Exact Numerical Method Research Articles

Long-Lived Coherence Originating from Electronic-Vibrational Couplings in Light-Harvesting Complexes

We theoretically investigate the evolutions of two-dimensional, third-order, nonlinear photon echo rephasing spectra with population time by using an exact numerical path integral method. It is shown that for the same system, the coherence time and relaxation time of excitonic states are short, however, if the couplings of electronic and intra-pigment vibrational modes are considered, the coherence time and relaxation time of this vibronic states are greatly extended. It means that the couplings between electronic and vibrational modes play important roles in keeping long-lived coherence in light-harvesting complexes. Particularly, by using the method we can fix the transition path of the energy transfer in bio-molecular systems.

Persistence of non-local correlations and quantum information theoretic measures in the thermal state of frustrated molecular wheels

ABSTRACTGenuine quantumness present in quantum systems is the resource for implementing quantum information and computation protocols which can outperform the classical counterparts. These quantumness measures encompass non-local ones known as quantum entanglement (QE) and quantum information theoretic ones, e.g. quantum discord (QD). In this paper, some well-known measures of QE and QD have been studied in two wheel-like frustrated molecular magnetic systems, with special emphasis on the survival of the measures in the thermal states. A molecular magnetic system similar to the first one (with half-integer spins ) has already been synthesised using coordination chemistry, and the other is hypothetical, where the dominant interaction is the spin–spin exchange interaction. Exact numerical diagonalisation methods have been used. Some non-trivial features, like nonmonotonicity of threshold temperatures with external magnetic field, persistence of multipartite entanglement and QD over bipartite entanglement, have been found. The measures, being operational ones, can be used to realise the resource of quantumness in experiments.

Generation of Nonclassical Light by Unsaturated Two-Photon Absorption

In this paper, we investigate the distribution statistics of photons in a single mode radiation field subjected to two-photon absorption (TPA) and the factors that contribute to squeezing and antibunching of photons, leading to the generation of nonclassical light. TPA is a nonlinear optical phenomenon in which the atoms interact with the light field by absorbing two photons simultaneously. The motivation to study TPA is the recent intense activity on nanocrystallites/quantum dots. Further, it is the only nonlinear optical phenomenon that can be analytically studied. The simultaneous occurrence of squeezing and antibunching is studied with small initial photon numbers by solving the master equation for TPA of a single mode radiation directly by numerical integration, without going through analytical procedure. The results are compared with those of analytical/numerical procedures available. Further, the discussion on the parameters of squeezing and antibunching for short-time (ST) as well as long-time is done comprehensively in the present work by taking up the ST approximation and summation of ST (SST) procedure along with the exact numerical method.

Light scattering by ice crystals of cirrus clouds: From exact numerical methods to physical-optics approximation

The problem of light scattering by ice crystals of cirrus clouds is considered in the case of a hexagonal ice plate with different distributions over crystal orientations. The physical-optics approximation based on (E, M)-diffraction theory is compared with two exact numerical methods: the finite difference time domain (FDTD) and the discontinuous Galerkin time domain (DGTD) in order to estimate its accuracy and limits of applicability. It is shown that the accuracy of the physical-optics approximation is estimated as 95% for the averaged backscattering Mueller matrix for particles with size parameter more than 120. Furthermore, the simple expression that allows one to estimate the minimal number of particle orientations required for appropriate spatial averaging has been derived.

On the analytical formulation of excess noise in avalanche photodiodes with dead space.

Simple, approximate formulas are developed to calculate the mean gain and excess noise factor for avalanche photodiodes using the dead-space multiplication theory in the regime of small multiplication width and high applied electric field. The accuracy of the approximation is investigated by comparing it to the exact numerical method using recursive coupled integral equations and it is found that it works for dead spaces up to 15% of the multiplication width, which is substantial. The approximation is also tested for real materials such as GaAs, InP and Si for various multiplication widths, and the results found are accurate within ∼ 15% of the actual noise, which is a significant improvement over the local-theory noise formula. The results obtained for the mean gain also confirm the recently reported relationship between experimentally determined local ionization coefficients and the enabled non-local ionization coefficients.

