Adiabatic Interaction

Domenico Monaco, Stefan Teufel

We prove an adiabatic theorem for general densities of observables that are sums of local terms in finite systems of interacting fermions, without periodicity assumptions on the Hamiltonian and with error estimates that are uniform in the size of the system. Our result provides an adiabatic expansion to all orders, in particular, also for the initial data that lie in eigenspaces of degenerate eigenvalues. Our proof is based on ideas from [ 10 ], where Bachmann et al. proved an adiabatic theorem for interacting spin systems. As one important application of this adiabatic theorem, we provide the first rigorous derivation of the adiabatic response formula for the current density induced by an adiabatic change of the Hamiltonian of a system of interacting fermions in a ground state, with error estimates uniform in the system size. We also discuss the application to quantum Hall systems.

A. S. Alexandrov, Bakhrom Yavidov

Two-site single electron system interacting with many vibrating ions of a lattice via a long-range (Fr\"ohlich) electron-phonon interaction is studied in the adiabatic regime. The renormalized hopping integral of small adiabatic Fr\"ohlich polarons is calculated and compared with the hopping integral of small adiabatic Holstein polarons.

Rachel Berkowitz

Jing Zhou, Zi Cai, Xu‐Bo Zou +1 more

We study the effect of interaction on the temperature change in the process of adiabatic mixing of two components of Fermi gases using the real-space Bogoliubov--de Gennes method. We find that in the process of adiabatic mixing, the competition between the adiabatic expansion and the attractive interaction makes it possible to cool or heat the system depending on the strength of the interaction and the initial temperature of the system. The changes of the temperature in a bulk system and in a trapped system are investigated.