Periodicity alters topological states in thermal diffusion system

Abstract

Topological edge states are a ubiquitous phenomenon across diverse wave systems, including electromagnetic, acoustic and quantum systems. In contrast to wave systems, thermal transport is a kind of diffusion system characterized by pure dissipation. The imposition of different boundary conditions can significantly influence the evolution of thermal system, leading to the appearance of different topological states, which haven't been systematically analyzed yet, especially in practical heat transfer structures. In this work, via a non-Hermitian thermal diffusion lattice model, we discuss the periodicity-dependent topological states. Through rigorous theoretical analysis and numerical simulations of the temperature field, the Hamiltonian is obtained whose eigenvalues are purely imaginary corresponding to the decay rate of the temperature field. Our work paves the way for the investigation of how periodicity alters topological states in thermal diffusion systems, potentially revolutionizing the design of thermal metamaterials for topological thermal protection in thermal management.