Dissipative spectral form factor for elliptic Ginibre unitary ensemble and applications
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| Format: | Preprint |
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2024
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| _version_ | 1866914198535012352 |
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| author | Sen, Sunidhi Kumar, Santosh Sarkar, Ayana Kulkarni, Manas |
| author_facet | Sen, Sunidhi Kumar, Santosh Sarkar, Ayana Kulkarni, Manas |
| contents | We investigate the dissipative spectral form factor (DSFF)--a widely used probe of non-Hermitian quantum chaos--in the elliptic Ginibre unitary ensemble (eGinUE), which interpolates between the non-Hermitian Ginibre unitary ensemble (GinUE) and the Hermitian Gaussian unitary ensemble (GUE) via a symmetry breaking parameter. We derive exact finite-dimensional results and large-dimensional approximations for the DSFF, revealing a scaling relationship that connects the DSFF of eGinUE to that of GinUE and the spectral form factor of GUE. This relation explains the distinct time scales underlying the characteristic \emph{dip-ramp-plateau} structure across GinUE, GUE, and crossover regimes. Additionally, we refine estimates of dip-ramp and ramp-plateau transition times for different symmetry regimes. We validate our results with Monte Carlo simulations and demonstrate applications to paradigmatic quantum-chaotic systems: the crossover Sachdev-Ye-Kitaev model and the crossover Power-law Banded random matrices. We highlight an analogy between eGinUE eigenvalues and the positions of a rotating fermionic gas in a two-dimensional anisotropic trap. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2407_17148 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Dissipative spectral form factor for elliptic Ginibre unitary ensemble and applications Sen, Sunidhi Kumar, Santosh Sarkar, Ayana Kulkarni, Manas Statistical Mechanics High Energy Physics - Theory Mathematical Physics Chaotic Dynamics 15B52, 60B20, 15A18, 81Q50, 62H20 We investigate the dissipative spectral form factor (DSFF)--a widely used probe of non-Hermitian quantum chaos--in the elliptic Ginibre unitary ensemble (eGinUE), which interpolates between the non-Hermitian Ginibre unitary ensemble (GinUE) and the Hermitian Gaussian unitary ensemble (GUE) via a symmetry breaking parameter. We derive exact finite-dimensional results and large-dimensional approximations for the DSFF, revealing a scaling relationship that connects the DSFF of eGinUE to that of GinUE and the spectral form factor of GUE. This relation explains the distinct time scales underlying the characteristic \emph{dip-ramp-plateau} structure across GinUE, GUE, and crossover regimes. Additionally, we refine estimates of dip-ramp and ramp-plateau transition times for different symmetry regimes. We validate our results with Monte Carlo simulations and demonstrate applications to paradigmatic quantum-chaotic systems: the crossover Sachdev-Ye-Kitaev model and the crossover Power-law Banded random matrices. We highlight an analogy between eGinUE eigenvalues and the positions of a rotating fermionic gas in a two-dimensional anisotropic trap. |
| title | Dissipative spectral form factor for elliptic Ginibre unitary ensemble and applications |
| topic | Statistical Mechanics High Energy Physics - Theory Mathematical Physics Chaotic Dynamics 15B52, 60B20, 15A18, 81Q50, 62H20 |
| url | https://arxiv.org/abs/2407.17148 |