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Miyao Lab
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The lab uncovers, as mathematical structures, the phenomena that occur in matter.
AboutAbout the lab
Seeing phenomena in matter as mathematical structures.
Prof. Miyao studies the mathematical structures of the diverse phenomena that appear in condensed matter physics.
The tools are methods from analysis, such as operator algebras, stochastic analysis, and spectral analysis.
The aim is not only to elucidate phenomena but also to deepen the theories used for that purpose.
Keywords include quantum field theory, quantum statistical mechanics, and topological phases.
Key terms
- Condensed matter physics
- A branch of physics that studies the behavior of matter, such as solids and liquids, made up of many particles
- Operator algebras
- A field that gathers together the "actions" on an object and studies their algebraic structure
- Spectral analysis
- A method that examines the set of characteristic values of an operator to read off the behavior of a system
ResearchResearch themes
The lab aims to elucidate the mathematical structures of the diverse phenomena that appear in condensed matter physics. Making full use of operator algebras, stochastic analysis, and spectral analysis, it also deepens these theories themselves.
*Illustrative imageGiving Condensed Matter Physics a Mathematical Foundation
The lab gives mathematically rigorous foundations to the theory of condensed matter physics, which explains the properties of matter from the interactions of many particles. Problems are formulated mathematically and solved with rigorous methods.
*Illustrative imageFrom Physical Phenomena to New Mathematics
Accurately describing puzzling physical phenomena sometimes requires creating new mathematics or finding new applications of existing mathematics. The lab aims to uncover the new mathematics hidden in the phenomena of matter.
MembersFaculty
- ProfessorTadahiro Miyao
VoicesStudent voices
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Report an errorAbout the images
The top and research theme images are illustrative and were not taken at the lab. They are cropped from Wikimedia Commons images. Cropped CC BY-SA images are provided under the same CC BY-SA license as the original (version shown on each line).
- Top image: “Hofstadter's butterfly” Mytomi / Public domain (cropped)
- Giving Condensed Matter Physics a Mathematical Foundation: “Bose Einstein condensate” NIST/JILA/CU-Boulder / Public domain (cropped)
- From Physical Phenomena to New Mathematics: “Quantum Harmonic Oscillator Levels” Inductiveload / Public domain (cropped)
- Related lab (Mathematical Sciences Lab): “Belousov Zhabotinsky reaction ( )” Stephen Morris / CC BY 2.0 (cropped)
- Related lab (Mathematical Sciences (Namiki) Lab): “CA3061-81k7” Maxter315 / CC BY-SA 4.0 (cropped)
- Related lab (Geometry (Nozaki) Lab): “Trefoil knot cgi” Altapedia / CC BY-SA 4.0 (cropped)
- Related lab (Analysis Lab (Hamamuki)): “Real snowflake macro photo” Alexey Kljatov / CC BY-SA 4.0 (cropped)
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