Quasiparticles in the spin-boson model do not exhibit Bose-Einstein condensation at finite temperature for moderate equilibrium states.
No-Go Theorem for Quasiparticle BEC
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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 of arXiv: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 time cluster properties on the $\beta$-KMS states precludes BEC. Second, under nonlinear dispersion with $s > 2$, the treatment of infrared divergences automatically reduces the algebra of physical observables, and BEC is mathematically excluded on the reduced algebra. In particular, the latter property admits an interpretation in terms of the ideal theory of the resolvent algebra.
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The paper is a set of notes on the van Hove model that covers cutoff removal, existence of ground and KMS states for a point source, and Bose-Einstein condensation in infinite volume, but states it contains no essentially new results.
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No-Go Theorem for Quasiparticle BEC in the Spin-Boson Model
Quasiparticles in the spin-boson model do not exhibit Bose-Einstein condensation at finite temperature for moderate equilibrium states.
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A Note on the Resolvent Algebra and Functional Integral Approach to the van Hove Model
The paper is a set of notes on the van Hove model that covers cutoff removal, existence of ground and KMS states for a point source, and Bose-Einstein condensation in infinite volume, but states it contains no essentially new results.