Regensburg 2025 – wissenschaftliches Programm

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TT: Fachverband Tiefe Temperaturen

TT 53: Topology: Other Topics

TT 53.1: Vortrag

Freitag, 21. März 2025, 09:30–09:45, H32

Quantum Geometric Tensor and Inertial Effects — •Maike Fahrensohn and Richard Matthias Geilhufe — Condensed Matter and Materials Theory Division, Department of Physics, Chalmers University of Technology, 41258 Göteborg, Sweden

The quantum geometric tensor (or Fubini-Study metric), defined on a parametrized quantum state manifold, encodes the full geometric structure of quantum space. The real part of the quantum geometric tensor, known as the quantum metric tensor, is a positive semi-definite Riemannian metric that measures the geometric distance between quantum states. This tensor has recently been shown to play a crucial role in the description of physical phenomena such as quantum transport, quantum noise, and optical conductivity. The antisymmetric part of the quantum geometric tensor, proportional to the Berry curvature, has been extensively studied and is central to the classification of topological insulators through their first Chern number.

While inertial effects have been well explored in classical mechanics, their role in quantum systems remains less understood. We build a connection between the quantum geometric tensor and inertial effects to bridge the geometric and topological properties of quantum systems to their physical response. This relationship may offer new insights into transport phenomena, stability, and collective dynamics in quantum systems.

Keywords: Quantum Geometric Tensor; Quantum Metric; Inertial Effects; Berry Curvature; Quantum Geometry