Temporal coupled mode analysis of one-dimensional magneto-photonic crystals with cavity structures

In this paper, we propose the time-dependent coupled mode analysis of one-dimensional magneto-photonic crystals including one, two or multiple defect layers. The performance of the structures, namely the total transmission, Faraday rotation and ellipticity, is obtained using the proposed method. The results of the developed analytic approach are verified by comparing them to the results of the exact numerical transfer matrix method. Unlike the widely used numerical method, our proposed analytic method seems promising for the synthesis as well as the analysis purposes. Moreover, the proposed method has not the restrictions of the previously examined analytic methods.

Kinetic study of ion acoustic twisted waves with kappa distributed electrons

The kinetic theory of Landau damping of ion acoustic twisted modes is developed in the presence of orbital angular momentum of the helical (twisted) electric field in plasmas with kappa distributed electrons and Maxwellian ions. The perturbed distribution function and helical electric field are considered to be decomposed by Laguerre-Gaussian mode function defined in cylindrical geometry. The Vlasov-Poisson equation is obtained and solved analytically to obtain the weak damping rates of the ion acoustic twisted waves in a non-thermal plasma. The strong damping effects of ion acoustic twisted waves at low values of temperature ratio of electrons and ions are also obtained by using exact numerical method and illustrated graphically, where the weak damping wave theory fails to explain the phenomenon properly. The obtained results of Landau damping rates of the twisted ion acoustic wave are discussed at different values of azimuthal wave number and non-thermal parameter kappa for electrons.

Discrete dipole approximation for black carbon-containing aerosols in arbitrary mixing state: A hybrid discretization scheme

An accurate and efficient simulation of light scattering by an atmospheric black carbon (BC)-containing aerosol—a fractal-like cluster of hundreds of carbon monomers that is internally mixed with other aerosol compounds such as sulfates, organics, and water—remains challenging owing to the enormous diversities of such aerosols׳ size, shape, and mixing state. Although the discrete dipole approximation (DDA) is theoretically an exact numerical method that is applicable to arbitrary non-spherical inhomogeneous targets, in practice, it suffers from severe granularity-induced error and degradation of computational efficiency for such extremely complex targets. To solve this drawback, we propose herein a hybrid DDA method designed for arbitrary BC-containing aerosols: the monomer-dipole assumption is applied to a cluster of carbon monomers, whereas the efficient cubic-lattice discretization is applied to the remaining particle volume consisting of other materials. The hybrid DDA is free from the error induced by the surface granularity of carbon monomers that occurs in conventional cubic-lattice DDA. In the hybrid DDA, we successfully mitigate the artifact of neglecting the higher-order multipoles in the monomer-dipole assumption by incorporating the magnetic dipole in addition to the electric dipole into our DDA formulations. Our numerical experiments show that the hybrid DDA method is an efficient light-scattering solver for BC-containing aerosols in arbitrary mixing states. The hybrid DDA could be also useful for a cluster of metallic nanospheres associated with other dielectric materials.

Quantum dynamics and spectra of vibrational Raman-resonance fluorescence in a two-mode cavity

We study the classically driven two-level system with its center-of-mass motion vibrating in a harmonic trap and coupled to the photons in a two-mode cavity. The first mode is resonant to the driving field and an electronic transition. The second mode is off-resonant, forming a vibrational-assisted Raman transition. Using an exact numerical method, we investigate the quantum dynamics of the light emitted by the atom and the cavity modes. We analyze and compare the corresponding atomic and intracavity photon spectra for a range of the driving laser field and the cavity coupling strengths. The results provide better understanding of the effects of the laser field and atom-cavity coupling strengths on quantum interference effects and photon blockade, particularly the Mollow's triplet and the Autler-Townes splitting in the good and bad cavity limits.

