Standard models of market impact assume that the resistance to order flow is local and mean-reverting, analogous to dislocation motion in a periodic crystal (Peierls-Nabarro pinning). This paper proposes an alternative analog: dislocation dynamics in quasicrystals. In quasicrystals, dislocations carry a six-dimensional Burgers vector whose perpendicular (phason) component leaves a non-canceling damage trail—a phason wall—that increases retarding stress proportionally to path length. We map this structure to financial markets: the observable price change corresponds to the physical Burgers component; the invisible restructuring of volatility surfaces, correlation structures, bid-ask spreads, and dealer positioning corresponds to the phason component. Market impact accumulates as a phason wall, producing self-locking liquidity crises that standard risk models fail to anticipate. Central bank liquidity intervention (quantitative easing, repo facilities) is reinterpreted as thermal phason healing. We propose measurable proxies (phason wall indicator, dislocation stress) and a criterion for distinguishing periodic (crystal) vs. aperiodic (quasicrystal) market regimes. The framework explains why historical covariance-based risk models (VaR, expected shortfall) break exactly when markets lack a repeating structural reference. JEL: G01, G10, G14, C02.
Mark David Louise Kruger (Tue,) studied this question.