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In these lecture notes, we review the adiabatic theorem in quantum mechanics, focusing on a recent extension to many-body systems.
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by same author, On the consistency, extremal, and global properties of counterdiabatic fields , J. Chem. Phys. 129
2008
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J.E. Avron, M. Fraas, G.M. Graf, and P. Grech, Adiabatic theorems for generators of contracting evolutions , Commun. Math. Phys. 314
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S. Bachmann, S. Michalakis, S. Nachtergaele, and R. Sims, Automorphic equivalence within gapped phases of quantum lattice systems , Commun. Math. Phys. 309
2012
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H. Saberi, T. Opatrnỳ, K. Mølmer, and A. del Campo, Adiabatic tracking of quantum many-body dynamics , Phys. Rev. A 90
2014
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M.B. Hastings and S. Michalakis, Quantization of Hall conductance for interacting electrons on a torus , Commun. Math. Phys. 334
2015
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2018
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by same author, The adiabatic theorem and linear response theory for extended quantum systems , Commun. Math. Phys. 361
2018
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by same author, Quantization of conductance in gapped interacting systems , Annales Henri Poincaré 19
2018
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D. Monaco and S. Teufel, Adiabatic currents for interacting electrons on a lattice , Rev. Math. Phys. 31
2019
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