Notes (PDFs)
Lecture-style notes I’ve written on topics in statistical mechanics, soft matter, and condensed matter — posted here for anyone who finds them useful.
A growing collection of notes I have written for myself while learning or teaching topics in statistical mechanics, soft matter, and condensed matter. They are not polished papers — closer to working derivations and explanations I wish I had had when first learning the material. Corrections and comments welcome at gjayasingh@ucsd.edu.
stat-mech soft matter condensed matter lecture notes
Notes
- Mean-field treatment of continuous and first-order transitions, order parameters, symmetry breaking, and the failure of Landau theory near criticality.
- Notes on SSB across statistical mechanics and field theory: Goldstone modes, order parameters, and the role of dimensionality.
- Phase separation in conserved order-parameter systems: derivation of the Cahn–Hilliard equation, linear instability, coarsening, and scaling.
- Classification of defects in ordered media via homotopy theory, with examples from nematics, superfluids, and XY models.
- Periodically driven quantum systems, effective Hamiltonians, and Floquet engineering of band structure.
- Slide deck: dimensional reduction and low-rank structure in complex networks and ecosystems.
- Compact reference of identities and results I reach for often.
If you spot a mistake or want a topic added, let me know. More notes will appear here over time.