An Index Theory with Applications to Homoclinic Orbits of Hamiltonian Systems and Dirac Equations
Sign Up to like & getrecommendations! Published in 2018 at "Journal of Dynamics and Differential Equations"
DOI: 10.1007/s10884-020-09846-3
Abstract: In this paper, we will define the index pair $$(i_A(B),\nu _A(B))$$ ( i A ( B ) , ν A ( B ) ) by the dual variational method, and show the relationship between the… read more here.
Keywords: dirac equations; index; homoclinic orbits; index theory ... See more keywords
K-homology and Fredholm operators I: Dirac operators
Sign Up to like & getrecommendations! Published in 2018 at "Journal of Geometry and Physics"
DOI: 10.1016/j.geomphys.2018.08.008
Abstract: This is an expository paper which gives a proof of the Atiyah-Singer index theorem for Dirac operators, presenting the theorem as a computation of the K-homology of a point. This paper and its follow up… read more here.
Keywords: index; dirac operators; homology fredholm; fredholm operators ... See more keywords
Topological edge states of 1D chains and index theory
Sign Up to like & getrecommendations! Published in 2023 at "Journal of Mathematical Physics"
DOI: 10.1063/5.0150870
Abstract: We provide an elementary proof and refinement of a well-known idea from physics: a chiral-symmetric local Hamiltonian on a half-space has the same signed number of edge-localized states with energies in the bulk bandgap as… read more here.
Keywords: physics; edge states; topological edge; index theory ... See more keywords
Locally equivalent quasifree states and index theory
Sign Up to like & getrecommendations! Published in 2022 at "Journal of Physics A: Mathematical and Theoretical"
DOI: 10.1088/1751-8121/ac508b
Abstract: We consider quasifree ground states of Araki’s self-dual canonical anti-commutation relation algebra from the viewpoint of index theory and symmetry protected topological (SPT) phases. We first review how Clifford module indices characterise a topological obstruction… read more here.
Keywords: ground states; index theory; locally equivalent; equivalent quasifree ... See more keywords