Materials that gradually change their composition across their surface follow a hidden set of quantum rules that break standard laws of symmetry.
Functionally graded materials possess electromagnetic properties that cannot be described by the standard tensors used in physics for decades. This new ab initio quantum framework proves that these substances require an entirely different rulebook for interaction with light and energy. Most physicists assumed that standard symmetry laws would scale down to the quantum level for any material. Establishing these rules allows engineers to design components that vary their properties continuously without losing performance. This opens the door to building aircraft wings or medical implants that are perfectly optimized at every individual point. It provides the first reliable manual for engineering the next generation of custom-built matter.
Quantum Theory of Functionally Graded Materials
SSRN · 6731328
Functionally graded materials (FGMs) are composites whose composition or microstructure varies continuously in space, producing position-dependent mechanical and functional properties. In recent years, FGMs have gained significant attention due to advances in additive manufacturing, which enable precise spatial control of composition and orientation. However, their graded, aperiodic structure breaks the assumptions of Bloch’s theorem, making first-principles electronic and electromagnetic calcul