Beyond Thermalization: New Insights into Quantum System Dynamics

ML4Q professor, David Luitz, contributes to a study on quantum system dynamics revealing unique correlations in chaotic quantum systems that are essential for understanding the nature of quantum chaos and thermalization processes.

The dynamics of isolated quantum systems—in which the system eventually reaches an equilibrium state where the initial conditions are forgotten—are encapsulated by the eigenstate thermalization hypothesis (ETH), formulated over thirty years ago. Recent research on many-body quantum systems has emphasized the dynamics of quantum information, which is not captured by ETH in its original form. Here, we show how one can characterize aspects of quantum dynamics, thus paving the way for a full understanding of thermalization in closed quantum systems.

In the framework of ETH, the dynamics of an isolated system are fully determined by the eigenvectors and eigenvalues of the system’s Hamiltonian, a matrix that fully describes the total energy for the system. The phenomenon of equilibration implies strong constraints on correlations between pairs of eigenvectors.

However, certain aspects are beyond the scope of ETH. For example, if a system with local interactions is disturbed at a point, the effects of this disturbance spread out in space at a definite speed. Equally, an initial state with low quantum entanglement evolves over time into one with high entanglement. We show how all these aspects of quantum dynamics can be combined by considering joint correlations between small numbers (pairs and sets of four) of eigenstates.

An important next step is to apply these findings toward slowly thermalizing or localized systems.

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