Operator-induced hyperuniformity of physical fields in ordinary disordered materials
Liyu Zhong, Haina Wang, and Yang Jiao
Phys. Rev. B 114, 254203 (2026) - Published 9 November, 2026
Fluctuations in disordered matter play a central role in determining material properties and physical responses. Recent studies have identified an exotic class of systems known as structurally hyperuniform materials, in which large-scale density fluctuations are anomalously suppressed through special spatial organization of particles, phases, or microstructural features. Here we demonstrate that ordinary, structurally nonhyperuniform disordered materials can nevertheless support hyperuniform physical source fields, including scalar, vector, or tensor observables such as incompatibility, bound charge, and bound current. These sources can also regularize the response fields they drive. We develop a general theoretical framework in which a physical field is generated from a more primitive parent field through a local physical operator. In Fourier space, the spectrum of the derived field is determined by the product of the parent-field spectrum and the Fourier symbol of the operator. When the operator has a small-wave-number zero of order , the derived source spectrum is suppressed by relative to the parent spectrum in the coupled spectral channels. For a parent spectrum scaling as , hyperuniformity is guaranteed if , provided the assumed infrared scaling holds; sufficiently infrared-divergent parent fluctuations need not yield a hyperuniform source. We demonstrate this mechanism in elastic, electrostatic, and magnetostatic settings, showing that operator-generated incompatibility, bound charge, and bound-current fields can become hyperuniform even when their parent eigenstrain, polarization, or magnetization fields remain conventionally disordered. These findings identify a general, explicitly conditional route to field hyperuniformity through local physical constraints and distinguish hyperuniform source generation from regularization of the resulting response fields.


