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Quantum Chaos 2020 Series: Detecting quantum chaos through sensitivity of eigenstates to adiabatic transformations

Thursday June 11, 2020
9:00 am


 Presenter:  Anatoli Polkovnikov, Boston University
 Series:  CQuIC Seminars
 Abstract:  A QUANTUM CHAOS SEMINAR presented in a Zoom meeting vetted by CQuIC, organized by Pablo Poggi in collaboration with Pieter Claeys.
See https://sites.google.com/view/pablopoggi/qchaos2020-seminars, where further information is provided, along with the actual streaming link. for the meeting link.
Abstract: In this talk I will discuss how one can use sensitivity of eigenstates to adiabatic deformations of the Hamiltonian as a very sensitive probe of emergence of quantum chaos. This probe can be equivalently viewed as a detector of the operator spreading at exponentially long times. Using several examples I will illustrate that the properly normalized norm of the adiabatic gauge potential, the generator of adiabatic transformations, can detect exponentially small in the system size integrability breaking perturbations. Surprisingly, using this probe and across many models, we found existence of a very robust and universal intermediate regime where the system is chaotic but non-ergodic, i.e. not-satisfying ETH. This regime is characterized by exponentially long in the system size relaxation times and the lack of complete thermalization. In this talk I will discuss how one can use sensitivity of eigenstates to adiabatic deformations of the Hamiltonian as a very sensitive probe of emergence of quantum chaos. This probe can be equivalently viewed as a detector of the operator spreading at exponentially long times. Using several examples I will illustrate that the properly normalized norm of the adiabatic gauge potential, the generator of adiabatic transformations, can detect exponentially small in the system size integrability breaking perturbations. Surprisingly, using this probe and across many models, we found existence of a very robust and universal intermediate regime where the system is chaotic but non-ergodic, i.e. not-satisfying ETH. This regime is characterized by exponentially long in the system size relaxation times and the lack of complete thermalization.
 Host:  Pablo Poggi
 Location:  Zoom, Physics & Astronomy

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