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.

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