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

• URL: http://arxiv.org/abs/2204.02177v2
• Date: Fri, 3 Feb 2023 07:42:02 GMT
• Title: A note on adiabatic time evolution and quasi-static processes in translation-invariant quantum systems
• Authors: Vojkan Jak\v{s}i\'c, Claude-Alain Pillet, Cl\'ement Tauber
• Abstract summary: We study the slowly varying, non-autonomous quantum dynamics of a translation invariant spin or fermion system on the lattice $mathbb Zd$. We consider realizations of quasi-static processes in the adiabatic limit.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: 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.

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