Time-dependent Lattice Research Articles

Time-dependent Lattice Cross Sections and Line Ratios for Solar Wind Charge Exchange: Bare Ne Incident on Atomic H and He

Charge exchange (CX) between highly charged ions and neutrals within the geocorona and heliosphere introduces a problematic background for every X-ray observation. For H-like ions the ℓ states within each n shell are degenerate. The majority of CX spectral models rely on calculated n-resolved cross sections, and the distribution of ℓ states is assumed to follow one of several analytical expressions. Laboratory data to validate these distributions at solar wind velocities is not available. Explicitly velocity-dependent calculations of n ℓ-resolved CX cross sections using the time-dependent lattice (TDL) method for Ne10+ incident on atomic H and He at 1–5 keV amu−1 are reported. The cross sections are incorporated into a radiative cascade model, and the influence of n- and n ℓ-resolved cross sections on possibly diagnostic emission line ratios is investigated. Comparisons of the ℓ distribution extracted from the TDL cross sections to the predominantly used analytical distributions reveals a consensus among n and n ℓ-resolved data at solar wind velocities, suggesting a statistical distribution is most appropriate for CX collisions involving atomic H. No consensus is found for atomic He targets, and the ℓ distribution extracted from n ℓ-resolved cross sections appears most appropriate. Open questions related to CX are discussed with emphasis on experimental methods to resolve them. Spectral measurements at an electron beam ion trap facility are planned to benchmark the presented cross section data.

Theoretical Simulation of the Temporal Behavior of Bragg Diffraction Derived from Lattice DeformationSupported by the National Key Research and Development Program of China under Grant Nos. 2016YFA0300303, 2017YFA0504703, and 2017YFA0302904, the National Basic Research Program of China under Grant No. 2015CB921304, the National Natural Science Foundation of China under Grant Nos. 11604372, 11474323, 11774391, 11774403, and 61575085, the Strategic Priority

A theoretical study on the structural dynamics of the temporal behavior of Bragg diffraction is presented and compared with experimental results obtained via ultrafast electron crystallography. In order to describe the time-dependent lattices and calculate the Bragg diffraction intensity, we introduce the basic vector offset matrix, which can be used to quantify the shortening, lengthening and rotation of the three lattice vectors (i.e., lattice deformation). Extensive simulations are performed to evaluate the four-dimensional electron crystallography model. The results elucidate the connection between structural deformations and changes in diffraction peaks, and sheds light on the quantitative analysis and comprehensive understanding of the structural dynamics.

Line intensities for x-ray emission in Mg12+ collisions with H and He atoms

State selective charge transfer cross sections are calculated in Mg12+ collisions with H and He atoms at incident energies of 1.0, 3.0, and 5.0 keV amu−1 using a time-dependent lattice method. Total capture cross sections using the time-dependent lattice method are found to be larger than those previously calculated using the Landau–Zener method. Lyman line ratios are calculated using the time-dependent lattice capture cross sections and standard radiative transitions for both the H and He atoms. Lyman line probabilities are presented for both H and He. The strongest probability for both H and He is the Lyman α emission, but relatively strong probabilities for He at an incident energy of 1.0 keV amu−1 are found for Lyman β, γ, δ, and ϵ emission.

Study on time-dependent lattice to alleviate space charge effects in CSNS/RCS

Purpose Tune shift and spread due to the space charge effects and collective instabilities in intense proton synchrotrons, such as the CSNS/RCS, a rapid cycling synchrotron at China Spallation Neutron Source, are the main causes of beam loss. Tune shift/spread is large when the beam kinetic energy is low and will cause particles to cross dangerous resonances, while they will gradually decay with the increase of kinetic energy.

Line ratios for x-ray emission in O8+ collisions with H and He atoms

A time-dependent lattice method is used to calculate state selective charge transfer cross sections in O8+ collisions with H and He atoms at incident energies of 1.00, 4.00, and 8.18 keV amu−1. Using standard radiative transitions, Lyman (β/α), Lyman (γ/α), and Lyman (δ/α) line ratios are calculated using time-dependent lattice capture cross sections for both H and He. The line ratios for He are found to be in good agreement with direct experimental measurements at 3.11 keV amu−1.

Integrating Ultrafast Coherent Diffractive Imaging and Atomistic Simulations to Investigate Externally Stimulated Metallic Nanocrystals

