Time-dependent Functional Response Research Articles

Probing the galactic and extragalactic gravitational wave backgrounds with space-based interferometers

We employ the formalism developed in [1] and [2] to study the prospect of detecting an anisotropic Stochastic Gravitational Wave Background (SGWB) with the Laser Interferometer Space Antenna (LISA) alone, and combined with the proposed space-based interferometer Taiji. Previous analyses have been performed in the frequency domain only. Here, we study the detectability of the individual coefficients of the expansion of the SGWB in spherical harmonics, by taking into account the specific motion of the satellites. This requires the use of time-dependent response functions, which we include in our analysis to obtain an optimal estimate of the anisotropic signal. We focus on two applications. Firstly, the reconstruction of the anisotropic galactic signal without assuming any prior knowledge of its spatial distribution. We find that both LISA and LISA with Taiji cannot put tight constraints on the harmonic coefficients for realistic models of the galactic SGWB. We then focus on the discrimination between a galactic signal of known morphology but unknown overall amplitude and an isotropic extragalactic SGWB component of astrophysical origin. In this case, we find that the two surveys can confirm, at a confidence level ≳ 3σ, the existence of both the galactic and extragalactic background if both have amplitudes as predicted in standard models. We also find that, in the LISA-only case, the analysis in the frequency domain (under the assumption of a time average of data taken homogeneously across the year) provides a nearly identical determination of the two amplitudes as compared to the optimal analysis.

Real-time reconstruction of the strong-field driven dipole response

SynopsisUsing ultrashort and phase-locked laser pulses, combined with an in situ measurement of a reference pulse, we present a method capable of retrieving the nonlinearly perturbed time-dependent response function of a quantum system driven by strong electric fields directly from spectroscopic absorption data with high precision.

Application of the coupled classical oscillators model to the Fano resonance build-up in a plasmonic nanosystem

We study the excitation dynamics of Fano resonance within the classical model framework of two linear coupled oscillators. An exact solution for the model with a damped harmonic force is obtained. Details of the growth of a Fano profile under the harmonic excitation are shown. For an incident ultra-wideband pulse, the reaction of the system becomes universal and coincides with the time-dependent response function. The results of numerical calculations clarify two alternative ways for the experimental measurement of complete characteristics of the system: via direct observation of the system response to a monochromatic force by frequency scanning or recording the time-dependent response to a d-pulse. As a specific example, the time-dependent excitation in a system consisting of a quantum dot and a metal nanoparticle is calculated. Then, we show the use of an extended model of damped oscillators with radiative correction to describe the plasmon Fano resonance build-up when a femtosecond laser pulse is scattered by a nanoantenna.

Estimating the contribution of crop residues to soil organic carbon conservation

Crop residues contribute to the maintenance of soil organic carbon (SOC) stores, a key component of soil fertility and soil-based climate change mitigation strategies, such as the ‘4 per 1000’ initiative. Residues are also in demand in sectors coupled to crop production, such as the supply chain of livestock and bioenergy production. Ongoing debate revolves around balancing these competing uses, but science-based assessments of the long-term sustainability of residue exploitation are rare. This work uses biophysical simulation modelling to explore the likely response of SOC to different management strategies, using the land area of North Rhine-Westphalia (Germany) as a case study. Four strategies are tested: zero, one third and 100% removal of cereal residues, plus an approach proposed by the State farm advisory service. Simulations are carried out for the period 1971–2050 and 19 crop rotations coincident with land use throughout the study area. Uncertainty associated with the modelled SOC changes is explored by sampling values of relevant parameters for SOC turnover and running an ensemble of model configurations. Simulated SOC is used to trace time-dependent response functions following a change in residue management under different soil textures, initial SOC levels and crop rotations. Results highlight a general exponential decrease in SOC, with relative changes in 2050 distributed between +10% and −40% with respect to a reference period. SOC loss can be buffered or offset by returning all crop residues to the soil. Under such management, an SOC increase can be achieved on clayey soils characterized by a low initial SOC. Under moderate crop residue removal, positive SOC trends are limited to a few crop rotations. In this context, 4 per 1000 increase rate in SOC appears largely out of reach through residue management, calling for additional measures to meet the targets of land-based mitigation of anthropogenic emissions.

