University of Twente Student Theses


Kinematic decomposition of quantum systems

Meijer, A.S. (2022) Kinematic decomposition of quantum systems.

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Abstract:Standard descriptions of both classical physics, as described by Hamiltonian dynamics, and quantum physics, as described by unitary dynamics, describe closed systems. Their formalism excludes the possibility of describing systems which exchange energy with their surroundings. In classical physics, this issue is remedied by port-Hamiltonian theory, which allows to describe open systems and their interaction with each other. In quantum mechanics no such comprehensive theory of open systems exists. Quantum systems are much harder to compose and decompose due to the tensor product constructions, by which the composition of quantum systems are defined. In this thesis, we successfully address the kinematic part of this problem by exploitation of the fact that any tensor product composition of finite-dimensional quantum systems can be rewritten as a direct sum decomposition. A unique such direct sum decomposition is obtained by considering, without loss of generality, only fundamental quantum systems whose Hilbert spaces are reducible or irreducible representations of SU(2). The description of the dynamics of a quantum system that is decomposed in quantum port-Hamiltonian fashion can now be erected on this result and is briefly touched upon.
Item Type:Essay (Bachelor)
Faculty:EEMCS: Electrical Engineering, Mathematics and Computer Science
Subject:31 mathematics, 33 physics
Programme:Applied Mathematics BSc (56965)
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