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Properties of Quantum Systems via Diagonalization of Transition Amplitudes I: Discretization Effects
- Source :
- Phys. Rev. E 80 (2009) 066705
- Publication Year :
- 2009
-
Abstract
- We analyze the method for calculation of properties of non-relativistic quantum systems based on exact diagonalization of space-discretized short-time evolution operators. In this paper we present a detailed analysis of the errors associated with space discretization. Approaches using direct diagonalization of real-space discretized Hamiltonians lead to polynomial errors in discretization spacing $\Delta$. Here we show that the method based on the diagonalization of the short-time evolution operators leads to substantially smaller discretization errors, vanishing exponentially with $1/\Delta^2$. As a result, the presented calculation scheme is particularly well suited for numerical studies of few-body quantum systems. The analytically derived discretization errors estimates are numerically shown to hold for several models. In the followup paper [1] we present and analyze substantial improvements that result from the merger of this approach with the recently introduced effective-action scheme for high-precision calculation of short-time propagation.<br />Comment: 8 pages, 7 figures, uses revtex4
Details
- Database :
- arXiv
- Journal :
- Phys. Rev. E 80 (2009) 066705
- Publication Type :
- Report
- Accession number :
- edsarx.0911.5145
- Document Type :
- Working Paper
- Full Text :
- https://doi.org/10.1103/PhysRevE.80.066705