even in the presence of intertube tunneling. It is demonstrated from the full numerical calculation of self-consistent equations that some of the Majorana modes survive against the intertube tunneling, when the number of one-dimensional tubes is odd in the y-direction. We also discuss a generalization of our consideration to nanowire topological superconductors.

Lower branch equilibria in Couette flow: the emergence of canonical states for arbitrary shear flows

AbstractWe consider the development of nonlinear three-dimensional vortex–wave interaction equilibria of laminar plane Couette flow for a range of spanwise wavenumbers. The results are computed using a hybrid approach that captures the required asymptotic structure while at the same time providing a direct link with full numerical calculations of equilibrium states. Each equilibrium state consists of a streak flow, a roll flow and a wave propagating on the streak. Direct numerical simulations at finite Reynolds numbers using initial conditions constructed from these parts confirm that the scheme generates equilibrium solutions of the Navier–Stokes equations. Consideration of the form of the vortex–wave interaction equations in the high-spanwise-wavenumber limit predicts that for small wavelengths the equilibria take on a self-similar structure confined near the centre of the flow. These states feel no influence from the walls, and lead to a class of canonical states relevant to arbitrary shear flows. These predictions are supported by an analysis of computational results at increasing values of the spanwise wavenumber. For the wave part of these new canonical states, it is shown that the mass-specific kinetic energy density per unit wavenumber scales with the $- 5/ 3$ power of the wavenumber.

The Effective Pore Diameter of a Three-Dimensional Numerical Model for Estimating Heat and Fluid Flow Characteristics in Metal Foams

A three-dimensional numerical model is proposed to determine heat and fluid flow characteristics in metal foams. A series of full three-dimensional numerical calculations was performed to reveal complex three-dimensional ve- locity, pressure and temperature fields within three-dimensional porous structures of the metal foams. These numerical re- sults are processed to obtain the macroscopic characteristics such as the permeability, inertia, dispersion and interstitial heat transfer coefficients. An effective pore diameter concept has been proposed to correlate the resulting heat and fluid flow characteristics with available empirical correlations. In this study, we shall conduct a numerical study on heat and fluid flow in metal foam using a three-dimensional nu- merical model of periodical structure. In order to capture irregularities in real foams, quantities calculated at specific flow angles are ensemble-averaged over the flow angle. A rational way to evaluate the effective pore diameter, which is used as the characteristic length of present three-dimensional numerical model, is proposed. Permeability, Forchheimer coefficient, thermal dispersion and volumetric heat transfer coefficient are determined by spatially averaging micro- scopic numerical results. The validity of the present numeri- cal model and the effective pore diameter are examined by comparing the numerical results with available empirical correlations. Furthermore, an interesting relationship be- tween the thermal dispersion conductivity and the volumet- ric heat transfer coefficient is elucidated.

Parametric validations of analytical lifetime estimates for radiation belt electron diffusion by whistler waves

Abstract. The lifetimes of electrons trapped in Earth's radiation belts can be calculated from quasi-linear pitch-angle diffusion by whistler-mode waves, provided that their frequency spectrum is broad enough and/or their average amplitude is not too large. Extensive comparisons between improved analytical lifetime estimates and full numerical calculations have been performed in a broad parameter range representative of a large part of the magnetosphere from L ~ 2 to 6. The effects of observed very oblique whistler waves are taken into account in both numerical and analytical calculations. Analytical lifetimes (and pitch-angle diffusion coefficients) are found to be in good agreement with full numerical calculations based on CRRES and Cluster hiss and lightning-generated wave measurements inside the plasmasphere and Cluster lower-band chorus waves measurements in the outer belt for electron energies ranging from 100 keV to 5 MeV. Comparisons with lifetimes recently obtained from electron flux measurements on SAMPEX, SCATHA, SAC-C and DEMETER also show reasonable agreement.

Microscopic theory for Doppler velocimetry of spin propagation in semiconductor quantum wells

We provide a microscopic theory for the Doppler velocimetry of spin propagation in the presence of spatial inhomogeneity, driving electric field, and the spin orbit coupling in semiconductor quantum wells in a wide range of temperature regime based on the kinetic spin Bloch equation. It is analytically shown that under an applied electric field, the spin density wave gains a time-dependent phase shift $\ensuremath{\phi}(t)$. Without the spin-orbit coupling, the phase shift increases linearly with time and is equivalent to a normal Doppler shift in optical measurements. Due to the joint effect of spin-orbit coupling and the applied electric field, the phase shift behaves differently at the early and the later stages. At the early stage, the phase shifts are the same with or without the spin-orbit coupling. While at the later stage, the phase shift deviates from the normal Doppler one when the spin-orbit coupling is present. The crossover time from the early normal Doppler behavior to the anomalous one at the later stage is inversely proportional to the spin diffusion coefficient, wave vector of the spin density wave, and the spin-orbit coupling strength. In the high temperature regime, the crossover time becomes large as a result of the decreased spin diffusion coefficient. The analytical results capture all the quantitative features of the experimental results, while the full numerical calculations agree quantitatively well with the experimental data obtained from the Doppler velocimetry of spin propagation [Nat. Phys. 8, 153 (2012).]. We further predict that the coherent spin precession, originally thought to be broken down at high temperature, is robust up to the room temperature for narrow quantum wells. We point out that one has to carry out the experiments longer to see the effect of the coherent spin precession at higher temperature due to the larger crossover time.

