In our group, a wide range of topics are studied with keywords of nonlinearity,
nonequilibrium, fluctuation, topology, complexity, information,
statistical analysis, and estimation. Below, the research topics by Shinichi Sasa,
Sigeru Shinomoto, Michikazu Kobayashi, and Hiroki Ohta are described.
Toward understanding order
(Shinichi Sasa)
The basic motivation of research is to fill in the gap between simple fundamental
law behind natural phenomena and phenomena at hand. With keeping the ultimate goal
of understanding the appearance of life and cognition as a natural phenomenon from
the standpoint of the physical law, we discuss the relationship between the
macroscopic laws of phenomena such as flow and the microscopic dynamics law
molecules and propose new phenomena. We also explore the possibility of actually
creating a system that is difficult to construct, and we study biological
functions based on physics.
 
Collective dynamics of manybody systems
The aim of my works is to find out mathematical expression for understanding how
interacting many elements lead to emergent collective behaviors in various
conditions. The core of my works include disordered systems or contact processes on
random graphs with emphasis on phase transitions, percolation, or bifurcation. A
challenging direction, for me, branched from such a motivation is mathematical
modeling of cell biology, which provide new insights to biological experiment.

Soft Matters
Soft matters are systems with mesoscopic internal structures such as polymers, colloids, glasses and liquid crystals, which we see and use in our daily life. Since the interaction mechanisms in soft matters are rich in variety and their characteristic energy scales are usually comparable with thermal fluctuation, they show a variety of nonequilibrium and nonlinear behaviors, and phase transitions. The aims of our study are to develop numerical and theoretical schemes for soft matters, focusing on their dynamically hierarchical structures. Recent topics are mixtures of different types of soft matters and topological defects in liquid crystals.


Quantum dynamics
Theoretical approaches combining statistical physics and quantum chemistry are developed to elucidate the interplay between macroscopic phase transitions, mesoscopic atomic clustering, and microscopic dynamics of electrons and ions in matter.
(1) Quantum kinetic theory based on the densitymatrix formalism with applications to ultrafast lightmatter interaction, electronic transport, intense xray phenomena, etc.
(2) Thermodynamics and elementary processes in materials over a wide range of temperatures and densities from cold solids to hot fluid metals and dense stellar plasmas.

Lattice Thermal Conduction
Thermal properties of equilibrium solids such as specific heat are well explained using systems of particles connected by linear springs as in Debye theory. In nonequilibrium systems, however, this model fails to explain Fourier heat law that heat current is proportional to the temperature gradient. It is because no phonon scattering occurs in the linear model. Nonlinear terms ignored in equilibrium theory become important in nonequilibrium systems. We have investigated various properties caused by the nonlinear terms and nonequilibrium boundary conditions. One example is the deformation of momentum distribution in heat conduction states. Moreover, we have also discussed heat conduction in quantum systems where spin degrees of freedom carry heat.
 
Cellular Automata with Conserved Quantities
Cellular automata (CAs) are fully discrete dynamical systems where dynamical variables on a lattice evolve their discrete values in discrete time steps. They are widely used to simulate various physical phenomena because they are well suited for computer treatment. We have investigated basic issues such as existence or nonexistence of conservation laws in CAs and statistical and dynamical properties of such conserved quantities. As the result, we have clarified that heat conduction can be argued in reversible CAs with conserved quantities. Moreover, nonreversible CAs with conserved quantities share transport properties with dissipative particle systems like granular systems and traffic flows.

Fracture Toughness in Composite Systems
Fracture of solids is an extremely nonequilibrium phenomenon that is not only technologically important but also physically interesting. It is modeled by a network of fuses or springs that are broken when current or force over a threshold value is exerted. We have investigated how fracture toughness changes if the spring constants or the resistances have randomness. Our results show that, although counterintuitive, composite systems can be tougher than uniform systems.
 