Adiabatic Times for Markov Chains and Applications |
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| Authors: | Kyle Bradford Yevgeniy Kovchegov |
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| Affiliation: | 1.Department of Mathematics,Oregon State University,Corvallis,USA |
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| Abstract: | We state and prove a generalized adiabatic theorem for Markov chains and provide examples and applications related to Glauber dynamics of the Ising model over ℤ d /nℤ d . The theorems derived in this paper describe a type of adiabatic dynamics for l1(mathbbRn+)ell^{1}(mathbb{R}^{n}_{+}) norm preserving, time inhomogeneous Markov transformations, while quantum adiabatic theorems deal with ℓ 2(ℂ n ) norm preserving ones, i.e. gradually changing unitary dynamics in ℂ n . |
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