Non-equilibrium almost-stationary states and linear response for gapped quantum systems

T. Kato: On the convergence of the perturbation method. I. Progress of Theoretical Physics 4:514–523 (1949)

1949

Earlier work this paper cites.

R. Kubo: Statistical-mechanical theory of irreversible processes. I. General theory and simple applications to magnetic and conduction problems, J. Phys. Soc. Japan 12:570–586 (1957)

1957

Earlier work this paper cites.

E. Lieb and D. Robinson: The finite group velocity of quantum spin systems. Communications in Mathematical Physics 28:251–257 (1972)

1972

Earlier work this paper cites.

R. Laughlin: Anomalous Quantum Hall Effect: An Incompressible Quantum Fluid with Fractionally Charged Excitations, Physical Review Letters 50:1395–1398 (1983)

1983

Earlier work this paper cites.

B. Simon. Fifteen problems in mathematical physics. Perspectives in mathematics, Birkhäuser, Basel 423 (1984)

1984

Earlier work this paper cites.

J. Bellissard, A. van Elst, and H. Schulz-Baldes: The noncommutative geometry of the quantum Hall effect. Journal of Mathematical Physics 35:5373–5451 (1994)

1994

Earlier work this paper cites.

G. Nenciu: On asymptotic perturbation theory for quantum mechanics: almost invariant subspaces and gauge invariant magnetic perturbation theory. Journal of Mathematical Physics 43:1273–1298 (2002)

2002

Earlier work this paper cites.

G. Panati, H. Spohn, and S. Teufel: Space-adiabatic perturbation theory in quantum dynamics. Physical Review Letters 88:250405 (2002)

2002

Earlier work this paper cites.

G. Panati, H. Spohn, and S. Teufel: Space-adiabatic perturbation theory. Advances in Theoretical and Mathematical Physics 7:145–204 (2003)

2003

Earlier work this paper cites.

G. Panati, H. Spohn, and S. Teufel: Effective dynamics for Bloch electrons: Peierls substitution and beyond. Communications in Mathematical Physics 242:547–578 (2003)

2003

Cited alongside, same era.

S. Teufel: Adiabatic Perturbation Theory in Quantum Dynamics. Lecture Notes in Mathematics 1821, Springer (2003)

2003

Cited alongside, same era.

A. Elgart and B. Schlein: Adiabatic charge transport and the Kubo formula for Landau-type Hamiltonians. Communications on Pure and Applied Mathematics 57, 590–615 (2004)

2004

Cited alongside, same era.

J. Bouclet, F. Germinet, A. Klein, and J. Schenker: Linear response theory for magnetic Schrödinger operators in disordered media. Journal of Functional Analysis 226:301–372 (2005)

2005

Cited alongside, same era.

M. Hastings and X.-G. Wen: Quasiadiabatic continuation of quantum states: The stability of topological ground-state degeneracy and emergent gauge invariance. Physical Review B 72:045141 (2005)

J.-B. Bru and W. de Siqueira Pedra: Lieb–Robinson Bounds for Multi-Commutators and Applications to Response Theory. Springer Briefs in Mathematical Physics Vol. 13, Springer (2016)

2016

Later among the works it cites.

G. De Nittis and M. Lein: Linear Response Theory: An Analytic-Algebraic Approach. Springer Briefs in Mathematical Physics Vol. 21, Springer (2017)

2017

Closest in time.

M. Hastings: The Stability of Free Fermi Hamiltonians. Preprint available at arXiv:1706.02270 (2017)

Original

2017

Closest in time.

S. Bachmann, A. Bols, W. De Roeck, and M. Fraas: Quantization of conductance in gapped interacting systems. Annales Henri Poincaré 19:695–708 (2018)

2018

Closest in time.

S. Bachmann, W. De Roeck, and M. Fraas: The adiabatic theorem and linear response theory for extended quantum systems. Communications in Mathematical Physics 361:997–1027 (2018)