Quantum walks accompanied by spin flipping in one-dimensional optical lattices

We investigate continuous-time quantum walks of two fermionic atoms loaded in one-dimensional optical lattices with on-site interaction and subjected to a Zeeman field. The quantum walks are accompanied by spin-flipping processes. We calculate the time-dependent density distributions of the two fermions with opposite spins which are initially positioned on the center site by means of exact numerical method. Besides the usual fast linear expansion behavior, we find an interesting spin-flipping induced localization in the time-evolution of density distributions. We show that the fast linear expansion behavior could be restored by simply ramping on the Zeeman field or further increasing the spin-flipping strength. The intrinsic origin of this exotic phenomenon is attributed to the emergence of a flat band in the single particle spectrum of the system. Furthermore, we investigate the effect of on-site interaction on the dynamics of the quantum walkers. The two-particle correlations are calculated and signal of localization is also shown therein. A simple potential experimental application of this interesting phenomenon is proposed.

Landau damping of Langmuir twisted waves with kappa distributed electrons

The kinetic theory of Landau damping of Langmuir twisted modes is investigated in the presence of orbital angular momentum of the helical (twisted) electric field in plasmas with kappa distributed electrons. The perturbed distribution function and helical electric field are considered to be decomposed by Laguerre-Gaussian mode function defined in cylindrical geometry. The Vlasov-Poisson equation is obtained and solved analytically to obtain the weak damping rates of the Langmuir twisted waves in a nonthermal plasma. The strong damping effects of the Langmuir twisted waves at wavelengths approaching Debye length are also obtained by using an exact numerical method and are illustrated graphically. The damping rates of the planar Langmuir waves are found to be larger than the twisted Langmuir waves in plasmas which shows opposite behavior as depicted in Fig. 3 by J. T. Mendoça [Phys. Plasmas 19, 112113 (2012)].

Erratum: Orientation dynamics of asymmetric rotors using random phase wave functions [Phys. Rev. A 91, 063420 (2015)

Intense terahertz-frequency pulses induce coherent rotational dynamics and orientation of polar molecular ensembles. Exact numerical methods for rotational dynamics are computationally not feasible for the vast majority of molecular rotors - the asymmetric top molecules at ambient temperatures. We exemplify the use of Random Phase Wave Functions (RPWF) by calculating the terahertz-induced rotational dynamics of sulfur dioxide (SO2) at ambient temperatures and high field strengths and show that the RPWF method gains efficiency with the increase in temperature and in the THz-field strengths. The presented method provides wide-ranging computational access to rotational dynamical responses of molecules at experimental conditions which are far beyond the reach of exact numerical methods.

Orientation dynamics of asymmetric rotors using random phase wave functions

Intense terahertz-frequency pulses induce coherent rotational dynamics and orientation of polar molecular ensembles. Exact numerical methods for rotational dynamics at room temperature are computationally not feasible for the vast majority of molecular rotors: the asymmetric top molecules at ambient temperatures. We exemplify the use of random phase wave functions (RPWFs) by calculating the terahertz-induced rotational dynamics of sulfur dioxide at ambient temperatures and high-field strengths and show that the RPWF method gains efficiency with the increase in temperature and in the terahertz-field strengths. The present method provides wide-ranging computational access to rotational dynamical responses of molecules at experimental conditions that are far beyond the reach of exact numerical methods.

