The three nodes of the National Institute for Theoretical Physics each have its distinct research focus. These research focuses were determined by historical factors and existing capacity.

Stellenbosch

The broad research themes at this node is many-body, condensed matter and statistical physics. Particular themes that are pursued range from highly correlated electronic systems, mesoscopic systems, aspects of non-commutative quantum mechanics and phase transitions. There is a close collaboration with the Institute of Theoretical Physics where themes in soft condensed matter, polymer physics and complex systems are also researched.

Statistical physics of phase transitions:

Cooperative effects can lead to remarkable properties of many-body systems, and the occurrence of a phase transition is a prime example of such an effect. At a phase transition, the macroscopic properties of a many-particle system change abruptly under variation of a control parameter. Typical examples of phase transitions are the evaporation of a liquid at temperatures above its boiling point, or the onset of a spontaneous magnetization in a ferromagnet below its Curie temperature. In a thermodynamic description, phase transitions are signaled by nonanalyticities of thermodynamic functions like the free energy density.

Statistical physics is the theoretical framework providing the microscopic foundations of thermodynamics, allowing to compute thermodynamic functions from the Hamiltonian H of the system under investigation. Depending on the microscopic interactions encoded in H, the thermodynamic functions turn out to be analytic in some cases, and nonanalytic in others. Since the exact calculation of thermodynamic functions from microscopic interactions is a challenging (and in most cases impossible) task, it is desirable to have general criteria on H which guarantee the presence or absence of a phase transition. Furthermore, such criteria might foster the general understanding of phase transitions and their microscopic origin.

The common theme behind our activities in this field is the use of geometrical and topological concepts. One approach focuses on the equipotential surfaces in configuration space. Remarkably, the topological properties of these surfaces are already sufficient to formulate criteria on the existence or absence of phase transitions (see here for a review). Via Morse theory, this topological approach can be linked to the study of stationary points of energy landscapes (as used extensively in the context of glassy systems, biomolecules, and clusters). In a different approach, Riemannian metrics in phase space are used in order to identify and analyze phase transitions.

Further activities in statistical physics are in the field of long-range interacting systems. For such systems, thermodynamics (and dynamics) can be quite different from that of standard short-range systems, leading to surprising phenomena like nonequivalence of statistical ensembles, negative response functions, and others.

Quantum transport and mesoscopic physics:

This branch of condensed matter physics deals with electronic systems of dimensions roughly in the few nanometer range. Examples of such systems include semi-conductor nano-devices such as quantum dots and point contacts, small metal grains, carbon nano-tubes, and carbon mono-layers. The field is driven by experimentalists' ability accurately to fabricate devices on the nanometer scale, and the availability of high precision tools that probe the distribution and flow of charge in these systems. Observed phenomena strikingly reveal the wave-nature of electrons. This includes among other things Aharonov-Bohm type interference effects, disorder induced localization, and conductance quantization in point contacts and Hall bars. While quantum mechanics rather than classical physics is required to explain these observations, the systems are not microscopic. They contain many atoms and electrons. Thus many-body correlations and interactions play a crucial role in understanding such phenomena as Coulomb blockade, the Kondo effect, and zero bias anomalies in tunneling experiments.