Sparsity-based super-resolved coherent diffraction imaging of one-dimensional objects.

Phase-retrieval problems of one-dimensional (1D) signals are known to suffer from ambiguity that hampers their recovery from measurements of their Fourier magnitude, even when their support (a region that confines the signal) is known. Here we demonstrate sparsity-based coherent diffraction imaging of 1D objects using extreme-ultraviolet radiation produced from high harmonic generation. Using sparsity as prior information removes the ambiguity in many cases and enhances the resolution beyond the physical limit of the microscope. Our approach may be used in a variety of problems, such as diagnostics of defects in microelectronic chips. Importantly, this is the first demonstration of sparsity-based 1D phase retrieval from actual experiments, hence it paves the way for greatly improving the performance of Fourier-based measurement systems where 1D signals are inherent, such as diagnostics of ultrashort laser pulses, deciphering the complex time-dependent response functions (for example, time-dependent permittivity and permeability) from spectral measurements and vice versa.

A Coarse-Mesh Method for the Time-Dependent Transport Equation

A new solution technique is derived for the time-dependent transport equation. This approach extends the steady-state coarse-mesh transport method that is based on global-local decompositions of large (i.e., full-core) neutron transport problems. The new method is based on polynomial expansions of the space, angle, and time variables in a response-based formulation of the transport equation. The local problem (coarse-mesh) solutions, which are entirely decoupled from each other, are characterized by space-, angle-, and time-dependent response functions. These response functions are, in turn, used to couple an arbitrary sequence of local problems to form the solution of a much larger global problem. In the current work, the local problem (response function) computations are performed using the Monte Carlo method, while the global (coupling) problem is solved deterministically. The spatial coupling is performed by orthogonal polynomial expansions of the partial currents on the local problem surfaces, and similarly, the time-dependent response of the system (i.e., the time-varying flux) is computed by convolving the time-dependent surface partial currents and time-dependent volumetric sources against precomputed time-dependent response kernels.

Linear Response of Biomolecules To External Perturbations: Revisit Induce-fit

Atoms in proteins, viewed as interlinked hubs, communicate with each other in complying with governed physical forces. The deviations of their positions from the mean, known as fluctuations, are essential in mediating functionally relevant biological processes maintaining one's daily life. The coupled fluctuations between pairs of atoms, the fluctuation covariance, can be determined analytically by Normal Mode Analysis, or numerically by MD simulations. Our study considers how this network of atoms reacts in response to external perturbations. Effects of such perturbations are exemplified by ligand- or (another) protein-induced conformational changes as well as the appreciated structural distortion of crystalline structures from its solution conformers. We assume the response of the system has linear departure from the mean under small perturbations on the Hamiltonian at equilibrium state. The formulated linear response theories, either time-dependent or -independent [1], says that the positional change of a given atom i is the accumulative sum of fluctuation covariance ij, at unperturbed state, multiplied by the force exerted on atom j. The time-dependent response function determined from MD simulation of carbonmonoxy myoglobin is used to track time-dependent conformational changes upon photo-dissociation of CO. The consequently obtained understanding of perturbation propagation is compared with experimental results. Also, the structural distortion of X-ray-characterized ubiquitin from its solution conformer can be well explained by the induce-fit theory, in a wider sense, while population-shift does not account for such a deviation.[1] Ikeguchi M, Ueno J, Sato M, and Kidera A. (2005) Phys Rev Lett, 94, 078102.

Hartree-Fock and Kohn-Sham time-dependent response theory in a second-quantization atomic-orbital formalism suitable for linear scaling

We present a second-quantization based atomic-orbital method for the computation of time-dependent response functions within Hartree-Fock and Kohn-Sham density-functional theories. The method is suited for linear scaling. Illustrative results are presented for excitation energies, one- and two-photon transition moments, polarizabilities, and hyperpolarizabilities for hexagonal BN sheets with up to 180 atoms.

