Wednesday, March 5, 2025 - 09:00 in Zoom
Non-linear sigma models for non-Hermitian random matrices in symmetry classes AI$^\dagger$ and AII$^\dagger$
A talk in the Seminar Zufallsmatrizen series by
Anish Kulkarni
| Abstract: |
Symmetry of non-Hermitian matrices underpins many physical phenomena. In particular, chaotic open quantum systems exhibit universal bulk spectral correlations classified on the basis of time-reversal symmetry$^\dagger$ (TRS$^\dagger$), coinciding with those of non-Hermitian random matrices in the same symmetry class. In my talk I will present our results on spectral statistics of non-Hermitian random matrices in the presence of TRS$^\dagger$ with signs +1 and −1, corresponding to symmetry classes AI$^\dagger$ and AII$^\dagger$, respectively. Using the fermionic replica non-linear sigma model approach, we derive n-fold integral expressions for the nth moment of the one-point and two-point characteristic polynomials. Performing the replica limit n→0, we qualitatively reproduce the density of states and level-level correlations of non-Hermitian random matrices with TRS$^\dagger$.
Within the CRC this talk is associated to the project(s): C6 |
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