T-5: Difference between revisions
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<strong>Goal: </strong> | <!--<strong>Goal: </strong> | ||
So far we have discussed the equilibrium properties of disordered systems, that are encoded in their partition function/free energy. When a system (following Langevin, Monte Carlo dynamics) equilibrates at sufficiently large times, its long-time properties are captured by these equilibrium calculations. In glassy systems the equilibration timescales are extremely large: for very large timescales the system does not visit equilibrium configurations, but rather metastable states. In this set of problems, we characterize the energy landscape of the spherical <math>p</math>-spin by studying its metastable states (local minima). | So far we have discussed the equilibrium properties of disordered systems, that are encoded in their partition function/free energy. When a system (following Langevin, Monte Carlo dynamics) equilibrates at sufficiently large times, its long-time properties are captured by these equilibrium calculations. In glassy systems the equilibration timescales are extremely large: for very large timescales the system does not visit equilibrium configurations, but rather metastable states. In this set of problems, we characterize the energy landscape of the spherical <math>p</math>-spin by studying its metastable states (local minima). | ||
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== Check out: key concepts == | == Check out: key concepts == | ||
Gradient descent, rugged landscapes, metastable states, Hessian matrices, random matrix theory, landscape’s complexity. | Gradient descent, rugged landscapes, metastable states, Hessian matrices, random matrix theory, landscape’s complexity.--> | ||
Revision as of 19:09, 15 February 2024