Eur. Phys. J. B 20, 349-366 (2001)
https://doi.org/10.1007/PL00011103

Bayesian reconstruction of approximately periodic potentials for quantum systems at finite temperature

Institut für Theoretische Physik, Universität Münster, 48149 Münster, Germany

Corresponding author: ^a lemm@uni-muenster.de

Received: 29 May 2000
Revised: 16 August 2000
Published online: 15 April 2001

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. Such potentials might for example correspond to periodic surfaces modified by point defects and observed by atomic force microscopy. The feasibility of the approach is demonstrated for a numerical model.