Abstract: In this paper, we present a quantum statistical
mechanical formulation from our recently analytical expressions for
partial-wave transition matrix of a three-particle system. We report
the quantum reactive cross sections for three-body scattering
processes 1+(2,3)→1+(2,3) as well as recombination
1+(2,3)→1+(3,1) between one atom and a weakly-bound dimer. The
analytical expressions of three-particle transition matrices and their
corresponding cross-sections were obtained from the threedimensional
Faddeev equations subjected to the rank-two non-local
separable potentials of the generalized Yamaguchi form. The
equilibrium quantum statistical mechanical properties such partition
function and equation of state as well as non-equilibrium quantum
statistical properties such as transport cross-sections and their
corresponding transport collision integrals were formulated
analytically. This leads to obtain the transport properties, such as
viscosity and diffusion coefficient of a moderate dense gas.
Abstract: The study of non-equilibrium systems has attracted
increasing interest in recent years, mainly due to the lack of
theoretical frameworks, unlike their equilibrium counterparts.
Studying the steady state and/or simple systems is thus one of the
main interests. Hence in this work we have focused our attention on
the driven lattice gas model (DLG model) consisting of interacting
particles subject to an external field E. The dynamics of the system
are given by hopping of particles to nearby empty sites with rates
biased for jumps in the direction of E. Having used small two
dimensional systems of DLG model, the stochastic properties at nonequilibrium
steady state were analytically studied. To understand the
non-equilibrium phenomena, we have applied the analytic approach
via master equation to calculate probability function and analyze
violation of detailed balance in term of the fluctuation-dissipation
theorem. Monte Carlo simulations have been performed to validate
the analytic results.
Abstract: On the basis of Bayesian inference using the
maximizer of the posterior marginal estimate, we carry out phase
unwrapping using multiple interferograms via generalized mean-field
theory. Numerical calculations for a typical wave-front in remote
sensing using the synthetic aperture radar interferometry, phase
diagram in hyper-parameter space clarifies that the present method
succeeds in phase unwrapping perfectly under the constraint of
surface- consistency condition, if the interferograms are not corrupted
by any noises. Also, we find that prior is useful for extending a phase
in which phase unwrapping under the constraint of the
surface-consistency condition. These results are quantitatively
confirmed by the Monte Carlo simulation.
Abstract: We constructed a method of phase unwrapping for a typical wave-front by utilizing the maximizer of the posterior marginal (MPM) estimate corresponding to equilibrium statistical mechanics of the three-state Ising model on a square lattice on the basis of an analogy between statistical mechanics and Bayesian inference. We investigated the static properties of an MPM estimate from a phase diagram using Monte Carlo simulation for a typical wave-front with synthetic aperture radar (SAR) interferometry. The simulations clarified that the surface-consistency conditions were useful for extending the phase where the MPM estimate was successful in phase unwrapping with a high degree of accuracy and that introducing prior information into the MPM estimate also made it possible to extend the phase under the constraint of the surface-consistency conditions with a high degree of accuracy. We also found that the MPM estimate could be used to reconstruct the original wave-fronts more smoothly, if we appropriately tuned hyper-parameters corresponding to temperature to utilize fluctuations around the MAP solution. Also, from the viewpoint of statistical mechanics of the Q-Ising model, we found that the MPM estimate was regarded as a method for searching the ground state by utilizing thermal fluctuations under the constraint of the surface-consistency condition.