Non-degenerate two photon absorption spectra of Si nanocrystallites

Iitaka, Toshiaki; Ebisuzaki, Toshikazu

doi:10.1016/s0167-9317(99)00224-5

Cited by 2 publications

(3 citation statements)

References 15 publications

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“…Using the unconditionally stable split-step Fast Fourier Transform (FFT) method to solve the TDSE, it was shown that the eigenvalue spectrum of a particle moving in continuum space can be computed in the same manner [5]. Fast algorithms of this kind proved useful to study various aspects of localization of waves [6][7][8] and other oneparticle problems [9,10]. Application of these ideas to quantum many-body systems triggered further development of flexible and efficient methods to solve the TDSE.…”

Section: Introductionmentioning

confidence: 99%

Fast algorithm for finding the eigenvalue distribution of very large matrices

Hams¹,

2000

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A theoretical analysis is given of the equation of motion method, due to Alben et al., to compute the eigenvalue distribution (density of states) of very large matrices. The salient feature of this method is that for matrices of the kind encountered in quantum physics the memory and CPU requirements of this method scale linearly with the dimension of the matrix. We derive a rigorous estimate of the statistical error, supporting earlier observations that the computational efficiency of this approach increases with matrix size. We use this method and an imaginary-time version of it to compute the energy and the specific heat of three different, exactly solvable, spin-1/2 models and compare with the exact results to study the dependence of the statistical errors on sample and matrix size.

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Section: Introductionmentioning

confidence: 99%

Fast algorithm for finding the eigenvalue distribution of very large matrices

Hams¹,

2000

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“…( 41) yield expressions that have the same structure as Eq. (33), with extra subscripts to account for the second spatial dimension. It follows that on the lattice,…”

Section: B Two Dimensionsmentioning

confidence: 99%

“…if we want to determine all eigenvalues, time-domain algorithms offer several advantages. In fact they are at the heart of so-called "fast" algorithms to compute the density of states (DOS) and other related quantities [28][29][30][31][32][33]. The basic idea of this approach was laid out by Alben et al [28] who used it to compute the DOS of models for one electron moving in a disordered alloy.…”

Section: Implementation: Summarymentioning

confidence: 99%

Unconditionally stable algorithms to solve the time-dependent Maxwell equations

2001

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Based on the Suzuki product-formula approach, we construct a family of unconditionally stable algorithms to solve the time-dependent Maxwell equations. We describe a practical implementation of these algorithms for one-, two-, and three-dimensional systems with spatially varying permittivity and permeability. The salient features of the algorithms are illustrated by computing selected eigenmodes and the full density of states of one-, two-, and three-dimensional models and by simulating the propagation of light in slabs of photonic band-gap materials.

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Non-degenerate two photon absorption spectra of Si nanocrystallites

Cited by 2 publications

References 15 publications

Fast algorithm for finding the eigenvalue distribution of very large matrices

Fast algorithm for finding the eigenvalue distribution of very large matrices

Unconditionally stable algorithms to solve the time-dependent Maxwell equations

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