dorsal/arxiv
View SchemaReconstruction of thermally-symmetrized quantum autocorrelation functions from imaginary-time data
| Authors | Cristian Predescu |
|---|---|
| Categories | |
| ArXiv ID | physics/0405051 |
| URL | https://arxiv.org/abs/physics/0405051 |
| DOI | 10.1103/PhysRevE.70.066705 |
| Journal | Phys. Rev. E 70, 066705 (2004) |
Abstract
In this paper, I propose a technique for recovering quantum dynamical information from imaginary-time data via the resolution of a one-dimensional Hamburger moment problem. It is shown that the quantum autocorrelation functions are uniquely determined by and can be reconstructed from their sequence of derivatives at origin. A general class of reconstruction algorithms is then identified, according to Theorem 3. The technique is advocated as especially effective for a certain class of quantum problems in continuum space, for which only a few moments are necessary. For such problems, it is argued that the derivatives at origin can be evaluated by Monte Carlo simulations via estimators of finite variances in the limit of an infinite number of path variables. Finally, a maximum entropy inversion algorithm for the Hamburger moment problem is utilized to compute the quantum rate of reaction for a one-dimensional symmetric Eckart barrier.
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"abstract": "In this paper, I propose a technique for recovering quantum dynamical\ninformation from imaginary-time data via the resolution of a one-dimensional\nHamburger moment problem. It is shown that the quantum autocorrelation\nfunctions are uniquely determined by and can be reconstructed from their\nsequence of derivatives at origin. A general class of reconstruction algorithms\nis then identified, according to Theorem 3. The technique is advocated as\nespecially effective for a certain class of quantum problems in continuum\nspace, for which only a few moments are necessary. For such problems, it is\nargued that the derivatives at origin can be evaluated by Monte Carlo\nsimulations via estimators of finite variances in the limit of an infinite\nnumber of path variables. Finally, a maximum entropy inversion algorithm for\nthe Hamburger moment problem is utilized to compute the quantum rate of\nreaction for a one-dimensional symmetric Eckart barrier.",
"arxiv_id": "physics/0405051",
"authors": [
"Cristian Predescu"
],
"categories": [
"physics.chem-ph",
"physics.comp-ph"
],
"doi": "10.1103/PhysRevE.70.066705",
"journal_ref": "Phys. Rev. E 70, 066705 (2004)",
"title": "Reconstruction of thermally-symmetrized quantum autocorrelation functions from imaginary-time data",
"url": "https://arxiv.org/abs/physics/0405051"
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