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Register a new userMode-space-compatible inelastic scattering in atomistic nonequilibrium Greens function implementations
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The nonequilibrium Greens function (NEGF) method is often used to predict transport in atomistically resolved nanodevices and yields an immense numerical load when inelastic scattering on phonons is included. To ease this load, this work extends the atomistic mode space approach of Ref. [1] to include inelastic scattering on optical and acoustic phonons in silicon nanowires. This work also includes the exact calculation of the real part of retarded scattering self-energies in the reduced basis representation using the Kramers-Kronig relations. The inclusion of the Kramers-Kronig relation for the real part of the retarded scattering self-energy increases the impact of scattering. Virtually perfect agreement with results of the original representation is achieved with matrix rank reductions of more than 97%. Time-to-solution improvements of more than 200$times$ and peak memory reductions of more than 7$times$ are shown. This allows for the solution of electron transport scattered on phonons in atomically resolved nanowires with cross-sections larger than 5 nm $times$ 5 nm.
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We propose a multi-resolution strategy that is compatible with the lattice Greens function (LGF) technique for solving viscous, incompressible flows on unbounded domains. The LGF method exploits the regularity of a finite-volume scheme on a formally unbounded Cartesian mesh to yield robust and computationally efficient solutions. The original method is spatially adaptive, but challenging to integrate with embedded mesh refinement as the underlying LGF is only defined for a fixed resolution. We present an ansatz for adaptive mesh refinement, where the solutions to the pressure Poisson equation are approximated using the LGF technique on a composite mesh constructed from a series of infinite lattices of differing resolution. To solve the incompressible Navier-Stokes equations, this is further combined with an integrating factor for the viscous terms and an appropriate Runge-Kutta scheme for the resulting differential-algebraic equations. The parallelized algorithm is verified through with numerical simulations of vortex rings, and the collision of vortex rings at high Reynolds number is simulated to demonstrate the reduction in computational cells achievable with both spatial and refinement adaptivity.
Distributions of inelastically scattered neutrons can be quantum dynamically described by a scattering kernel. We present an accurate and computationally efficient rejection method for sampling a given scattering kernel of any isotropic material. The proposed method produces continuous neutron energy and angular distributions, typically using just a single interpolation per sampling. We benchmark the results of this method against those from accurate analytical models and one of the major neutron transport codes. We also show the results of applying this method to the conventional discrete double differential cross sections.
A Greens function approach to the inclusive quasielastic ($e,e$) scattering is presented. The components of the nuclear response are written in terms of the single-particle optical model Greens function. The explicit calculation of the Greens function can be avoided by its spectral representation, which is based on a biorthogonal expansion in terms of the eigenfunctions of the non-Hermitian optical potential and of its Hermitian conjugate. This allows one to treat final state interactions consistently in the inclusive ($e,e$) and in the exclusive ($e,eN$) reactions. Numerical results for the longitudinal and transverse response functions obtained in a nonrelativistic and in a relativistic framework are presented and discussed also in comparison with data.
We present an ab initio theory of core- and valence resonant inelastic x-ray scattering (RIXS) based on a real-space multiple scattering Greens function formalism and a quasi-boson model Hamiltonian. Simplifying assumptions are made which lead to an approximation of the RIXS spectrum in terms of a convolution of an effective x-ray absorption signal with the x-ray emission signal. Additional many body corrections are incorporated in terms of an effective energy dependent spectral function. Example calculations of RIXS are found to give qualitative agreement with experimental data. Our approach also yields simulations of lifetime-broadening suppressed XAS, as observed in high energy resolutionfluorescence detection experiment (HERFD). Finally possible improvements to our approach are briefly discussed.
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