A note on adiabatic time evolution and quasi-static processes in translation-invariant quantum systems

Vojkan Jakšić (1) , Claude-Alain Pillet (2, 3) , Clément Tauber (4, 5)

1 Department of Mathematics and Statistics McGill University
2 CPT - E5 Physique statistique et systèmes complexes
3 CPT - Centre de Physique Théorique - UMR 7332
4 IRMA - Institut de Recherche Mathématique Avancée
5 ITP - Institute for Theoretical Physics [ETH Zürich]

We study the slowly varying, non-autonomous quantum dynamics of a translation invariant spin or fermion system on the lattice $\mathbb Z^d$. This system is assumed to be initially in thermal equilibrium, and we consider realizations of quasi-static processes in the adiabatic limit. By combining the Gibbs variational principle with the notion of quantum weak Gibbs states introduced in [Jak\v{s}i\'c, Pillet, Tauber, arXiv:2204.00440], we establish a number of general structural results regarding such realizations. In particular, we show that such a quasi-static process is incompatible with the property of approach to equilibrium studied in this previous work.

Domaines: Physique mathématique [math-ph]; Mécanique statistique [cond-mat.stat-mech]; Physique Quantique [quant-ph]

Vojkan Jakšić, Claude-Alain Pillet, Clément Tauber. A note on adiabatic time evolution and quasi-static processes in translation-invariant quantum systems. Annales Henri Poincaré, 2023, ⟨10.1007/s00023-023-01282-5⟩. ⟨hal-03633713⟩