Universal scaling laws for correlated decay of many-body quantum systems

Abstract

Quantum systems are inevitably open, continually exchanging energy and information with the surrounding environment. This interaction leads to decoherence and decay of quantum states. In complex systems, formed by many particles, decay can become correlated and enhanced. A fundamental question then arises: what is the maximal decay rate of a large quantum system, and how does it scale with its size? Computing this rate exactly is as hard as finding the ground-state energy of a generic spin Hamiltonian—a notoriously intractable problem. Here we exploit this correspondence to establish rigorous and general upper and lower bounds on the maximal decay rate. These bounds are universal, as they hold for a broad class of Markovian many-body quantum systems. For many physically relevant systems, the bounds are asymptotically tight, resulting in exact scaling laws with system size. Specifically, for large atomic arrays in free space, these scalings depend only on the dimensionality of the array and are insensitive to details at short length scales. The scaling laws set fundamental limits on the decay rates of all quantum states, shed light on the behaviour of generic driven-dissipative systems, and may ultimately constrain the scalability of quantum processors and simulators based on atomic arrays.