Mathematical Perspectives on Quantum Mechanics: Decoherence, Open Systems, and Infinite-Dimensional Hilbert Spaces

Abstract:

Realistic models of quantum systems must take into account their unavoidable interaction with environments that lie beyond our experimental control. This gives rise to phenomena, such as decoherence and noise, that significantly undermine our ability to harness key quantum features like entanglement. As such, incorporating these effects in our mathematical models is of key importance for advancing quantum technologies, as well as for a deeper grasp of quantum mechanics itself.

In this talk we propose a mathematical journey through the framework necessary to describe open quantum systems, emphasizing the role of infinite-dimensional Hilbert spaces and linear unbounded operators as a natural tool to provide insights into the nature of decoherence and noise. We will specifically focus on the spin–boson model, which serves as a quintessential example of an open quantum system interacting with an infinite-dimensional environment. Some recent related results will be introduced and discussed.