In this thesis we develop a mathematically rigorous framework of the so-called ''classical limit'' of quantum systems and their semi-classical properties. Our methods are based on the theory of strict, also called C*- algebraic deformation quantization. Since this C*-algebraic approach encapsulates both quantum as classical theory in one single framework, it provides, in particular, an excellent setting for studying natural emergent phenomena like spontaneous symmetry breaking (SSB) and phase transitions typically showing up in the classical limit of quantum theories. To this end, several techniques from functional analysis and operator algebras have been exploited and specialised to the context of Schrödinger operators and quantum spin systems. Their semi-classical properties including the possible occurrence of SSB have been investigated and illustrated with various physical models. Furthermore, it has been shown that the application of perturbation theory sheds new light on symmetry breaking in Nature, i.e. in real, hence finite materials. A large number of physically relevant results have been obtained and presented by means of diverse research papers.

Quantum Systems and their Classical Limit A C*- Algebraic Approach / Van De Ven, Christiaan Jozef Farielda. - (2021 Dec 14), pp. 1-164. [10.15168/11572_324358]

Quantum Systems and their Classical Limit A C*- Algebraic Approach

Van De Ven, Christiaan Jozef Farielda
2021-12-14

Abstract

In this thesis we develop a mathematically rigorous framework of the so-called ''classical limit'' of quantum systems and their semi-classical properties. Our methods are based on the theory of strict, also called C*- algebraic deformation quantization. Since this C*-algebraic approach encapsulates both quantum as classical theory in one single framework, it provides, in particular, an excellent setting for studying natural emergent phenomena like spontaneous symmetry breaking (SSB) and phase transitions typically showing up in the classical limit of quantum theories. To this end, several techniques from functional analysis and operator algebras have been exploited and specialised to the context of Schrödinger operators and quantum spin systems. Their semi-classical properties including the possible occurrence of SSB have been investigated and illustrated with various physical models. Furthermore, it has been shown that the application of perturbation theory sheds new light on symmetry breaking in Nature, i.e. in real, hence finite materials. A large number of physically relevant results have been obtained and presented by means of diverse research papers.
14-dic-2021
XXXIV
2019-2020
Matematica (29/10/12-)
Mathematics
Moretti, Valter
no
Inglese
Settore MAT/07 - Fisica Matematica
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Descrizione: PhD thesis
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11572/324358
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