Discrete Variable Representations in Quantum Dynamics

Light, John C.

doi:10.1007/978-1-4899-2326-4_14

Cited by 38 publications

(22 citation statements)

References 60 publications

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“…The primary purpose of the model is to investigate the performance of the different Padéextrapolations given precise input data. The model itself is solved with a discrete variable representation, 49 and the computed energies have full numeric precision. In contrast, electron binding energies computed with ab initio packages typically have errors in the range of 10 −6 or 10 −5 eV.…”

Section: Resultsmentioning

confidence: 99%

Resonance Energies and Lifetimes from the Analytic Continuation of the Coupling Constant Method: Robust Algorithms and a Critical Analysis

Sommerfeld

Melugin

Hamal

et al. 2017

J. Chem. Theory Comput.

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The energy of a metastable state can be computed by adding an artificial stabilizing potential to the Hamiltonian, increasing the stabilization until the metastable state is turned into a bound one, and then further increasing the stabilization until enough bound-state data have been collected so that these can be extrapolated back to vanishing stabilization. The lifetime of the metastable state can be obtained from the same data, but only if the extrapolation is performed by analytic continuation. This extrapolation method is called analytic continuation of the coupling constant (ACCC). Here we introduce preconditioning schemes for two of the three established extrapolation algorithms and critically compare results from all three extrapolation schemes in a variety of situations: As examples for resonance states serve the π* temporary anions of ethylene and formaldehyde as well as a model potential, which provides a case where input data with full numeric precision are available. In the data collection step, three different stabilizing potentials are employed, a Coulomb potential, a short-range Coulomb potential, and a soft-box Voronoi potential. Effects of different orders of the extrapolating Padé approximant are investigated, and last, the energy range of input data for the extrapolation is studied. Moreover, all ACCC results are compared to resonance parameters that have been independently obtained with the same theoretical method, but with a different continuum approach-complex scaling for the model and complex absorbing potentials for the temporary anions.

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Section: Resultsmentioning

confidence: 99%

Resonance Energies and Lifetimes from the Analytic Continuation of the Coupling Constant Method: Robust Algorithms and a Critical Analysis

Sommerfeld

Melugin

Hamal

et al. 2017

J. Chem. Theory Comput.

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show abstract

“…These permanents are labelled by an integer vector n = (n 1 , ..., n i , ..., n M ), where n i is the occupation number of the i-th three-dimensional, time-dependent single-particle function [81,84] or a Fast-Fourier Transformation based grid [85,86],…”

Section: Tunability Of Model Interaction Potentialsmentioning

confidence: 99%

Beyond mean-field dynamics of ultra-cold bosonic atoms in higher dimensions: facing the challenges with a multi-configurational approach

Bolsinger

Krönke

Schmelcher

2017

J. Phys. B: At. Mol. Opt. Phys.

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Exploring the impact of dimensionality on the quantum dynamics of interacting bosons in traps including particle correlations is an interesting but challenging task. Due to the different participating length scales the modelling of the short-range interactions in three dimensions plays a special role. We review different approaches for the latter and elaborate that for multi-configurational computational strategies finite range potentials are adequate resulting in the need of large grids to resolve the relevant length scales. This results in computational challenges which include also the exponential scaling of complexity with the number of atoms. We show that the recently developed The beneficial scaling of our approach is demonstrated by studying the tunnelling dynamics of bosonic ensembles in a double well. Comparing three-dimensional with quasi-one dimensional simulations, we find dimensionality-induced effects in the density. Furthermore, we study the crossover from weak transversal confinement, where a mean-field description of the system is sufficient, towards tight transversal confinement, where particle correlations and beyond mean-field effects are pronounced.

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“…The primitive basis is normally a time-independent discrete variable representation (DVR) basis. 1, 38,91,92 Other bases like PvB can be used as well. In the latter case, the primitive basis becomes nonorthogonal and the overlap matrix of the primitive basis has to be included in the equations of motion (EOM) for the matrix U (κ) .…”

Section: A General Mctdh Theorymentioning

confidence: 99%

“…37 We use the standard Ansatz of a time-independent direct-product basis but employ basis functions that lead to a sparse representation of the wavefunction. The basis functions are either coordinate-space-localized discretevariable-representation (DVR) functions, 1,38 phasespace-localized projected von Neumann functions, PvB, 35,[39][40][41][42] or phase-space-localized but momentumsymmetric projected Weylets, pW. 37,[43][44][45][46][47][48] If the wavefunction is expanded in one of these bases, large parts of the wavefunction coefficient tensor have negligible amplitude, i. e. they are sparse and the values are below a certain threshold.…”

Section: Introductionmentioning

confidence: 99%

Dynamical pruning of the multiconfiguration time-dependent Hartree (DP-MCTDH) method: An efficient approach for multidimensional quantum dynamics

Larsson

Tannor

2017

The Journal of Chemical Physics

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We present two strategies for combining dynamical pruning with the multiconfiguration time-dependent Hartree (DP-MCTDH) method, where dynamical pruning means on-the-fly selection of relevant basis functions. The first strategy prunes the primitive basis that represents the single-particle functions (SPFs). This is useful for smaller systems that require many primitive basis functions per degree of freedom, as we will illustrate for NO. Furthermore, this allows for higher-dimensional mode combination and partially lifts the sum-of-product-form requirement onto the structure of the Hamiltonian, as we illustrate for nonadiabatic 24-dimensional pyrazine. The second strategy prunes the set of configurations of SPF at each time step. We show that this strategy yields significant speed-ups with factors between 5 and 50 in computing time, making it competitive with the multilayer MCTDH method.

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Discrete Variable Representations in Quantum Dynamics

Cited by 38 publications

References 60 publications

Resonance Energies and Lifetimes from the Analytic Continuation of the Coupling Constant Method: Robust Algorithms and a Critical Analysis

Resonance Energies and Lifetimes from the Analytic Continuation of the Coupling Constant Method: Robust Algorithms and a Critical Analysis

Beyond mean-field dynamics of ultra-cold bosonic atoms in higher dimensions: facing the challenges with a multi-configurational approach

Dynamical pruning of the multiconfiguration time-dependent Hartree (DP-MCTDH) method: An efficient approach for multidimensional quantum dynamics

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