| 1. |
- Aurbakken, Einar, et al.
(author)
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Transient spectroscopy from time-dependent electronic-structure theory without multipole expansions
- 2024
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In: Physical Review A: covering atomic, molecular, and optical physics and quantum information. - : American Physical Society. - 2469-9926 .- 2469-9934. ; 109:1
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Journal article (peer-reviewed)abstract
- Based on the work done by an electromagnetic field on an atomic or molecular electronic system, a general gauge-invariant formulation of transient absorption spectroscopy is presented within the semiclassical approximation. Avoiding multipole expansions, a computationally viable expression for the spectral response function is derived from the minimal-coupling Hamiltonian of an electronic system interacting with one or more laser pulses described by a source-free, enveloped electromagnetic vector potential. With a fixed-basis expansion of the electronic wave function, the computational cost of simulations of laser-driven electron dynamics beyond the dipole approximation is the same as simulations adopting the dipole approximation. We illustrate the theory by time-dependent configuration interaction and coupled-cluster simulations of core-level absorption and circular dichroism spectra.
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| 2. |
- Jarlebring, Elias, et al.
(author)
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An Inverse Iteration Method for Eigenvalue Problems with Eigenvector Nonlinearities
- 2014
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In: SIAM Journal on Scientific Computing. - : Society for Industrial & Applied Mathematics (SIAM). - 1064-8275 .- 1095-7197. ; 36:4, s. A1978-A2001
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Journal article (peer-reviewed)abstract
- Consider a symmetric matrix A(v) is an element of R-nxn depending on a vector v is an element of R-n and satisfying the property A(alpha v) = A(v) for any alpha is an element of R\{0}. We will here study the problem of finding (lambda,v) is an element of R x R-n\{0} such that (lambda,v) is an eigenpair of the matrix A(v) and we propose a generalization of inverse iteration for eigenvalue problems with this type of eigenvector nonlinearity. The convergence of the proposed method is studied and several convergence properties are shown to be analogous to inverse iteration for standard eigenvalue problems, including local convergence properties. The algorithm is also shown to be equivalent to a particular discretization of an associated ordinary differential equation, if the shift is chosen in a particular way. The algorithm is adapted to a variant of the Schrodinger equation known as the Gross-Pitaevskii equation. We use numerical simulations to illustrate the convergence properties, as well as the efficiency of the algorithm and the adaption.
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| 3. |
- Kvaal, Simen, et al.
(author)
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Computing singularities of perturbation series
- 2011
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In: Physical Review A. Atomic, Molecular, and Optical Physics. - 1050-2947 .- 1094-1622. ; 83:3, s. 032505-
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Journal article (peer-reviewed)abstract
- Many properties of current ab initio approaches to the quantum many-body problem, both perturbational and otherwise, are related to the singularity structure of the Rayleigh-Schrodinger perturbation series. A numerical procedure is presented that in principle computes the complete set of singularities, including the dominant singularity which limits the radius of convergence. The method approximates the singularities as eigenvalues of a certain generalized eigenvalue equation which is solved using iterative techniques. It relies on computation of the action of the Hamiltonian matrix on a vector and does not rely on the terms in the perturbation series. The method can be useful for studying perturbation series of typical systems of moderate size, for fundamental development of resummation schemes, and for understanding the structure of singularities for typical systems. Some illustrative model problems are studied, including a helium-like model with delta-function interactions for which Moller-Plesset perturbation theory is considered and the radius of convergence found.
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