A famous 'impossible' state of matter has just been mathematically banned from existing in crystal vibrations.
April 14, 2026
Original Paper
No-Go Theorem for Quasiparticle BEC
arXiv · 2604.10838
The Takeaway
Bose-Einstein Condensates (BECs) are usually thought to be achievable for any particle if you cool it enough. This 'no-go theorem' proves that for certain quasiparticles like phonons, the math simply won't allow them to condense, overturning long-standing assumptions in solid-state physics.
From the abstract
We discuss a no-go theorem for Bose-Einstein condensation (BEC) of quasiparticles (phonons) from the viewpoint of operator algebras, using the van Hove model. The $\beta$-KMS states of the van Hove model satisfy the self-consistency condition ofarXiv:1207.4621. However, the self-consistency condition is a constraint concerning the definition of the field, and is insufficient to establish the no-go theorem for BEC. In this paper, we prove the no-go theorem for BEC via two routes. First, imposing