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2022-03 NITheCS Mini-School: Dr Fabio Anzà, Geometric Quantum Mechanics of finite-dimensional systems
2022-03 NITheCS Mini-School:
Dr Fabio Anzà
(Templeton Independent Research Fellow, Complexity Sciences Center, University of California, Davis)

Geometric Quantum Mechanics of finite-dimensional systems

Abstract: The wonderful development of digital and nanoscale technology of the past 20 years has led to a new wave of interest for quantum-information-processing technologies. While the landscape is broad, a common goal of crucial relevance is to build a comprehensive understanding of how complex (many-body and out of equilibrium) quantum systems can exchange, store and process information. This is a huge, community-wide, effort that requires both experimental and theoretical advances to build a clear path towards the understanding and control of complex quantum phenomena. It is therefore appropriate to aim beyond the existing paradigms and tools of analysis to explore new ways of understanding quantum phenomena. I will argue that Geometric Quantum Mechanics (GQM) is one of such promising ways.
GQM is a formulation of quantum mechanics based on differential geometry which leads to interesting implications, new tools of analysis and, most importantly, new ways of thinking about quantum phenomena. With this perspective in mind, in this lecture series I will present the basics of Geometric Quantum Mechanics (GQM), a quick review of its historic development, some applications, and interesting future directions.

Only preliminary knowledge of Standard Quantum Mechanics is required. Prior knowledge of differential geometry is not necessary or required.
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