A note on adiabatic time evolution and quasi-static processes in translation-invariant quantum systems. (English) Zbl 1540.81073
Summary: 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 [V. Jakšić et al., Ann. Henri Poincaré 25, No. 1, 715–749 (2024; Zbl 07802657)], 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.
MSC:
| 81R25 | Spinor and twistor methods applied to problems in quantum theory |
| 82C10 | Quantum dynamics and nonequilibrium statistical mechanics (general) |
| 81V74 | Fermionic systems in quantum theory |
| 81Q35 | Quantum mechanics on special spaces: manifolds, fractals, graphs, lattices |
| 82B30 | Statistical thermodynamics |
| 70H11 | Adiabatic invariants for problems in Hamiltonian and Lagrangian mechanics |
Citations:
Zbl 07802657References:
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