Condensed Matter & Many-Body Physics

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Abstractions about collective quantum behavior in materials, spanning superconductivity and pairing phenomena (BCS theory, Josephson effect, topological superconductor), periodic-lattice and band-structure models (particle in a one-dimensional lattice, Zak phase, plane wave expansion method), and correlated many-body methods (dynamical mean-field theory, Hartree-Fock method, Frenkel-Kontorova model).

16 abstractions in this family — domain-specific abstractions that sit near one another in structural-signature space (k-means over structural-signature embeddings). Each is shown with its short description.

• BCS theory — Model conventional superconductivity microscopically by an effective attraction that pairs fermions near the Fermi surface into a phase-coherent many-body state with a self-consistent excitation gap, while separating the original weak-coupling isotropic theory from justified extensions.
• Cophonicity — A vibrational-overlap metric measuring how strongly two atomic species contribute together within a selected frequency range.
• Dynamical mean-field theory — A nonperturbative many-body method that maps a correlated lattice model to a self-consistent quantum impurity problem with a frequency-dependent bath.
• Frenkel–Kontorova model — A model of elastically coupled particles in a periodic substrate potential that captures competition between a preferred spacing and an imposed lattice.
• Hartree–Fock method — A self-consistent mean-field approximation representing a many-fermion stationary state by one Slater determinant.
• Josephson effect — Quantum current and phase phenomena across a weak link between superconductors, including zero-voltage supercurrent and voltage-driven oscillation.
• Kitaev chain — A spinless one-dimensional lattice Hamiltonian with hopping and p-wave pairing that models Majorana end modes in its gapped topological regime.
• Particle in a one-dimensional lattice — The quantum model of a particle moving in a spatially periodic one-dimensional potential, whose stationary states have Bloch form and organize into energy bands separated by gaps.
• Periodic Table of Topological Insulators and Topological Superconductors — A tenfold table mapping a gapped free-fermion system's symmetry class and spatial dimension to its possible stable topological classification group.
• Phase space crystal — A state exhibiting discrete translational or rotational order in phase space rather than ordinary real-space position.
• Plane wave expansion method — A frequency-domain eigenmethod that expands periodic material parameters and electromagnetic fields in reciprocal-lattice plane waves to compute photonic-crystal band structures.
• Rule 184 — A synchronous binary cellular-automaton rule whose local update moves each unblocked occupied site one step right while conserving occupancy on a ring.
• Second sound — Wave-like propagation of temperature or entropy disturbances in a material where heat transport becomes hydrodynamic rather than diffusive.
• Superradiant phase transition — A collective quantum phase transition from a weakly excited state to one with macroscopic coherent occupation of a radiation mode and correlated emitter polarization.
• Topological superconductor — A superconducting phase with a nontrivial bulk topological invariant and protected boundary or defect excitations.
• Zak phase — The Berry phase accumulated by a Bloch band along a closed noncontractible loop through the Brillouin zone.