Phonon Spectral Density
Phonon dispersion and density of states for 1D chain and 2D square lattice — van Hove singularities
1D Chain Parameters
Spring constant k₁:
1.00
Mass m₁:
1.00
2nd neighbor coupling k₂:
0.20
ω(q) = 2√(k/m)|sin(qa/2)|
ω_max = 2√(k/m)
2D Square Lattice
Spring constant K:
1.00
Mass M:
1.00
Broadening η:
0.05
ω²(qx,qy) = (4K/M)[sin²(qxa/2)+sin²(qya/2)]
van Hove singularity at ω_max/√2