Application of a Modified Boundary-Element Method to Problems of the Elasticity Theory in Piecewise Homogeneous Anisotropic Media

UDC 539.3 We study the problem of determination of the stress-strain state of a thin elastic orthotropic plate with orthotropic inclusions of any shape under loads applied to its edges. To solve the problem, we propose a modified direct boundary-element method capable of the simultaneous determination of all necessary quantities on the contact surfaces of each inclusion with the matrix by using a two-dimensional approximation of the components of the vector of displacements and stress tensor in every element of the discretization. The governing input relations are obtained for all components of the vector of displacements and stress tensor on the boundary and at inner points of the body under consideration. Recent years are marked by the extensive application of materials and structural elements with anisotropic properties. The use of these materials makes it possible to get the required operating characteristics of strength and stiffness. For their efficient and safe application, we need the exact and reliable numerical methods aimed at the determination of their stress-strain state. The customary numerical methods based on the discretization of the domain itself (finite-element method) or its boundary (boundary-element method) exhibit high efficiency in the case where the corresponding fundamental solutions of the problem under study are available. The presence of anisotropy increases the number of elastic constants in Hooke’s law and, hence, complicates the procedure of construction of the fundamental solutions. However, the fundamental solutions of the two-dimensional problems of elasticity theory are, as a rule, available [5, 6]. The analysis of the stress-strain state for these class of problems was carried out, e.g., in [4, 7, 8]. If we use the ordinary boundary-element method, then the solution of boundary integral equations enables one to find only a part of the components of the stress tensor, namely, the components appearing in the contact conditions. To find the other components of the stress tensor, it is necessary to perform the limit transition both in the integral representations of the vector of displacements and in their differentiated representations. The two-dimensional approximation of displacements on the boundaries of inclusions [1] removes the necessity of differentiation of the representations and makes it possible to determine all components of the vector of displacements and stress tensor on the boundaries of the analyzed bodies already directly from the boundary integral equations. In what follows, we apply this approach to the construction of constitutive relations for the plane problem of elasticity for orthotropic bodies. Consider a thin elastic orthotropic plate with orthotropic inclusions of any shape. The plate suffers the action of muss forces Xi and distributed forces pi applied to its edges. Thus, it can be regarded as an elastic orthotropic matrix with elastic orthotropic inclusions.

General transient solution of the one-step master equation in one dimension.

Exact analytical solutions of the master equation are limited to special cases and exact numerical methods are inefficient. Even the generic one-dimensional, one-step master equation has evaded exact solution, aside from the steady-state case. This type of master equation describes the dynamics of a continuous-time Markov process whose range consists of positive integers and whose transitions are allowed only between adjacent sites. The solution of any master equation can be written as the exponential of a (typically huge) matrix, which requires the calculation of the eigenvalues and eigenvectors of the matrix. Here we propose a linear algebraic method for simplifying this exponential for the general one-dimensional, one-step process. In particular, we prove that the calculation of the eigenvectors is actually not necessary for the computation of exponential, thereby we dramatically cut the time of this calculation. We apply our new methodology to examples from birth-death processes and biochemical networks. We show that the computational time is significantly reduced compared to existing methods.

Near-Field Thermal Radiation: Recent Progress and Outlook

Any materials at temperatures higher than absolute zero emit electromagnetic waves due to the thermal fluctuations of free charges or ions. When two or more bodies at different temperatures are brought sufficiently close to each other with vacuum gap spacing smaller than the characteristic thermal wavelength, near-field radiative heat flux can exceed the far-field blackbody limit, governed by the well-known Stefan-Boltzmann law, by orders of magnitude. This article reviews the recent progress on both theoretical and experimental studies of near-field thermal radiation with an emphasis on its potential applications. Recent theoretical developments are presented, such as near-field radiation of general anisotropic materials and 2D materials, application condition of effective medium theory, and exact numerical methods for dealing with arbitrary particles or periodic nanostructures. Recent experimental achievements are also discussed, focusing on tip–plane and plane–plane configurations with various materials. The wide applications of near-field radiation are summarized in terms of thermal imaging, energy harvesting, and contactless thermal management such as modulation, rectification, and amplification. An outlook is provided on the promise of near-field thermal radiation in energy harvesting, novel thermal sources, and sensing, as well as the development of related fields such as reducing Casimir stiction, minimizing noise current, and increasing spontaneous emission rate. Challenges are also discussed, such as developing exact and fast computational techniques for complex metamaterials, understanding near-field radiation at extreme gap spacing, overcoming weak mode coupling in thermophotovoltaic (TPV) systems, measuring large-area plane–plane configuration at small gap spacing, and realizing devices based on near-field radiation.

