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

Quantum systems are 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? In this work, we address these issues by reformulating the problem into finding the ground state energy of a generic spin Hamiltonian. Inspired by recent work in Hamiltonian complexity theory, we 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 arrays' dimensionality 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 behavior of generic driven-dissipative systems, and may ultimately constrain the scalability of quantum processors and simulators based on atom arrays.