We propose a unifying framework for nonequilibrium relaxation dynamics in ensembles of positionally disordered interacting quantum spins based on the statistical properties, such as mean and variance, of the underlying disorder distribution. Our framework is validated through extensive exact numerical calculations and we use it to disentangle and understand the importance of dimensionality and interaction range for the observation of glassy (i.e., sub-xponential) decay dynamics. Leveraging the deterministic control of qubit positioning enabled by modern tweezer array architectures, we also introduce a method (“$J$-mapping”) that can be used to emulate the relaxation dynamics of a disordered system with arbitrary dimensionality and interaction range in bespoke one-dimensional arrays. Our approach paves the way towards tunable relaxation dynamics that can be explored in quantum simulators based on arrays of neutral atoms and molecules.

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• Cold gases in optical lattices
• Collective effects in atomic physics
• Long-range interactions
• Quantum simulation
• Rydberg gases
• Rydberg atoms & molecules
• Trapped atoms
• Schroedinger equation