MO-D-T-6E-05: Biological Optimization of Fractionated IMRT Using Fraction Groups

Purpose: To describe software for biological optimization of fractionated IMRT where the fluence profiles are not restricted to be identical for all fractions and to investigate the impact of fractionated time-dependent response functions on the optimization result. Method and Materials: If the fluence profiles of all beams in every fraction are optimized the number of variables is proportional to the number of fractions. Each new fraction consumes memory and slows down the optimization. In order to reduce the number of variables similar fractions are assigned to the same fraction group. The same fluence profile is delivered for every fraction in a fraction group. To test the method the Poisson-LQ model is extended with a time-dependent bi-exponential repair model. Results: In all tests the NTCP was minimized while the TCP was kept constant. If the time between consecutive fractions is long enough to cause complete repair there is not much gain in optimizing several fraction groups. In the case of incomplete repair, the NTCP was reduced by assigning Monday morning and Friday afternoon to a second fraction group. Adding more fraction groups did not improve the response significantly. Conclusion: The use of fraction groups enables an efficient implementation of IMRT-optimization of a fractionated treatment and makes it possible to study time-dependent biological models. In the case of Poisson-LQ with repair, two fraction groups can improve the biological response. This is only true in the case of incomplete repair and the impact of the fractionation depends on the repair half times. Conflict of Interest: Some of the authors are employees and some are stock owners of the submitting company.

Cubic response functions in time-dependent density functional theory

We present density-functional theory for time-dependent response functions up to and including cubic response. The working expressions are derived from an explicit exponential parametrization of the density operator and the Ehrenfest principle, alternatively, the quasienergy ansatz. While the theory retains the adiabatic approximation, implying that the time-dependency of the functional is obtained only implicitly-through the time dependence of the density itself rather than through the form of the exchange-correlation functionals-it generalizes previous time-dependent implementations in that arbitrary functionals can be chosen for the perturbed densities (energy derivatives or response functions). In particular, general density functionals beyond the local density approximation can be applied, such as hybrid functionals with exchange correlation at the generalized-gradient approximation level and fractional exact Hartree-Fock exchange. With our implementation the response of the density can always be obtained using the stated density functional, or optionally different functionals can be applied for the unperturbed and perturbed densities, even different functionals for different response order. As illustration we explore the use of various combinations of functionals for applications of nonlinear optical hyperpolarizabilities of a few centrosymmetric systems; molecular nitrogen, benzene, and the C(60) fullerene. Considering that vibrational, solvent, and local field factors effects are left out, we find in general that very good experimental agreement can be obtained for the second dynamic hyperpolarizability of these systems. It is shown that a treatment of the response of the density beyond the local density approximation gives a significant effect. The use of different functional combinations are motivated and discussed, and it is concluded that the choice of higher order kernels can be of similar importance as the choice of the potential which governs the Kohn-Sham orbitals.

Real-space and real-time imaging of polariton wavepackets

Coherent optic phonon–polaritons generated through impulsive stimulated Raman scattering in a ferroelectric crystal are imaged with 5-μm spatial resolution and 35-fs time resolution. This imaging spectroscopy allows us to perform direct measurement of space- and time-dependent response function induced by the propagating phonon-polaritons. The method will also permit direct examination of nonlinear lattice dynamics and will provide feedback in coherent control system.

Fluctuations, response and aging dynamics in a simple glass-forming liquid out of equilibrium

By means of molecular dynamics computer simulations we investigate the out of equilibrium relaxation dynamics of a simple glass former, a binary Lennard-Jones system, after a quench to low temperatures. We study both one time quantities and two-times correlation functions. Two-times correlation functions show a strong time and waiting time $t_w$ dependence. For large $t_w$ and times corresponding to the early $\beta$-relaxation regime the correlators approach the Edwards-Anderson value by means of a power-law in time. at long times $\tau$ the correlation functions can be expressed as $C_{\rm AG}(h(t_w+\tau)/h(t_w))$ and compute the function $h(t)$. This function is found to show a $t$-dependence which is a bit stronger than a logarithm and to depend on the observable considered. Finally we discuss our measurements of the time dependent response function. We find that at long times the correlation functions and the response are not related by the usual fluctuation dissipation theorem but that this relation is similar to the one found for spin glasses with one step replica symmetry breaking.

