Quantifying quantum chaos from microcanonical fluctuations

IQSE AMO QO Seminar Series

Pizza will be served for IQSE members at 11:00 am. The talk will start around 11:30 am.

Speaker: Dr. Joaquin Rodriguez-Nieva

Venue: IQSE SEMINAR ROOM (MPHY 578)

ABOUT THE SPEAKER: Quantum matter away from thermodynamic equilibrium can exhibit rich classes of dynamical behaviors that have no equilibrium analogue. An overarching goal of my research is to discover universal principles governing the dynamics and thermalization of quantum matter beyond equilibrium paradigms. Such principles can be applied to describe dynamics in a wide range of many-body systems, from electrons in solid-state materials to cold atoms in optical lattices to ensembles of spin defects, in spite of the apparent microscopic differences between such systems. More specifically, my research involves developing theoretical frameworks at the interface between non-equilibrium statistical mechanics and quantum information that can be used to describe, understand and, ultimately, control these novel dynamical behaviors. My research also studies how to exploit these novel behaviors for potential applications in emergent areas such as quantum sensing and metrology. Other research interests include the physics of low-dimensional electronic systems, and developing a deeper understanding of machine learning by drawing insights from statistical mechanics.

EVENT DETAILS: The emergence of statistical mechanics in isolated quantum many-body systems has been a topic of foundational interest since the birth of quantum mechanics. Unlike classical systems, notions of chaos and ergodicity in many-body quantum systems still remain ill-defined. For this reason, designing quantitative measures of quantum chaos are of fundamental importance. One widely-accepted definition is through the random matrix behavior of Hamiltonian eigenstates. In this talk, I will introduce an eigenstate metric for quantum chaos that quantifies the distance between the microcanonical distribution of entanglement entropy produced by eigenstates and that produced by pure random states with appropriate constraints. We find that, for chaotic systems, the distribution of entanglement entropy of eigenstates deviates from random matrix theory predictions for all models and systems sizes studied. In particular, we show that the variance of the microcanonical entanglement entropy distribution of eigenstates is an extremely sensitive probe of quantum chaos. I will show numerical results in a variety of physical Hamiltonians having both chaotic and integrable limits as well as Floquet systems with and without randomness. When employing our metric of chaos in Hamiltonian systems known to exhibit strongly chaotic behavior, we find that deviations from random matrix behavior are negligible only in small pockets of parameter space. This suggests that maximally chaotic Hamiltonians, those with eigenstates exhibiting random matrix behavior, exist only in fine-tuned regions of parameter space.

ZOOM information:

https://tamu.zoom.us/j/98156251523?pwd=QVdSdGxtL1UyY0g1L083SU5QR0QrUT09

Meeting ID: 981 5625 1523
Passcode: 297578

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