Adiabatic times for Markov chains and applications

Details Adiabatic times for Markov chains and applications Adiabatic times for Markov chains and applications

2010-08-11

arxiv.org/abs/1008.1824v1

Mathematics

Probability

Scientific paper

We state and prove a generalized adiabatic theorem for Markov chains and provide examples and applications related to Glauber dynamics of Ising model over Z^d/nZ^d. The theorems derived in this paper describe a type of adiabatic dynamics for l^1(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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