Adiabaticity and Quantum Geometry

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:2311.12729
[2] R. Resta, Quantum geometry and adiabaticity in molecules and in condensed matter, J. Chem. Phys. 162, 234102 (2025).

About the speaker

Raffaele Resta is a retired professor of physics. Previously he served in Trieste, first at SISSA (1983-1994) and then at the University of Trieste (1995-2017). Since the beginning of professional life his main interest has been in the theory of materials, using a variety of approaches, from analytical theories and models to first–principle computations. Since the birth (about 1980) of the modern computational theory of materials, his mainstream research activity has been in this area, working both at the development of new methods and at actual computations. He has made crucial advances in the understanding of macroscopic polarization, orbital magnetization, magnetoelectric couplings, flexoelectricity, and the nature of the insulating state. He is the author of several review papers on the above topics. He is a fellow of the American Physical Society, and a former (2002-08) Divisional Associate Editor for Physical Review Letters.

Prof. Resta's web page