L-2: Difference between revisions
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<strong>Goal: </strong> The physical properties of many materials are controlled by the interfaces embedded in it. This is the case of the dislocations in a crystal, the domain walls in a ferromagnet or the vortices in a supercoductors. In the next lecture we will discuss how impurities affect the behviour of these interfaces. Today we focus on thermal fluctuations and introduce two important equations for the interface dynamics: the Edwards Wilkinson (EW) and the Kardar Parisi Zhang (KPZ) equations. | <strong>Goal: </strong> The physical properties of many materials are controlled by the interfaces embedded in it. This is the case of the dislocations in a crystal, the domain walls in a ferromagnet or the vortices in a supercoductors. In the next lecture we will discuss how impurities affect the behviour of these interfaces. Today we focus on thermal fluctuations and introduce two important equations for the interface dynamics: the Edwards Wilkinson (EW) and the Kardar Parisi Zhang (KPZ) equations. | ||
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=Edwards Wilkinson: an interface at equilibrium: = | =Edwards Wilkinson: an interface at equilibrium: = | ||
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===The d=1 case=== | ===The d=1 case=== | ||
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Revision as of 16:17, 19 January 2024
Goal: The physical properties of many materials are controlled by the interfaces embedded in it. This is the case of the dislocations in a crystal, the domain walls in a ferromagnet or the vortices in a supercoductors. In the next lecture we will discuss how impurities affect the behviour of these interfaces. Today we focus on thermal fluctuations and introduce two important equations for the interface dynamics: the Edwards Wilkinson (EW) and the Kardar Parisi Zhang (KPZ) equations.