Despite the increasing role of nanomaterials in technology, the mechanical and dynamical properties of single nanoparticles at picosecond timescales are not well understood. In particular, core-shell nanocrystals are an important class of nanoparticles for catalysis, biomedical and energy applications. The effect of the nanoscale interface between the core and shell material on coherent lattice vibrations (phonons) is yet to be investigated in detail. Understanding the temporal behavior of such nanomaterials under conditions of external thermal stimulation is crucially important for energy research. In addition, observing ultrafast lattice distortions can provide key insights into the behavior of nanomaterials and nanoscale interfaces. Recently, experimental techniques have evolved to conduct time-dependent lattice dynamics measurements in nanomaterials. In particular, Bragg Coherent Diffraction Imaging (BCDI) in conjunction with optical pump-probe experiments via ultrafast x-ray lasers has been used to directly image the generation and subsequent evolution of coherent acoustic phonons within nanocrystals. In particular, experiments on bimetal (Au/Al) core-shell nanocrystals have revealed inhomogeneous effects in the lattice breathing upon heating with femtosecond x-ray lasers. Conventional theoretical models cannot be used to explain the physics of the phenomena in such non-equilibrium environments that involve extreme heat fluxes and temperature gradients. Atomistic molecular dynamics (MD) simulation is an appropriate technique to investigate lattice dynamics in such environments, particularly in core-shell structures where interfacial effects can play an important role in phonon scattering. With the convergence of time and length scales accessible by both experiments and simulations, we are now able to integrate experimental observations with multi-million atom MD simulations to enhance the fundamental understanding of materials behavior under external stimulation. In this talk, we demonstrate the workflow to integrate ultrafast time-resolved coherent diffractive imaging with large-scale atomistic molecular dynamics simulations to investigate lattice dynamics in externally stimulated core-shell bimetallic nanocrystals. We will focus, primarily, on the MD simulations performed on core-shell bimetallic nanocrystals under the influence of extreme heat fluxes. We explore the vibrational modes that dominate lattice breathing and look into the effect the nanoparticle size and shape have on the same. In addition, we attempt to identify the origin of the inhomogeneous effects, observed experimentally, in the lattice breathing of core-shell structures. Figure 1

Single charge transfer in collisions with H and He atoms

A time-dependent lattice (TDL) method is used to calculate state selective charge transfer cross sections in collisions with H and He atoms. The (nl) capture cross sections for energies of 2.7, 5.2, and 8.3 keV amu−1 are found to be in good agreement with recent atomic-orbital close-coupling (AOCC) calculations for H and somewhat larger than previous AOCC calculations for He. Using standard radiative transition rates, Lyman β/α and γ/α line ratios are calculated using TDL and AOCC capture cross sections for both H and He. The theoretical line ratios for He are found to bracket recent experimental measurements.

The Multiscale Loop Vertex Expansion

The loop vertex expansion (LVE) is a constructive technique which uses only canonical combinatorial tools and no space–time dependent lattices. It works for quantum field theories without renormalization. Renormalization requires scale analysis. In this paper, we provide an enlarged formalism which we call the multiscale loop vertex expansion (MLVE). We test it on what is probably the simplest quantum field theory which requires some kind of renormalization, namely a combinatorial model of the vector type with quartic interaction and a propagator which mimicks the power counting of \({\phi^4_2}\) . An ordinary LVE would fail to treat even this simplest superrenormalizable model, but we show how to perform the ultraviolet limit and prove its analyticity in the Borel summability domain of the model with the MLVE.

Local Versus Global Equilibration near the Bosonic Mott-Insulator–Superfluid Transition

We study the time scales for adiabaticity of trapped cold bosons subject to a time-varying lattice potential using a dynamic Gutzwiller mean-field theory. We explain apparently contradictory experimental observations by demonstrating a clear separation of time scales for local dynamics (~ ms) and global mass redistribution (~1 s). We provide a simple explanation for the short and fast time scales, finding that while density or energy transport is dominated by low energy phonons, particle-hole excitations set the adiabaticity time for fast ramps. We show how mass transport shuts off within Mott-insulator domains, leading to a chemical potential gradient that fails to equilibrate on experimental time scales.

Compression and localization of an atomic cloud in a time dependent optical lattice

We analyze a method of compressing a cloud of cold atoms by dynamic control of a far off-resonance optical lattice. We show that by reducing the lattice spacing either continuously or in discrete steps while cooling the atoms with optical molasses large compression factors can be achieved. Particle motion in the time-dependent lattice is studied numerically using a three-dimensional semiclassical model. Two experimentally realistic models are analyzed. In the first we continuously vary the lattice beam angles to compress atoms initially in a Gaussian distributed cloud with standard deviation of 250 µm into a single site of a two-dimensional lattice of area A ∼ 35 × 35λ2, with λ the wavelength of the lattice beams. This results in an optical depth for an on-resonant probe beam >80 which is an increase by a factor of about 1800 compared to the uncompressed cloud. In the second approach we use a discrete set of lattice beam angles to decrease the spatial scale of the cloud by a factor of 500, and localize a few atoms to a single lattice site with an area A ≲ λ2.

