Equivalence of topological and scattering approaches to quantum pumping

DOI10.1007/s00220-009-0983-1zbMath1227.34089arXiv0902.4638OpenAlexW3101399663MaRDI QIDQ981708

G. Ortelli, Gian Michele Graf, Gerhard Bräunlich

Publication date: 2 July 2010

Published in: Communications in Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/0902.4638

zbMATH Keywords

scatteringSchrödingerquantum pump

Mathematics Subject Classification ID

Scattering theory, inverse scattering involving ordinary differential operators (34L25) Special quantum systems, such as solvable systems (81Q80) Quantum dots, waveguides, ratchets, etc. (81Q37)

Related Items (8)

Topology in shallow-water waves: a violation of bulk-edge correspondence ⋮ A many-body index for quantum charge transport ⋮ Bulk-edge correspondence for two-dimensional topological insulators ⋮ Edge states for second order elliptic operators in a channel ⋮ Dimensional reduction and scattering formulation for even topological invariants ⋮ Edge states in ordinary differential equations for dislocations ⋮ FROM ANDERSON LOCALIZATION TO MESOSCOPIC PHYSICS ⋮ Levinson's theorem and higher degree traces for Aharonov-Bohm operators

Cites Work

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• Adiabatic theorems and applications to the quantum Hall effect
• Erratum: Adiabatic theorems and applications to the quantum Hall effect
• Linear adiabatic theory. Exponential estimates
• On the deficiency indices and self-adjointness of symmetric Hamiltonian systems
• Transport and dissipation in quantum pumps
• Quantised adiabatic charge transport in the presence of substrate disorder and many-body interaction
• Adiabatic charge pumping in open quantum systems
• On Povzner–Wienholtz-type self-adjointness results for matrix-valued Sturm–Liouville operators

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