"Static fluctuations of a thick 1D interface in the 1+1 Directed Polymer
formulation"
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The one-dimensional Kardar-Parisi-Zhang (KPZ) equation is at the crossroad
between a wide range of theoretical models and experimental systems such as
roughening phenomena and stochastic growth, the Burgers equation in
hydrodynamics or the 1+1 Directed Polymer, and the very definition and
implications of the KPZ universality class have been expanding since the 1980',
both in physicists and mathematicians communities.
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We have tackled the interplay between thermal fluctuations and a correlated
disordered energy landscape, from the vantage point of static 1D elastic
interfaces in a random-bond disorder. The experimental realizations of such
interfaces always exhibit a non-zero disorder correlation length or thickness
(typically tens of nanometers for domain walls in ferromagnetic thin films), and
turn out to display a low-temperature regime where thermal fluctuations have not
totally erased the imprint of the disorder correlation. This low-temperature
regime is experimentally relevant for ferromagnetic domain walls, but thanks to
the KPZ connections it might also describe the high-velocity steady-state
dynamics of interfaces in nematic liquid crystals (even though without
impurities).