Theory for determination of the low-frequency time-dependent response function in liquids using time-resolved terahertz pulse spectroscopy

With the current rapid improvement in techniques for generating and detecting femtosecond terahertz (fs-THz) pulses, it is now possible to detect time-dependent perturbations to low-frequency intermolecular far-infrared modes during solvation events. The interpretation of these time-resolved terahertz spectroscopy experiments has generally relied on a collapse of the information available in the fs-THz pulse to give a one-dimensional time-dependent function, whose physical significance is not well defined. We describe a method to exploit the full electric field profile of the pulse as a function of pump/probe delay time to obtain a two-dimensional function that describes the system’s time-dependent dielectric response. We discuss the physical significance of this response function in terms of the time evolution of solute/solvent modes following photoexcitation, and give examples to show how its qualitative features relate to the measurable signal.

The CC3 model: An iterative coupled cluster approach including connected triples

An alternative derivation of many-body perturbation theory (MBPT) has been given, where a coupled cluster parametrization is used for the wave function and the method of undetermined Lagrange multipliers is applied to set up a variational coupled cluster energy expression. In this variational formulation, the nth-order amplitudes determine the energy to order 2n+1 and the nth-order multipliers determine the energy to order 2n+2. We have developed an iterative approximate coupled cluster singles, doubles, and triples model CC3, where the triples amplitudes are correct through second order and the singles amplitudes are treated without approximations due to the unique role of singles as approximate orbital relaxation parameters. The compact energy expressions obtained from the variational formulation exhibit in a simple way the relationship between CC3, CCSDT-1a [Lee et al., J. Chem. Phys. 81, 5906 (1984)] CCSDT-1b models [Urban et al., J. Chem. Phys. 83, 4041 (1985)], and the CCSD(T) model [Raghavachari et al., Chem. Phys. Lett. 157, 479 (1989)]. Sample calculations of total energies are presented for the molecules H2O, C2, CO, and C2H4. Comparisons are made with full CCSDT, CCSDT-1a, CCSDT-1b, CCSD(T), and full configuration interaction (FCI) results. These calculations demonstrate that CC3 and CCSD(T) give total energies of a similar quality. If results obtained by CC3 and CCSD(T) differ significantly, neither method can be trusted. In contrast to CCSD(T), time-dependent response functions can be obtained for CC3.

Time-domain reflectometry in magnetic studies: lumped inductance method

Relationships are obtained for determining time-dependent response functions and the complex susceptibility of a magnetic sample from observed time-domain reflectograms within the approximation of lumped inductance for the measuring coil. The experiment is carried out on a sample of FeY garnet.

Characteristics of synchrotron C-caronerenkov radiation.

A diagrammatic technique has been worked out in the framework of nonequilibrium statistical mechanics as developed by Prigogine and co-workers to tackle the problem of radiation emission from a relativistic electron in an ambient plasma embedding an axial-wiggler magnetic field. The theory is exact in that the diagrams contributing towards the self-consistent-field approximation have been summed up exactly and one obtains a time-dependent response function. The kinetic regime has been obtained by eliminating the memory by taking an asymptotic limit in time. Explicit calculations have been affected to obtain functions like the \ifmmode \check{C}\else \v{C}\fi{}erenkov angle and the refractive index as well as the power emitted by the system. It has been shown that the radiation emitted has very peculiar polarization features.

A Two-Dimensional Time-Dependent Neutron Transport Calculation Using One-Dimensional Equations

In this Note we report on a technique for determining a two-dimensional time-dependent response function using a one-dimensional solution of the transport equation for a homogeneous medium. Basic to this technique is the calculation of the adjoint function. We have determined the asymmetric energy deposition rate in air from a spatial asymmetric source as an example of the method.

Time-dependent transport processes in the adiabatic approximation

We consider the Liouville equation for systems subject to strong, but slowly varying, externally applied forces and we integrate this equation to obtain non-linear, time-dependent response functions which are generalizations of Kubo's formula, on the one hand, and of results obtained by Weare and Oppenheim, on the other hand.