Jun-ichi Inoue (Hokkaido University)
Title: Analysis of quantum Monte Carlo dynamics in infinite-range Ising spin systems: theory and its possible applications
In terms of the stochastic process of quantum Monte Carlo method,
we analytically derive macroscopically deterministic flow equations
of order parameters such as spontaneous magnetization in infinite-range
quantum spin systems . By means of the Suzuki-Trotter decomposition,
we consider the transition probability of glauber-type dynamics
of microscopic states for the corresponding (d+1)-dimensional
classical system. Under the static approximation, differential equations
with respect to macroscopic order parameters are explicitly obtained
from the Master equation that describes the microscopic-law.
In the steady state, the equations are identical to the
saddle point equations for the equilibrium state of the same system.
The equation for the dynamical Ising model is recovered
in the classical limit. We also check the validity of the static
approximation by making use of computer simulations
for finite size systems. We also discuss several
possible applications of our approach to several research areas,
say, statistical-mechanical informatics  and neural networks .
J. Inoue, Journal of Physics: Conference Series 233, 012010 (2010).
J. Inoue, Journal of Physics: Conference Series 297, 012012 (2011).