2021 Fiscal Year Research-status Report
Deriving Novel Bulk-Boundary Correspondences for Pseudo-Hermitian Systems
| Project/Area Number |
20K03761
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| Research Institution | Tohoku University |
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Principal Investigator |
LEIN MAXIMILIAN 東北大学, 材料科学高等研究所, 准教授 (50769891)
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| Project Period (FY) |
2020-04-01 – 2025-03-31
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| Keywords | condensed matter / topological insulators / classical waves / non-hermitian |
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| Outline of Annual Research Achievements |
In FY2021 my efforts involved 3 international collaborators. (1) With Gihyun Lee I have finished a work on a magnetic pseudodifferential calculus for operators on non-commutative Lp spaces; it has been tentatively accepted for publication. We intend to apply it to linear response theory in order to prove the existence of topologically protected currents in e.g. non-selfadjoint systems. (2) Giuseppe De Nittis, Marcello Seri and I have developed an equivariant magnetic pseudodifferential calculus; it gives rigorous meaning to perturbed periodic operators, including non-selfadjoint ones.
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| Current Status of Research Progress |
Current Status of Research Progress
2: Research has progressed on the whole more than it was originally planned.
Reason
Regarding collaboration (1) together with my collaborator Gihyun Lee I am currently incorporating the suggestions by the referee to publish our first work. We have also made progress on a follow-up work on Lp boundedness for these pseudodifferential super operators. Regarding (2), we are almost finished with our first manuscript. Another work with De Nittis and Seri that focusses on applications in condensed matter is also 70 % finished. After that I plan to revise a manuscript with my collaborator Vicente Lenz to address the referee's criticisms.
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| Strategy for Future Research Activity |
As for collaboration (1), the next work with Gihyun Lee will focus on developing a C*- and von Neumann algebraic point of view of our magnetic pseudodifferential calculus in terms of twisted crossed product algebras. This should make it more suitable for applying K-theoretic and operator-algebraic techniques to it.
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| Causes of Carryover |
Due to the global Covid-19 pandemic I was unable to travel. National and international travel has either been strictly forbidden or at the very least strongly discouraged. Since most of my funds are intended to be used either for traveling or inviting guests, I was unable to spend money in accordance with my research plan. However, in April 2022 I spent 1 month in Europe to work with my collaborators in the Netherlands and Germany.
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