Quantum Geometric Tensor (Fubini-Study Metric) in Simple Quantum System: A pedagogical Introduction

Ran Cheng

doi:10.48550/arxiv.1012.1337

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qcr:2606.48565.1

Quantum Geometric Tensor (Fubini-Study Metric) in Simple Quantum System: A pedagogical Introduction

arXiv

Ran Cheng

Geometric Quantum Mechanics is a novel and prospecting approach motivated by the belief that our world is ultimately geometrical. At the heart of that is a quantity called Quantum Geometric Tensor (or Fubini-Study metric), which is a complex tensor with the real part serving as the Riemannian metric that measures the `quantum distance', and the imaginary part being the Berry curvature. Following a physical introduction of the basic formalism, we illustrate its physical significance in both the adiabatic and non-adiabatic systems.

10.48550/arxiv.1012.1337

Published 2010

Uploaded 3 days ago

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