2017/08/29 by Vittorio Peano, Hermann Schulz‐Baldes, Hermann Schulz-Baldes · 2 citations
Mathematics · Physics and Astronomy · #Chern class #Cold Atom Physics and Bose-Einstein Condensates #Combinatorics #Geometry #Hamiltonian (control theory) #Hilbert space #Mathematical analysis #Mathematical physics #Mathematics #Physics #Pure mathematics #Quadratic equation #Quantum many-body systems #Quantum mechanics #Space (punctuation) #Topological Materials and Phenomena #Topology (electrical circuits) #Winding number #math-ph #math.MP
paper · pdf · doi:10.1063/1.5002094
arxiv created 2017/08/29 · openalex publication_date 2018/03/01 · arxiv updated 2018/04/04 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
Quadratic bosonic Hamiltonians over a one-particle Hilbert space can be described by a Bogoliubov-de Gennes (BdG) Hamiltonian on a particle-hole Hilbert space. In general, the BdG Hamiltonian is not self-adjoint, but only J-self-adjoint on the particle-hole space viewed as a Krein space. Nevertheless, its energy bands can have non-trivial topological invariants like Chern numbers or winding numbers. By a thorough analysis for tight-binding models, it is proved that these invariants lead to bosonic edge modes which are robust to a large class of possibly disordered perturbations. Furthermore, general scenarios are presented for these edge states to be dynamically unstable even though the bulk modes are stable.