The forced sound transmission of finite single leaf walls using a variational technique

The single wall is the simplest element of concern in building acoustics, but there still remain some open questions regarding the sound insulation of this simple case. The two main reasons for this are the effects on the excitation and sound radiation of the wall when it has a finite size, and the fact that the wave field in the wall is consisting of two types of waves, namely forced waves due to the exciting acoustic field, and free bending waves due to reflections in the boundary. The aim of the present paper is to derive simple analytical formulas for the forced part of the airborne sound insulation of a single homogeneous wall of finite size, using a variational technique based on the integral-differential equation of the fluid loaded wall. The so derived formulas are valid in the entire audible frequency range. The results are compared with full numerical calculations, measurements and alternative theory, with reasonable agreement.

Full density-matrix numerical renormalization group calculation of impurity susceptibility and specific heat of the Anderson impurity model

Recent developments in the numerical renormalization group (NRG) allow the construction of the full density matrix (FDM) of quantum impurity models (see A. Weichselbaum and J. von Delft) by using the completeness of the eliminated states introduced by F. B. Anders and A. Schiller (2005). While these developments prove particularly useful in the calculation of transient response and finite temperature Green's functions of quantum impurity models, they may also be used to calculate thermodynamic properties. In this paper, we assess the FDM approach to thermodynamic properties by applying it to the Anderson impurity model. We compare the results for the susceptibility and specific heat to both the conventional approach within NRG and to exact Bethe ansatz results. We also point out a subtlety in the calculation of the susceptibility (in a uniform field) within the FDM approach. Finally, we show numerically that for the Anderson model, the susceptibilities in response to a local and a uniform magnetic field coincide in the wide-band limit, in accordance with the Clogston-Anderson compensation theorem.

Analytic Theory of the Resonance Properties of Metallic Nanoslit Arrays

By applying formulation based on time reversibility, we provide the analytic theory of resonance properties of metallic nanoslit arrays. We model lossy resonant systems in which a resonance is induced by a single quasi-bound mode (QBM). It is consistent with the Fano resonance theory of quantum interference of auto-ionizing atoms and captures the essential characteristics of dissipative resonant systems. We show that time-reversibility requirements lead to analytical solutions for the resonant transmission and the associated nonreciprocal absorption in terms of a minimal number of independent basic parameters that include partial decay probabilities of resonant pathways and the non-resonant transmission amplitude. With a clear view of interfering electromagnetic field configurations and the associated absorbing processes, the theory reveals the essential physics of resonant optical transmission. In particular, the enhanced transmission peak is given by the product of partial decay probabilities and is independent of the non-resonant light wave amplitude. In a highly asymmetric coupling regime, the excitation of the QBM leads to anti-resonant extinction of the transmission, indicating a negative role of the QBM. The parity of the QBM determines occurrence of red or blue tails in the spectral profile. Absorbance measurements yield direct determination of the partial decay probabilities by which the main features of the resonant transmission are quantitatively explained. Thus, these basic parameters can be directly established experimentally. Full numerical calculations of the transmission spectra are in complete quantitative agreement with our analytical formulation for optical transmission mediated by both slit cavity modes and plasmonic modes.

Universal low-temperature crossover in two-channel Kondo models

An exact expression is derived for the electron Green function in two-channel Kondo models with one and two impurities, describing the crossover from non-Fermi liquid (NFL) behavior at intermediate temperatures to standard Fermi liquid (FL) physics at low temperatures. Symmetry-breaking perturbations generically present in experiment ensure the standard low-energy FL description, but the full crossover is wholly characteristic of the unstable NFL state. Distinctive conductance lineshapes in quantum dot devices should result. We exploit a connection between this crossover and one occurring in a classical boundary Ising model to calculate real-space electron densities at finite temperature. The single universal finite-temperature Green function is then extracted by inverting the integral transformation relating these Friedel oscillations to the t matrix. Excellent agreement is demonstrated between exact results and full numerical renormalization group calculations.

Timescales for electron quasi‐linear diffusion by parallel and oblique lower‐band chorus waves

The loss of relativistic electrons from the Earth's radiation belts can be described in terms of the quasi‐linear pitch angle diffusion by cyclotron‐resonant waves, provided that their frequency spectrum is broad enough. Chorus waves at large wave‐normal angles with respect to the magnetic field are often present in CLUSTER and THEMIS measurements in the outer belt at moderate to high latitudes. An approximate analytical formulation of diffusion coefficients has been derived in the low‐frequency limit, leading to a simplified analytical expression of diffusion coefficients and lifetimes for energetic trapped electrons. Large values of the wave‐normal angles between the Gendrin and resonance angles are shown to induce important increases in diffusion, thereby strongly reducing the particle lifetimes (by almost two orders of magnitude). The analytical diffusion coefficients and lifetimes obtained here are found to be in a good agreement with full numerical calculations based on CLUSTER chorus waves measurements in the outer belt for electron energies ranging from 100 keV to 2 MeV. Such very oblique chorus waves could contribute to a predominantly perpendicular anisotropy of the global equatorial electron population on the dayside and to a relative isotropization at low energy under disturbed conditions. It is also suggested that they might play a significant role in pulsating auroras.