Bose–Einstein condensation of quasiparticles

Bose–Einstein condensation can occur in quasiparticles, particles that are effective descriptions of collective excitations in materials. Some have integer spins and can be expected to obey Bose–Einstein statistics like traditional particles. Conditions for condensation of various quasiparticles have been predicted and observed. The topic continues to be an active field of study.

BECs form when low temperatures cause nearly all particles to occupy the lowest quantum state. Condensation of quasiparticles occurs in ultracold gases and materials. The lower masses of material quasiparticles relative to atoms lead to higher BEC temperatures. An ideal Bose gas has a phase transitions when inter-particle spacing approaches the thermal De-Broglie wavelength: ${\displaystyle k_{B}T=~\hbar ^{2}n^{2/3}/M}$. The critical concentration is then ${\displaystyle N\propto (T/2\pi )^{3}u^{1/2}P/v\hbar ^{3}}$, leading to a critical temperature: ${\displaystyle T_{c}<32\pi ^{3}\hbar ^{6}V^{2}u_{0}P^{2}}$. The particles obey the Bose–Einstein distribution and all occupy the ground state:

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