Publication:
Boundary dynamics and topology change in quantum mechanics

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2015-09
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World Scientific
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Abstract
We show how to use boundary conditions to drive the evolution on a quantum mechanical system. We will see how this problem can be expressed in terms of a time-dependent Schrodinger equation. In particular, we will need the theory of self-adjoint extensions of differential operators in manifolds with boundary. An introduction of the latter as well as meaningful examples will be given. It is known that different boundary conditions can be used to describe different topologies of the associated quantum systems. We will use the previous results to study the topology change and to obtain necessary conditions to accomplish it in a dynamical way.
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Boundary dynamics, Topology change, Domain-dependent Schrödinger equation, Quantum Faraday law
Bibliographic citation
Pérez-Pardo, J. M., Barbero-Liñán, M., Ibort, A. (2015).Boundary dynamics and topology change in quantum mechanics. International Journal of Geometric Methods in Modern Physics, 12(08), 1560011