Speaker
Description
The geometric properties of quantum states are crucial for understanding many physical phenomena in quantum mechanics, condensed matter physics, and optics. The central object describing these properties is the quantum geometric tensor, which unifies the Berry curvature and the quantum metric. I will introduce the differential-geometric framework of vector bundles to analyze the properties of parameter-dependent quantum states and generalize the quantum geometric tensor to this setting. To illustrate these results, I will briefly discuss the sub-bundle geometry arising in the semiclassical treatment of Dirac fields propagating in curved spacetime and show how the quantum geometric tensor. This is based on https://doi.org/10.22331/q-2026-01-14-1965.
| Topic | Recent developments in differential geometry, Quantum groups and algebras, deformed quantum systems, Quantum information |
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