2020 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 FY2020, my efforts involved two international collaborators. (1) I have completed a preprint on the topological classification of non-hermitian systems. Together with my collaborator Vicente Lenz I am working on a revision. It proposed physical criteria that select the relevant classification and it extends the classification result from periodic tight-binding operators to generic spectral operators. This extends earlier classification results to e.g. certain random operators. (2) With Gihyun Lee I am developing on a magnetic pseudodifferential calculus for operators on non-commutative Lp spaces. We intend to apply it to an algebraic-analytic framework for linear response theory in order to prove the existence of topologically protected currents in e.g. non-selfadjoint systems.
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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
Together with my collaborator Vicente Lenz I am currently working on a revision to the preprint. The work with Gihyun Lee should produce a pre-print by early June.
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| Strategy for Future Research Activity |
As for collaboration 1, as a next step, I wish to investigate K-theory for operator algebras on Krein spaces, which I believe is the natural setting for proving bulk-boundary correspondences. 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.
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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.
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