Adiabaticity and Quantum Geometry

Colloquia

Speaker

Raffaele Resta
CNR-IOM Istituto Officina dei Materiali, Trieste, Italy

When

2025/11/20
16:00

Place

DIPC Josebe-Olarra Lecture Hall

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The adiabatic theorem states that when the time evolution of the Hamiltonian is "infinitely slow", a system, when started in the ground state, remains in the instantaneous ground state at all times. This, however, does not mean that the adiabatic evolution of a generic observable obtains simply as its expectation value over the instantaneous eigenstate. As a general principle there is an additional adiabatic term, of quantum-geometrical nature, which is the relevant one for several observables. This is shown explicitly for a few adiabatic linear-response functions: permittivity, infrared charges, quantized Faraday charges in electrolytes, and dc Hall conductivity. Remarkably, the adiabatic limit is well defined even in metals, despite the absence of a spectral gap therein.

[1] R. Resta, Adiabatic observables and Berry curvatures in insulators and metals, arxiv.org/abs/2311.12729.