Deriving Novel Bulk-Boundary Correspondences for Pseudo-Hermitian Systems

• Project/Area Number: 20K03761
• Research Category: Grant-in-Aid for Scientific Research (C)
• Allocation Type: Multi-year Fund
• Section: 一般
• Review Section: Basic Section 13010:Mathematical physics and fundamental theory of condensed matter physics-related
• Research Institution: Tohoku University
• Principal Investigator: LEIN MAXIMILIAN 東北大学, 材料科学高等研究所, 准教授 (50769891)
• Project Period (FY): 2020-04-01 – 2023-03-31
• Project Status: Discontinued (Fiscal Year 2022)
• Budget Amount: ¥4,420,000 (Direct Cost: ¥3,400,000、Indirect Cost: ¥1,020,000); Fiscal Year 2024: ¥780,000 (Direct Cost: ¥600,000、Indirect Cost: ¥180,000); Fiscal Year 2023: ¥780,000 (Direct Cost: ¥600,000、Indirect Cost: ¥180,000); Fiscal Year 2022: ¥780,000 (Direct Cost: ¥600,000、Indirect Cost: ¥180,000); Fiscal Year 2021: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000); Fiscal Year 2020: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
• Keywords: condensed matter / topological insulators / classical waves / non-hermitian / トポロジカル絶縁体 / 物性物理学 / 数理物理学

Outline of Research at the Start

We start by reformulating my recent work on bulk-boundary correspondences for surface waves at metal-dielectric interfaces in the language of operators on Krein spaces and find derivations for the bulk-boundary correspondences. This particular case will help us generalize the construction of bulk-boundary correspondences to other pseudo-hermitian systems. As our focus is to link physics (observable phenomena) and mathematics (which makes the notion of topology precise), we expect we will need to include data from physics.

Outline of Annual Research Achievements

In FY2022 my efforts involved 3 international collaborators. (1) With Gihyun Lee I have published a work on magnetic pseudodifferential super operators; we are very close to finishing a follow-up work on boundedness criteria for magnetic pseudodifferential super operators. (2) Giuseppe De Nittis, Marcello Seri and I have applied the equivariant magnetic pseudodifferential calculus developed previously to perturbed periodic pseudodifferential operators from condensed matter physics.

Research Products

• [Int'l Joint Research] University of Groningen(オランダ)
• [Int'l Joint Research] Catholic University of Santiago(チリ)
• [Int'l Joint Research] Max Planck Institute for Mathematics/Technical University Munich(ドイツ)
• [Int'l Joint Research] University of Ghent(ベルギー)
• [Int'l Joint Research] University of Cergy/University Paris City(フランス)
• [Int'l Joint Research] Pontifical Catholic University of Chile(チリ)
• [Int'l Joint Research] Max Planck Institute for Mathematics(ドイツ)
• [Int'l Joint Research] University of Groningen/TU Delft(オランダ)
• [Int'l Joint Research] Technical University Delft(オランダ)
• [Int'l Joint Research] Max Planck Institute for Mathematics(ドイツ)
• [Journal Article] A calculus for magnetic pseudodifferential super operators (2022)
  • Author(s): Lee Gihyun、Lein Max
  • Journal Title: Journal of Mathematical Physics Volume: 63 Issue: 10 Pages: 103506-103506
  • DOI: 10.1063/5.0090191
  • Peer Reviewed / Int'l Joint Research
• [Journal Article] A Magnetic Pseudodifferential Calculus for Operator-Valued and Equivariant Operator-Valued Symbols (2022)
  • Author(s): Giuseppe De Nittis、Max Lein、Marcello Seri
  • Journal Title: arxiv Volume: 137 Pages: 1-137
• [Journal Article] A Calculus for Magnetic Pseudodifferential Super Operators (2022)
  • Author(s): Gihyun Lee and Max Lein
  • Journal Title: Journal of Mathematical Physics Volume: xxx Pages: 1-80
  • Peer Reviewed / Int'l Joint Research
• [Presentation] An Introduction to the Theory of Topological Insulators - At the Intersection of Analysis and Topology (2022)
  • Author(s): Max Lein
  • Organizer: Mini Workshop on Topological Insulators, University of Groningen, The Netherlands
  • Invited
• [Presentation] Magnetic Pseudodifferential Super Operators - At the Intersection of Functional Analysis and Operator Algebras (2022)
  • Author(s): Max Lein
  • Organizer: Analysis Seminar, Max Planck Institute for Mathematics, Bonn, Germany
• [Presentation] Having a Fresh Look at the Conductivity in Metals - A Semiclassical Definition of the Fermi Surface (2022)
  • Author(s): Max Lein
  • Organizer: Physics Colloqium, University of Cergy Paris, Cergy, France
• [Presentation] On the Classification of Non-Selfadjoint Topological Insulators Modeled by Spectral Operators (2022)
  • Author(s): Max Lein
  • Organizer: Probability Seminar, Tohoku University
• [Presentation] On the Bulk Classification of Non-Selfadjoint Topological Insulators Modeled by Spectral Operators (2022)
  • Author(s): Max Lein
  • Organizer: Mathematical approach for topological physics (III), Nagoya University, Japan
  • Invited
• [Presentation] An Introduction to the Theory of Topological Insulators (2022)
  • Author(s): Max Lein
  • Organizer: Mini symposium "Mathematical physics and topology", University of Groningen, The Netherlands
  • Invited
• [Presentation] A Definition of Fermi Surface in the Presence of Perturbations (2022)
  • Author(s): Max Lein
  • Organizer: Physics seminar, Cergy Paris University, France
  • Invited
• [Presentation] Magnetic Pseudodifferential Super Operators - At the Intersection of Functional Analysis and Operator Algebras (2022)
  • Author(s): Max Lein
  • Organizer: Mathematisches Oberseminar, Max Planck Institute for Mathematics, Bonn, Germany
  • Invited
• [Presentation] Mini Course on Semiclassics (2021)
  • Author(s): Max Lein
  • Organizer: Learning from Insulators: New Trends in the Study of Conduction Properties of Metals, Lorentz Center, The Netherlands
  • Invited
• [Presentation] On the Bulk Classification of Non-Hermitian Topological Insulators Modeled by Spectral Operators ― Physical Principles to Choose a Physically Meaningful Classification (2020)
  • Author(s): Max Lein
  • Organizer: Theoretical studies of topological phases of matter (hybrid workshop, participated virtually), Yukawa Institute, Kyoto University
  • Invited
• [Presentation] On the Classification of Non-Hermitian Topological Insulators ― Physical Principles to Choose a Physically Meaningful Classification (2020)
  • Author(s): Max Lein
  • Organizer: MSM-AIMR Joint Online Workshop 2020, Cambridge University & AIMR, Tohoku University,
  • Invited
• [Presentation] On the Classification of Non-Hermitian Topological Insulators ― Physical Principles to Choose a Physically Meaningful Classification (2020)
  • Author(s): Max Lein
  • Organizer: Mathematical Physics Seminar, Shinshu University
• [Book] A Mathematical Journey Through Differential Equations of Physics (2022)
  • Author(s): Lein Max
  • Total Pages: 457
  • Publisher: World Scientific Publishing
  • ISBN: 9789811225376
• [Funded Workshop] Learning from Insulators: New Trends in the Study of Conduction Properties of Metals (2021)