Noise and Topology in Driven Systems - an Application to Interface Dynamics

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• 𝒮⌉↕{↖≀∇}⊣\⟩‡⌉⌈ ⌋∇⟩⊔⟩⌋⊣↕⟩⊔†↙

  𝒫↙ ℬ⊣∥⇔ 𝒞↙ 𝒯⊣\}⇔ ⊣\⌈ 𝒦↙ 𝒲⟩⌉∫⌉\{⌉↕⌈↙

  Cited in the paper.

• ℱ∇⊣⌋⊔⊣↕ 𝒞≀\⌋⌉√⊔∫ ⟩\ 𝒮⊓∇{⊣⌋⌉ 𝒢∇≀⊒⊔⟨

  𝒜↙↖ℒ↙ ℬ⊣∇⊣⌊⊣∫⟩ ⊣\⌈ ℋ↙ ℰ↙ 𝒮⊔⊣\↕⌉†↙

  Cited in the paper.

• 𝒞⊓∇∇⌉\⊔↖∫√⟩\ ⌋≀⊓√↕⟩\} {≀∇ {⌉∇∇≀⇕⊣}\⌉⊔⟩⌋ ⌈≀⇕⊣⟩\ ⊒⊣↕↕∫ ⟩\ {⟩\⌉ ⊒⟩∇⌉∫↙

  𝒮↙ ℰ↙ ℬ⊣∇\⌉∫ ⊣\⌈ 𝒮↙ ℳ⊣⌉∥⊣⊒⊣↙

  Cited in the paper.

• 𝒟⌉∇≀⊓}⟨⌉\⟩\} ≀{ ⌈≀⇕⊣⟩\ ⊒⊣↕↕ √⊣⟩∇∫ ⌊† ⌈⟩√≀↕⊣∇ ∇⌉√⊓↕∫⟩≀\↙

  ℳ↙ ℬ⊣⊓⌉∇⇔ 𝒜↙ ℳ≀⊓}⟩\⇔ 𝒥↙ 𝒫↙ 𝒥⊣⇕⌉⊔⇔ 𝒱↙ ℛ⌉√⊣⟩\⇔ 𝒥↙ ℱ⌉∇∇⌉́⇔ ℛ↙ ℒ↙ 𝒮⊔⊣⇕√∫⇔ ℋ↙ ℬ⌉∇\⊣∫⇔ ⊣\⌈ 𝒞↙ 𝒞⟨⊣√√⌉∇⊔↙

  Cited in the paper.

• 𝒯⟨⌉∇⇕⊣↕↕† ⊣∫∫⟩∫⊔⌉⌈ ⌋⊓∇∇⌉\⊔↖⌈∇⟩⊑⌉\ ⌈≀⇕⊣⟩\↖⊒⊣↕↕ ⇕≀⊔⟩≀\↙

  ℛ↙ 𝒜↙ 𝒟⊓⟩\⌉⇔ 𝒜↙ 𝒮↙ 𝒩⊓́\̃⌉‡⇔ ⊣\⌈ 𝒜↙ ℋ↙ ℳ⊣⌋𝒟≀\⊣↕⌈↙

  Cited in the paper.

• ℐ\⊔⌉∇⇕⟩⊔⊔⌉\⌋† ⟩\ ⊔⟨⌉ √∇⌉∫⌉\⌋⌉ ≀{ \≀⟩∫⌉↙

  𝒥↙↖𝒫↙ ℰ⌋∥⇕⊣\\⇔ ℒ↙ 𝒯⟨≀⇕⊣∫⇔ ⊣\⌈ 𝒫↙ 𝒲⟩⊔⊔⊒⌉∇↙

  Cited in the paper.

• ℛ⊣\⌈≀⇕ √⌉∇⊔⊓∇⌊⊣⊔⟩≀\∫ ≀{ ⌈†\⊣⇕⟩⌋⊣↕ ∫†∫⊔⌉⇕∫

  ℋ↙ ℱ∇⌉⟩⌈↕⟩\ ⊣\⌈ 𝒟↙ 𝒲⌉\⊔‡⌉↕↕↙

  Cited in the paper.

• 𝒮⊔⊣⊔⟩⌋∫ ⊣\⌈ ⌈†\⊣⇕⟩⌋∫ ≀{ ⌈⟩∫≀∇⌈⌉∇⌉⌈ ⌉↕⊣∫⊔⟩⌋ ∫†∫⊔⌉⇕∫

  𝒯↙ 𝒢⟩⊣⇕⊣∇⌋⟨⟩ ⊣\⌈ 𝒫↙ ℒ⌉ 𝒟≀⊓∫∫⊣↕↙

  Cited in the paper.

• 𝒩≀\⌉∐⊓⟩↕⟩⌊∇⟩⊓⇕ ⌈†\⊣⇕⟩⌋∫ ≀{ ⟩\⊔⌉∇{⊣⌋⌉∫ ⊣\⌈ ↕⟩\⌉∫↙

  ℳ↙ 𝒦⊣∇⌈⊣∇↙

  Cited in the paper.

• ℰ§√⌉∇⟩⇕⌉\⊔⊣↕ ≀⌊∫⌉∇⊑⊣⊔⟩≀\ ≀{ ∫⌉↕{↖⊣{{⟩\⌉ ∫⌋⊣↕⟩\} ⊣\⌈ ∥⟩\⌉⊔⟩⌋ ∇≀⊓}⟨⌉\⟩\} ⊣⊔ ∫⊓⌊⇕⟩⌋∇≀\ ↕⌉\}⊔⟨ ∫⌋⊣↕⌉∫↙

  𝒥↙ 𝒦∇⟩⇕ ⊣\⌈ 𝒢↙ 𝒫⊣↕⊣∫⊣\⊔‡⊣∫↙

  Cited in the paper.

• 𝒟⌉√⟩\\⟩\} ≀{ ⌈≀⇕⊣⟩\ ⊒⊣↕↕∫ ⊒⟩⊔⟨ ⊣\ ⟩\⊔⌉∇\⊣↕ ⌈⌉}∇⌉⌉ ≀{ {∇⌉⌉⌈≀⇕↙

  𝒱↙ ℒ⌉⌋≀⇕⊔⌉⇔ 𝒮↙ ℰ↙ ℬ⊣∇\⌉∫⇔ 𝒥↙↖𝒫↙ ℰ⌋∥⇕⊣\\⇔ ⊣\⌈ 𝒯↙ 𝒢⟩⊣⇕⊣∇⌋⟨⟩↙

  Cited in the paper.

• 𝒟≀⇕⊣⟩\ ⊒⊣↕↕ ⌋∇⌉⌉√ ⟩\ ⊣\ ⟩∫⟩\} ⊓↕⊔∇⊣⊔⟨⟩\ ⇕⊣}\⌉⊔⟩⌋ {⟩↕⇕↙

  𝒮↙ ℒ⌉⇕⌉∇↕⌉⇔ 𝒥↙ ℱ⌉∇∇⌉́⇔ 𝒞↙ 𝒞⟨⊣√√⌉∇⊔⇔ 𝒱↙ ℳ⊣⊔⟨⌉⊔⇔ 𝒯↙ 𝒢⟩⊣⇕⊣∇⌋⟨⟩⇔ ⊣\⌈ 𝒫↙ ℒ⌉ 𝒟≀⊓∫∫⊣↕↙

  Cited in the paper.

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