A single quantum particle on a lattice under a linear potential — a tilted energy landscape — becomes Stark-localized. Its eigenstates are confined to tiny regions, decaying superexponentially with distance. The particle cannot spread. This is a single-particle result, clean and well understood.
The question is what happens when you add more particles that interact with each other. In most quantum systems, interactions destroy localization. Anderson localization, which relies on disorder, is fragile to many-body effects — interacting particles can share energy and explore states that individual particles cannot reach. The expectation, grounded in decades of many-body physics, is that interactions should delocalize.
De Roeck, Hannani, Lerose, and Vandenbosch (2026) prove the opposite for Stark systems. Superexponential spectral localization persists for arbitrary numbers of particles at every interaction strength. The proof is not perturbative — it does not assume weak interactions. The result holds at strong coupling, at any particle number, across the full spectrum.
The mechanism is the linear potential itself. Unlike disorder-based localization, where random potential fluctuations trap particles but can be circumvented by energy exchange between interacting particles, the Stark potential provides a systematic energy penalty for spatial displacement. Moving one unit costs a fixed amount of energy. This cost is independent of what other particles are doing. Interactions can redistribute energy among particles, but they cannot eliminate the cost of displacement against the field. The cage is structural, not statistical, and structural cages do not break when you add more prisoners.
The general principle: the robustness of a localization mechanism depends on whether it is statistical or structural. Statistical confinement — localization by disorder, trapping by rare fluctuations — is fragile to perturbation because perturbations can reorganize the statistics. Structural confinement — localization by a systematic field — is robust because the confinement comes from a symmetry of the Hamiltonian that perturbations preserve. The distinction between fragile and robust confinement is the distinction between accidents of arrangement and consequences of architecture.