Geometric Collocation Method on SO(3) with Application to Optimal Attitude Control of a 3D Rotating Rigid Body

The collocation method is extended to the special orthogonal group SO(3) with application to optimal attitude control (OAC) of a rigid body. A left-invariant rigid-body attitude dynamical model on SO(3) is established. For the left invariance of the attitude configuration equation in body-fixed frame, a geometrically exact numerical method on SO(3), referred to as the geometric collocation method, is proposed by deriving the equivalent Lie algebra equation inso(3)of the left-invariant configuration equation. When compared with the general Gauss pseudo-spectral method, the explicit RKMK, and Lie group variational integrator having the same order and stepsize in numerical tests for evolving a free-floating rigid-body attitude dynamics, the proposed method is higher in accuracy, time performance, and structural conservativeness. In addition, the numerical method is applied to solve a constrained OAC problem on SO(3). The optimal control problem is transcribed into a nonlinear programming problem, in which the equivalent Lie algebra equation is being considered as the defect constraints instead of the configuration equation. The transcription method is coordinate-free and does not need chart switching or special handling of singularities. More importantly, with the numerical advantage of the geometric collocation method, the proposed OAC method may generate satisfying convergence rate.

Proximity-induced superconductivity and Josephson critical current in quantum spin Hall systems

We consider recent experiments on wide superconductor-quantum spin Hall insulator (QSHI)-superconductor Josephson junctions, which have shown preliminary evidence of proximity-induced superconductivity at the edge-modes of the QSHI system based on an approximate analysis of the observed Fraunhofer spectra of the Josephson critical current as a function of the applied magnetic field. Using a completely independent exact numerical method involving a non-linear constrained numerical optimization, we calculate the supercurrent profiles, comparing our results quantitatively with the experimental Fraunhofer patterns in both HgCdTe and InAs-GaSb based QSHI Josephson junctions. Our results show good qualitative agreement with the experiments, verifying that the current distribution in the 2D sample indeed has peaks at the sample edges when the system is in the QSHI phase, thus supporting the interpretation that superconductivity has indeed been induced in the QSHI edge-modes. On the other hand, our numerical work clearly demonstrates that it will be very difficult, if not impossible, to obtain detailed quantitative information about the super-current distribution just from the analysis of the Josephson Fraunhofer spectra, and, therefore, conclusions regarding the precise width of the edge modes or their topological nature are most likely premature at this stage.

Electron-spin dynamics in elliptically polarized light waves

We investigate the coupling of the spin angular momentum of light beams with elliptical polarization to the spin degree of freedom of free electrons. It is shown that this coupling, which is of similar origin as the well-known spin-orbit coupling, can lead to spin precession. The spin-precession frequency is proportional to the product of the laser-field's intensity and its spin density. The electron-spin dynamics is analyzed by employing exact numerical methods as well as time-dependent perturbation theory based on the fully relativistic Dirac equation and on the nonrelativistic Pauli equation that is amended by a relativistic correction that accounts for the light's spin density.

Characteristic Brewster angles for anisotropic interfaces

The effect of nanoscopically stratified anisotropic transmission layer between two isotropic dielectric medium on the characteristic Brewster angles is carried out. The analysis is based on the second-order approximate formulas for the quasi-Brewster, polarization (second Brewster), and principal (third Brewster) angles obtained in the framework of a long-wavelength approximation. The accuracy of these analytical expressions is estimated by using exact numerical methods for the solution of the anisotropic reflection problem. It is shown that the characteristics Brewster angles for real physical interfaces may differ considerably from the classical Brewster angle ϕB=arctg(nb/na), for certain material parameters even then, if the thickness of a transition layer is very significantly smaller than the wavelength of optical radiation.