The recent success in quantum annealing, i.e., optimization of the cost or energy functions of complex systems utilizing quantum fluctuations is reviewed here. The concept is introduced in successive steps through studying the mapping of such computationally hard problems to classical spin-glass problems, quantum spin-glass problems arising with the introduction of quantum fluctuations, and the annealing behavior of the systems as these fluctuations are reduced slowly to zero. This provides a general framework for realizing analog quantum computation.

The fiber bundle model describes a collection of elastic fibers under load. The fibers fail successively and, for each failure, the load distribution among the surviving fibers changes. Even though very simple, this model captures the essentials of failure processes in a large number of materials and settings. A review of the fiber bundle model is presented with different load redistribution mechanisms from the point of view of statistics and statistical physics rather than materials science, with a focus on concepts such as criticality, universality, and fluctuations. The fiber bundle model is discussed as a tool for understanding phenomena such as creep and fatigue and how it is used to describe the behavior of fiber-reinforced composites as well as modeling, e.g., network failure, traffic jams, and earthquake dynamics.

The present status of research and understanding regarding the dynamics and the statistical properties of earthquakes is reviewed, mainly from a statistical physical viewpoint. Emphasis is put both on the physics of friction and fracture, which provides a microscopic basis for our understanding of an earthquake instability, and on the statistical physical modelling of earthquakes, which provides macroscopic aspects of such phenomena. Recent numerical results from several representative models are reviewed, with attention to both their critical and their characteristic properties. Some of the relevant notions and related issues are highlighted, including the origin of power laws often observed in statistical properties of earthquakes, apparently contrasting features of characteristic earthquakes or asperities, the nature of precursory phenomena and nucleation processes, and the origin of slow earthquakes, etc.

We propose a minimal multiagent model for the collective dynamics of opinion formation in the society by modifying kinetic exchange dynamics studied in the context of income, money, or wealth distributions in a society. This model has an intriguing spontaneous symmetry-breaking transition to polarized opinion state starting from nonpolarized opinion state. In order to analyze the model, we introduce an iterative map version of the model, which has very similar statistical characteristics. An approximate theoretical analysis of the numerical results is also given, based on the iterative map version.