Publications by authors named "Saumya Shivam"
We show that non-Hermitian Ginibre random matrix behaviors emerge in spatially extended many-body quantum chaotic systems in the space direction, just as Hermitian random matrix behaviors emerge in chaotic systems in the time direction. Starting with translational invariant models, which can be associated with dual transfer matrices with complex-valued spectra, we show that the linear ramp of the spectral form factor necessitates that the dual spectra have nontrivial correlations, which in fact fall under the universality class of the Ginibre ensemble, demonstrated by computing the level spacing distribution and the dissipative spectral form factor. As a result of this connection, the exact spectral form factor for the Ginibre ensemble can be used to universally describe the spectral form factor for translational invariant many-body quantum chaotic systems in the scaling limit where t and L are large, while the ratio between L and L_{Th}, the many-body Thouless length is fixed.
View Article and Find Full Text PDFWe study the consequences of having translational invariance in space and time in many-body quantum chaotic systems. We consider ensembles of random quantum circuits as minimal models of translational invariant many-body quantum chaotic systems. We evaluate the spectral form factor as a sum over many-body Feynman diagrams in the limit of large local Hilbert space dimension q.
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- The study presents a Reed-Frost epidemic model incorporating recursive contact tracing and asymptomatic transmission, expanding previous work on branching processes to finite populations and diverse contact networks.
- The model was numerically simulated on two types of networks: a complete graph and a square lattice, revealing a notable transition from an 'epidemic phase' to an 'immune phase' as the extent of contact tracing increased.
- The research confirms that outside the ideal scenario of complete tracing, the behavior of the contact-tracing phase transition aligns with percolation theory, and it assesses the effectiveness of recursive contact tracing in controlling outbreak spread.
A population can be immune to epidemics even if not all of its individual members are immune to the disease, so long as sufficiently many are immune-this is the traditional notion of herd immunity. In the smartphone era a population can be immune to epidemics-a notion we call 'digital herd immunity', which is similarly an emergent characteristic of the population. This immunity arises because contact-tracing protocols based on smartphone capabilities can lead to highly efficient quarantining of infected population members and thus the extinguishing of nascent epidemics.
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