In condensed matter physics, it is easy to get lost in the details of one’s day-to-day work. It is important to sometimes take the time to reflect upon what you’ve done and learned and think about what it all means. In this spirit, below is a list of some of the most important ideas related to condensed matter physics that I picked up during my time as an undergraduate and graduate student. This is of course personal, and I hope that in time I will add to the list.
- Relationship between measurements and correlation functions
- Relationship between equilibrium fluctuations and non-equilibrium dissipative channels (i.e. the fluctuation-dissipation theorem)
- Principle of entropy maximization/free-energy minimization for matter in equilibrium
- Concept of the quasi-particle and screening
- Concept of Berry phase and the corresponding topological and geometrical consequences
- Broken symmetry, the Landau paradigm of phase classification and the idea of an order parameter
- Sum rules and the corresponding constraints placed on both microscopic theories and experimental spectra
- Bose-Einstein and Cooper Pair condensation and their spectacular properties
- Logical independence of physical theories on the theory of everything
- Effects of long-range vs. short-range interactions on macroscopic properties of solids
- Role of dimensionality in observing qualitatively different physical properties and phases of matter
The first two items on the list are well-explained in Forster’s Hydrodynamics, Fluctuations, Broken Symmetry and Correlation Functions without the use of Green’s functions and other advanced theoretical techniques. Although not yet a condensed matter phenomenon, Bell’s theorem and non-locality rank among the most startling consequences of quantum mechanics that I learned in graduate school. I suspect that its influence will be observed in a condensed matter setting in due time.
Please feel free to share your own ideas or concepts you would add to the list.