An interdimensional funnel enhances topologically protected oscillations in high-dimensional stochastic systems

Abstract

Biochemical systems such as protein complexes often occupy configuration spaces whose dimensionality grows with the number of molecular components. Although usually viewed as an obstacle to coherent dynamics, here we show that high dimensionality can enhance topologically protected oscillations. In the topological regime, a stochastic system with a $D$-dimensional configuration space develops a steady-state current confined to a one-dimensional edge cycle. The intervening boundary faces between the $D$-dimensional bulk and the one-dimensional cycle form an interdimensional funnel, sequentially pushing the system towards lower dimensional faces, down to the one-dimensional cycle. As a consequence, increasing $D$ enhances the funnel, leading to improved one-dimensional localization and oscillatory coherence. A quantized biorthogonal Zak phase identifies the transition to the topological regime, which additionally exhibits a highly structured non-Hermitian skin effect. In contrast with previous realizations of topological states in stochastic systems, the phenomena we uncover have no counterpart in quantum condensed matter or active matter systems.