## Research overview

The general goal of this research theme is to obtain a fundamental understanding of macroscopic phenomena on the basis of microscopic many-body theories. Within the theme a division can be made into topics that are intrinsically of a quantum-mechanical nature and topics that are essentially classical. The former includes quantum-Hall effects and other topological states of matter, superconductivity and superfluidity, Bose-Einstein condensation, quantum magnetism and quantum computation. The latter not only includes soft-matter systems such as liquid crystals, colloidal dispersions, and electrolytes, but also biophysical or bio-inspired systems such as active or living matter, the mechanical properties of biological cells and stochastic population dynamics. In general, the focus is on identifying and understanding fundamental mechanisms, possibly with direct practical applications in devices with for instance energy and health applications such as supercapacitors, LED’s, solar cells, spintronic computer memory, organ-on-a-chip.

The theme thus covers a large number of research topics. It shows nevertheless a strong cohesion, because in all cases many-body system are involved of which the microscopic details are (presumed) known and the macroscopic properties are to be determined. As a result, the theme heavily builds on methods from statistical physics, for instance mean-field theory, renormalization-group theory, density functional theory, Landau theory, and the scaling theory of critical phenomena play a central role. Moreover, in many cases not only the static equilibrium properties are of interest, but also kinetics, transport, and dynamics. Determining these requires the use of nonequilibrium statistical physics and hydrodynamics. Some examples are kinetic theory, the theory of stochastic processes, and dynamic density functional theory.

As can be expected in theoretical quantum and soft condensed-matter physics, many contacts exist with experimental physics, physical chemistry, and biology. These include explanations of existing and ongoing experiments, predictions for possible new experiments, and explorations of properties of theoretical models that share essential features with experimental systems. However, direct contact with experiments can usually only be made after the theory has been tailored to the specific details of the experiment of interest. This often requires numerical means at some stage. Therefore, a variety of numerical methods are also used and developed in this research theme, including simulations (Monte Carlo, Molecular Dynamics, Lattice Boltzmann), machine learning, and sophisticated finite-element methods to solve coupled nonlinear partial differential or integral equations.