On Classical and Quantum Mechanical Energy Spectra of Finite Heisenberg Spin Systems

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Title: On Classical and Quantum Mechanical Energy Spectra of Finite Heisenberg Spin Systems
Authors: Exler, Matthias
Thesis advisor: Apl. Prof. Dr. Jürgen Schnack
Thesis referee: Jun.-Prof. Dr. Jochen Gemmer
Abstract: Since the synthesis of Mn12, which can be regarded as the birth of the class of magnetic molecules, many different molecules of various sizes and structures have been produced. The magnetic nature of these molecules originates from a number of paramagnetic ions, whose unpaired electrons form collective angular momenta, referred to as spins. The interaction between these spins can often be described in the Heisenberg model. In this work, we use the rotational band model to predict the energy spectrum of the giant Keplerate {Mo72Fe30}. Based on the approximate energy spectrum, we simulate the cross-section for inelastic neutron scattering, and the results are compared to experimental data. The successful application of our approach substantiates the validity of the rotational band model. Furthermore, magnetic molecules can serve as an example for studying general questions of quantum mechanics. Since chemistry now allows the preparation of magnetic molecules with various spin quantum numbers, this class of materials can be utilized for studying the relations between classical and quantum regime. Due to the correspondence principle, a quantum spin system can be described exactly by classical physics for an infinitely large spin quantum number s. However, the question remains for which quantum numbers s a classical calculation yields a reasonable approximation. Our approach in this work is to develop a converging scheme that adds systematic quantum corrections to the classical density of states for Heisenberg spin systems. To this end, we establish a correspondence of the classical density of states and the quantum spectrum by means of spin-coherent states. The algorithm presented here allows the analysis of how the classical limit is approached, which gives general criteria for the similarity of the classical density of states to the quantum spectrum.
URL: https://repositorium.ub.uni-osnabrueck.de/handle/urn:nbn:de:gbv:700-2006051610
Subject Keywords: Magnetic molecules; Heisenberg model; Spin systems; Classical limit; Spin-coherent states
Issue Date: 16-May-2006
Type of publication: Dissertation oder Habilitation [doctoralThesis]
Appears in Collections:FB04 - E-Dissertationen

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