Excitation and charge transfer inp+H(2s)collisions

Excitation and charge transfer cross sections for proton collisions with $2s$ excited state hydrogen are calculated using time-dependent lattice, atomic-orbital close-coupling with pseudostates, and classical trajectory Monte Carlo methods. The time-dependent lattice calculation yields $\ensuremath{\Delta}n=1$ excitation and $\ensuremath{\Delta}n=0$ and $\ensuremath{\Delta}n=1$ charge transfer cross sections at 5, 10, and $15\phantom{\rule{0.3em}{0ex}}\mathrm{keV}$ incident energy. The atomic-orbital close-coupling with pseudostates calculation yields excitation cross sections to $n=3--5$ and charge transfer cross sections to $n=1--5$ at a number of incident energies between 1 and $100\phantom{\rule{0.3em}{0ex}}\mathrm{keV}$. The time-dependent lattice and close-coupling pseudostates calculations are found to be in good agreement with previous standard close-coupling results. The close-coupling with pseudostates calculations are used to benchmark the classical trajectory Monte Carlo calculations, which are widely used in astrophysical and laboratory plasma modelling.

Drift compression and final focus for intense heavy ion beams with nonperiodic, time-dependent lattice

In the currently envisioned configurations for heavy ion fusion, it is necessary to longitudinally compress the beam bunches by a large factor after the acceleration phase. Because the space-charge force increases as the beam is compressed, the beam size in the transverse direction will increase in a periodic quadrupole lattice. If an active control of the beam size is desired, a larger focusing force is needed to confine the beam in the transverse direction, and a nonperiodic quadrupole lattice along the beam path is necessary. In this paper, we describe the design of such a focusing lattice using the transverse envelope equations. A drift compression and final focus lattice should focus the entire beam pulse onto the same focal spot on the target. This is difficult with a fixed lattice, because different slices of the beam may have different perveance and emittance. Four time-dependent magnets are introduced in the upstream of drift compression to focus the entire pulse onto the same focal spot. Drift compression and final focusing schemes are developed for a typical heavy ion fusion driver and for the integrated beam experiment being designed by the Heavy Ion Fusion Virtual National Laboratory.

Quantum interference in a driven washboard potential

The dynamics of a quantum particle in a one-dimensional, tilted (“washboard”) and time-dependent lattice is studied. The approach uses quantum mechanics at the undergraduate level and leads to analytical results that show a rich variety of dynamical behavior and illustrate the fundamental role of interference in quantum systems.

Stroboscopic X-Ray Diffraction Measurements of sub-ns Domain Dynamics in Ferroelectric Films

ABSTRACTWe used the Advanced Photon Source (APS) at Argonne National Laboratory to perform fast (ps range) time-resolved diffraction measurements of the dynamic characteristics in BaTiO3 films subjected to strong high-frequency electric fields. The time-dependent lattice response measured at frequencies between 6.5 MHz and 1.3 GHz revealed damped domain movements with attenuation time rapidly increasing with electric field frequency, v. We found that at frequencies higher than ν ∼ 600 MHz the domain motions in BaTiO3 films become heavily damped, information that may be important to future device operation. A minimum attenuation time, τ ∼ 330 ps, measured at ν = 1.3 GHz was limited by the time constant of the electrical circuit.

Theoretical analysis of quantum dynamics in one-dimensional lattices: Wannier-Stark description

This paper presents a formalism describing the dynamics of a quantum particle in a one-dimensional, tilted, time-dependent lattice. The description uses the Wannier-Stark states, which are localized in each site of the lattice, and provides a simple framework leading to fully analytical developments. Particular attention is devoted to the case of a time-dependent potential, which results in a rich variety of quantum coherent dynamics.

Quantum transport of atoms in optical lattices

Recent work in atom optics has led to enormous progress in the study of quantum chaos and has addressed a broad range of problems in quantum transport, traditionally studied in the context of condensed matter physics. This issue brings together the various researchers working in the border domain between atom optics and solid state physics and focuses on atomic motion in light fields in a regime that is dominated by quantum effects. The topics discussed in this issue include: • quantum effects of atomic motion in light fields; • quantum chaos in time dependent lattices; • tunnelling in stationary or time-dependent lattices; • Wannier-Stark ladder and Bloch oscillations; • atomic band structures; • many-body effects on transport in optical lattices; • effects of decoherence on quantum transport; • weak and dynamical localization. At this point we take the opportunity to express our gratitude to the authors of the papers of this issue and the reviewers for their efforts in preparing and ensuring the high quality of the state of the art presentation.

Measurement of residual strain in InGaAs buffer layers

InxGa1−xAs layers have been grown with different indium compositions and thicknesses above the critical layer thickness and the extent of strain relaxation has been measured using high-resolution x-ray diffraction. Our results show that, in thick layers, the residual strain is dependent upon the lattice mismatch. In a range from 30 times up to 300 times the critical layer thickness, the residual strain represents about 15% of the lattice mismatch, regardless of the In composition. Comparison with published experimental data shows that the magnitude of the residual strain is difficult to predict and depends upon parameters which are yet to be identified. Our data also shows a different behavior for a sample with thickness 450 times the critical layer thickness where strain relaxation is almost complete. One possible explanation is a relaxation process which takes place during the growth of the structure, leading to a time dependent lattice mismatch.