Topology protects equilibrium structures in a classical system of interacting lines
Location: MSRI: Simons Auditorium
Topological materials can exhibit robust properties that are protected
against disorder even in the absence of quantum effects. In
optics, topological protection has been primarily
applied to linear waves and
non-interacting systems at zero temperature. In this talk, we demonstrate
how to construct topologically protected states that arise from the
combination of strong interactions and thermal fluctuations inherent to soft
matter. Specifically, we consider fluctuating lines under tension, subject to a class of
spatially modulated substrate potentials. At equilibrium, the lines acquire
a collective tilt proportional to an integer topological invariant called the
Chern number. This quantized tilt is robust against substrate disorder,
as verified by classical Langevin dynamics simulations. We establish the
topological underpinning of this pattern via a mapping that we develop
between the line fluid and Thouless pumping of an imaginary-time Mott insulator in which
excitations are gapped by interactions. Our work points to a new class of classical
topological phenomena in which the topological signature manifests itself in a
structural property rather than a transport measurement.
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