Complex absorbing potential and Chebyshev propagation scheme

Midgley, Stuart; Wang, Jingbo

doi:10.1103/physreve.61.920

Cited by 8 publications

(5 citation statements)

References 9 publications

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“…This could result in reflection of the wave packet back at the boundary of the numerical grid, causing interference which destroys the real dynamics (Manolopoulos 2002). Instead of enlarging the grid we solved the problem by employing a complex absorbing potential (Migdley andWang 2000, Muga et al 2004). As a consequence of using a formalism that is easy to implement we pay the price of having a non-Hermitian Hamiltonian operator and of losing some parts of the wave packet.…”

Section: Computational Proceduresmentioning

confidence: 99%

A wave packet method for treating nuclear dynamics on complex potentials

Taioli¹,

Tennyson²

2006

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

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A general time-dependent description of the dissociative attachment of a triatomic molecule is presented. The approach presented works within the Feshbach projection operator formalism and gives an algorithm for solving the nuclear motion problem which reduces the computational effort required. The method uses a complex potential energy surface to characterize the formation and decay of resonances as modified by the coupling to the nuclear motion which are treated using multidimensional complex wave packets. A basis-independent wave packet method is developed and used to treat the propagation of a wave packet on a complex three-dimensional potential appropriate for resonance states of the water anion. A complete derivation of the system of linear equations used in the time iteration is presented. The method can be applied to resonant vibrational excitation, for which the electron impact vibrational excitation of water is considered.

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Section: Computational Proceduresmentioning

confidence: 99%

A wave packet method for treating nuclear dynamics on complex potentials

Taioli¹,

Tennyson²

2006

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

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“…2. There have been many studies of a complex absorbing potential in the continuum limit based on various calculational schemes. [3][4][5][6][7][8][9][10][11][12] The approach followed in this paper requires the diagonalization of a complex symmetric Hamiltonian defined on a lattice, as will be described below.…”

Section: Introductionmentioning

confidence: 99%

Electron and spin transport in the presence of a complex absorbing potential

et al. 2008

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We examine the impact of a complex absorbing potential on electron transport both in the continuum and on a lattice. This requires the use of non-Hermitian Hamiltonians; the required formalism is briefly outlined. The lattice formulation allows us to study the interesting problem of an electron interacting with a stationary spin and the subsequent time evolution of the electron and spin properties as the electron is absorbed after the initial interaction. Remarkably, the properties of the localized spin are affected "at a distance" by the interaction of the ͑now entangled͒ electron with a complex potential.

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“…Other popular techniques are based on polynomial expansions of exp(A). For example, the Chebyshev approximation method is based on the Chebyshev expansion of the matrix exponential about the point [λ min , λ max ] ∈ C, where λ min and λ max are the eigenvalues of A with the smallest and largest real values [19][20][21].…”

Section: Matrix Exponentiationmentioning

confidence: 99%

QSW_MPI: a framework for parallel simulation of quantum stochastic walks

Matwiejew,

Wang

2020

Preprint

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QSW MPI is a python package developed for the modeling of quantum stochastic walks, a generalization of the classical random walk and continuous-time quantum walk in the Lindblad formalism. This model allows for the study of a wide range of Markovian open quantum systems subject to varying degrees of incoherent scattering. Consisting of a python interface built on parallelized Fortran libraries utilizing sparse data structures; QSW MPI is scalable to massively parallel computers, making possible the simulation of walks on graphs with many thousands of vertices. QSW MPI also provides explicit support for an extension of the standard quantum stochastic walk model to the study of non-Hermitian absorption and emission processes.

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Complex absorbing potential and Chebyshev propagation scheme

Cited by 8 publications

References 9 publications

A wave packet method for treating nuclear dynamics on complex potentials

A wave packet method for treating nuclear dynamics on complex potentials

Electron and spin transport in the presence of a complex absorbing potential

QSW_MPI: a framework for parallel simulation of quantum stochastic walks

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