The dynamics of large quantum systems is currently an active topic of research due to the great progress on experimental setups. These dynamics appear to often obey certain universal features, consistent with the principles of statistical mechanics. One of the more prominent ones is equilibration: despite the inherent unitarity and reversibility, the evolution appears to converge to a fixed equilibrium value for very long times, until Poincaré recurrences happen.
Here, we show that this equilibration happens in a more dramatic way than previously thought: we prove that the dynamics of generic quantum systems concentrate around their equilibrium value when measuring at arbitrary times. This means that the probability of finding them away from equilibrium is exponentially suppressed, with a decay rate given by the effective dimension, which is itself exponential in system size. Our result allows us to place a lower bound on the recurrence time of quantum systems, since recurrences corresponds to the rare events of finding a state away from equilibrium. In many-body systems, this bound is doubly exponential in system size. We also show corresponding results for free fermions, which display a weaker concentration and earlier recurrences.
Alvaro Alhambra is a postdoctoral researcher and Humboldt Fellow at Max Planck Institute for Quantum Optics. Previously, he was a postdoctoral researcher at Perimeter Institute for Theoretical Physics in Waterloo (Canada), where he arrived after finishing his PhD studies on quantum thermodynamics at University College London. His research lies at the interface of quantum information theory and quantum many-body physics, with a particular interest in the physics at finite temperature, both at equilibrium and away from it, and on how these can be described through classical and quantum algorithms.