Markov random fields (M.R.F.) on a lattice system and Gibbs distribution provide a wide area of models for interacting particle systems in image analysis, mechanical physics and statistical mechanics. Physical properties of the neighbors could be explained by partial differential equation (PDE) inside the potential function introducing PDE-MRF models. In image analysis, they have been used to d...

The relativistic mean-field theory provides a framework in which the nuclear many-body problem is described as a self-consistent system of nucleons and mesons. In the mean-field approximation, the self-consistent time evolution of the nuclear system describes the dynamics of collective motion: nuclear compressibility from monopole resonances, regular and chaotic dynamics of isoscalar and isovec...

Recently, variational approximations such as the mean field approximation have received much interest. We extend the standard mean field method by using an approximating dis­ tribution that factorises into cluster poten­ tials. This includes undirected graphs, di­ rected acyclic graphs and junction trees. We derive generalised mean field equations to op­ timise the cluster potentials. We show t...

The exceptional properties of strongly correlated electron systems have fascinated physicists for several decades already [1–9]. New correlated electron materials and unexpected correlation phenomena are discovered every year. Often the properties of those systems are influenced by disorder. Unfortunately, real materials and even model systems with strong electronic correlations and disorder ar...

This paper discusses the dynamical properties of p-spin models with Kac kind interactions. For large but finite interaction range R one finds two different time scales for relaxation. A first relaxation roughly independent of R where the system is confined to limited regions of the configuration space and an R dependent time scale where the system is able to escape the confining regions. I will...

The time evolution of a closed system of mean fields and fluctuations is Hamiltonian, with the canonical variables parameterizing the general time-dependent Gaussian density matrix of the system. Yet, the evolution manifests both quantum decoherence and apparent irreversibility of energy flow from the coherent mean fields to fluctuating quantum modes. Using scalar QED as an example we show how ...

We propose an image segmentation algorithm under an expectation-maximum scheme using a Bethe approximation. In the stochastic image processing, the image data is usually modeled in terms of Markov random fields, which can be characterized by a Gibbs distribution. The Bethe approximation, which takes account of nearest-neighbor correlations, provides us with a better approximation to the Gibbs f...