Quantum and electromagnetic propagation with the conjugate symmetric Lanczos method
- Department of Chemistry, Rice Quantum Institute, and Laboratory for Nanophotonics, MS 60, Rice University, Houston, Texas 77005 (United States)
The conjugate symmetric Lanczos (CSL) method is introduced for the solution of the time-dependent Schroedinger equation. This remarkably simple and efficient time-domain algorithm is a low-order polynomial expansion of the quantum propagator for time-independent Hamiltonians and derives from the time-reversal symmetry of the Schroedinger equation. The CSL algorithm gives forward solutions by simply complex conjugating backward polynomial expansion coefficients. Interestingly, the expansion coefficients are the same for each uniform time step, a fact that is only spoiled by basis incompleteness and finite precision. This is true for the Krylov basis and, with further investigation, is also found to be true for the Lanczos basis, important for efficient orthogonal projection-based algorithms. The CSL method errors roughly track those of the short iterative Lanczos method while requiring fewer matrix-vector products than the Chebyshev method. With the CSL method, only a few vectors need to be stored at a time, there is no need to estimate the Hamiltonian spectral range, and only matrix-vector and vector-vector products are required. Applications using localized wavelet bases are made to harmonic oscillator and anharmonic Morse oscillator systems as well as electrodynamic pulse propagation using the Hamiltonian form of Maxwell's equations. For gold with a Drude dielectric function, the latter is non-Hermitian, requiring consideration of corrections to the CSL algorithm.
- OSTI ID:
- 21024772
- Journal Information:
- Journal of Chemical Physics, Vol. 128, Issue 6; Other Information: DOI: 10.1063/1.2828502; (c) 2008 American Institute of Physics; Country of input: International Atomic Energy Agency (IAEA); ISSN 0021-9606
- Country of Publication:
- United States
- Language:
- English
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