dorsal/arxiv
View SchemaBayesian Reconstruction of Approximately Periodic Potentials at Finite Temperature
| Authors | J. C. Lemm, J. Uhlig, A. Weiguny |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0005122 |
| URL | https://arxiv.org/abs/quant-ph/0005122 |
| DOI | 10.1007/PL00011103 |
Abstract
The paper discusses the reconstruction of potentials for quantum systems at finite temperatures from observational data. A nonparametric approach is developed, based on the framework of Bayesian statistics, to solve such inverse problems. Besides the specific model of quantum statistics giving the probability of observational data, a Bayesian approach is essentially based on "a priori" information available for the potential. Different possibilities to implement "a priori" information are discussed in detail, including hyperparameters, hyperfields, and non--Gaussian auxiliary fields. Special emphasis is put on the reconstruction of potentials with approximate periodicity. The feasibility of the approach is demonstrated for a numerical model.
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"abstract": "The paper discusses the reconstruction of potentials for quantum systems at\nfinite temperatures from observational data. A nonparametric approach is\ndeveloped, based on the framework of Bayesian statistics, to solve such inverse\nproblems. Besides the specific model of quantum statistics giving the\nprobability of observational data, a Bayesian approach is essentially based on\n\"a priori\" information available for the potential. Different possibilities to\nimplement \"a priori\" information are discussed in detail, including\nhyperparameters, hyperfields, and non--Gaussian auxiliary fields. Special\nemphasis is put on the reconstruction of potentials with approximate\nperiodicity. The feasibility of the approach is demonstrated for a numerical\nmodel.",
"arxiv_id": "quant-ph/0005122",
"authors": [
"J. C. Lemm",
"J. Uhlig",
"A. Weiguny"
],
"categories": [
"quant-ph",
"cond-mat.stat-mech",
"physics.data-an"
],
"doi": "10.1007/PL00011103",
"title": "Bayesian Reconstruction of Approximately Periodic Potentials at Finite Temperature",
"url": "https://arxiv.org/abs/quant-ph/0005122"
},
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