What theories in solid state should every physicist know?

In summary, every physicist should know concepts like BCS theory, Ginzburg Landau theory, the fermi liquid theory, and real meaning of "band structure".
  • #1
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[Moderator's Note: Changed level of thread to "Advanced" based on the topics being asked about, all are graduate level topics.]

I feel that I have an inadequate understanding of many important concepts in condensed matter physics, so I want to try to learn at least the most basic parts. So what concepts/theories/papers in condensed/solid state physics should every physicist know? I can think of the following

BCS theory and Ginzburg Landau theory

Landau theory of phase transitions

The fermi liquid theory

What else?
 
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  • #2
This is not a theory, but one thing I would hope physicists would learn is the real meaning of "band structure". I.e., the connection between determinant wave functions, Hartree-Fock/Kohn-Sham, and then canonical molecular orbitals and electron bands on one side (which transform according to irreps of the spatial symmetry group), and localized molecular orbitals, atomic orbitals, and Wannier functions on the other side (which do not). One should think that this lies at the very basis of solid state electronic structure theory, but in practice even theorists are sometimes confused about these topics and their connections.

There is a good introductory article by Roald Hoffmann (Solids and surfaces: a chemist's view of bonding in extended structures, pdf on net) relating these things (and other) to each other. If anyone else has a good textbook suggestion, I'd also like to hear it.
 
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  • #3
Maybe the largest conceptual difference between molecular and solid state physics lies in treating a crystal as an object of infinite extent. Only in this limit concepts like phase transitions emerge and get a precise meaning. This goes in hand with quantum field theoretical techniques becoming powerful.
In this limit, it is possible to have different ground states which live in completely different Hilbert spaces. Superconductivity is but one example.
 
  • #4
The title says 'solid state', but the post says 'condensed matter'. In that spirit, I would add:

Mean-field theory, scaling, and the renormalization group
Fluctuation-dissipation theorem
 
  • #5
Thanks for your replies. If you know any specific reading material, don't hesitate to post them :).
 

FAQ: What theories in solid state should every physicist know?

1. What is the significance of solid state physics in the field of physics?

Solid state physics is the study of the physical properties of solid materials, which are the building blocks of our everyday world. It is an essential part of physics as it helps us understand the behavior of matter at a microscopic level and has numerous applications in technology, such as in the development of new materials and devices.

2. What are the basic principles of solid state physics?

The basic principles of solid state physics include quantum mechanics, thermodynamics, and statistical mechanics. These principles are used to describe the behavior of atoms and molecules in solids and how they interact with each other to form different physical properties, such as electrical conductivity and magnetism.

3. What are the key theories in solid state physics?

Some of the key theories in solid state physics include crystal structure, band theory, and phonon theory. Crystal structure explains how atoms are arranged in a regular and repeating pattern in solids, while band theory describes the electronic properties of materials. Phonon theory explains the vibrational motion of atoms in a solid and how it affects the thermal and mechanical properties of materials.

4. What are the practical applications of solid state physics?

Solid state physics has numerous practical applications, including the development of semiconductors for electronic devices, such as computers and smartphones. It is also used in the development of new materials for energy production, such as solar cells and batteries. Other applications include the development of advanced materials for medical devices and sensors.

5. How does solid state physics contribute to our understanding of the universe?

Solid state physics plays a crucial role in our understanding of the universe as it helps us understand the behavior of matter at a fundamental level. It provides insights into the properties of materials in extreme conditions, such as in the core of stars or in the early universe. Solid state physics also helps us understand the properties of materials that are essential for the development of advanced technologies used in space exploration.

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