Adiabatic Times for Markov Chains and Applications

作者：Bradford Kyle; Kovchegov Yevgeniy^*

来源：Journal of Statistical Physics, 2011, 143(5): 955-969.

DOI：10.1007/s10955-011-0219-6

• Time inhomogeneous Markov processes
• Ergodicity
• Mixing times
• Adiabatic
• Glauber dynamics
• Ising model

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 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).

• 出版日期2011-6