For elastic manifolds in high-dimensional random landscapes, the annealed complexity of stationary points and of minima is derived explicitly; both vanish at the Larkin mass, with quadratic and cubic scaling, and a depinning bound follows.
Statics and Dynamics of Disordered Elastic Systems
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abstract
We examine here various aspects of the statics and dynamics of disordered elastic systems such as manifolds and periodic systems. Although these objects look very similar and indeed share some underlying physics, periodic systems constitute a class of their own with markedly different properties. We focus on such systems, review the methods allowing to treat them, emphasize the shift of viewpoint compared to the physics of manifolds and discuss their physics in detail. As for the statics, periodicity helps the system to retain a quasi-translational order and to be stable with respect to the proliferation of free topological defects such as dislocations. A disordered periodic system thus leads to a glass phase with Bragg peaks: the Bragg glass. On the other hand, for driven lattices, transverse periodicity allows the system to retain its glassy nature, leading to a moving glass phase. The existence of these two phases has important theoretical and experimental consequences, in particular for vortex physics in superconductors, the physical system which is mainly focused here.
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cond-mat.dis-nn 1years
2019 1verdicts
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Manifolds in high dimensional random landscape: complexity of stationary points and depinning
For elastic manifolds in high-dimensional random landscapes, the annealed complexity of stationary points and of minima is derived explicitly; both vanish at the Larkin mass, with quadratic and cubic scaling, and a depinning bound follows.