Lecture Desciption
In the first part of the lecture, the principles of statistical physics developed in Statistical Thermodynamics I—in particular the calculation of the various partition functions and the thermodynamic quantities derived from them—are applied to quantum gases, namely the ideal Bose gas and the ideal Fermi gas. In contrast to the semiclassical description used in Statistical Thermodynamics I, the full quantum nature of the particles is taken into account here. This leads to genuinely quantum effects with no classical analogue, such as Bose–Einstein condensation. The theory of quantum gases has a wide range of applications, from the description of superfluidity to the modeling of neutron stars.
The second part of the lecture is devoted to the study of phase transitions and so-called critical phenomena. Phase transitions are part of everyday experience and constitute a highly interesting and practically relevant area of physics. Various theoretical models exhibiting phase transitions are discussed. The phenomenon of universality allows us to study the theoretically simplest model within a given universality class. The standard example considered is the ferromagnet, in particular the spin-1/2 Ising model. In low dimensions, this model is simple enough to allow for exact solutions. We examine both the direct calculation of the partition function of the one-dimensional Ising model and its solution using the more generally applicable transfer matrix method. In addition, approximate approaches such as mean-field theory and Landau theory are discussed. Finally, the basic ideas of renormalization group theory, one of the central concepts of modern theoretical physics, are introduced.
