• Corpus ID: 119568435

Proof of phase transition in homogeneous systems of interacting bosons

@article{Suto2017ProofOP,
  title={Proof of phase transition in homogeneous systems of interacting bosons},
  author={Andras Suto},
  journal={arXiv: Mathematical Physics},
  year={2017}
}
  • A. Suto
  • Published 12 October 2017
  • Physics
  • arXiv: Mathematical Physics
Using the rigorous path integral formalism of Feynman and Kac we prove London's eighty years old conjecture that during the superfluid transition in liquid helium Bose-Einstein condensation (BEC) takes place. The result is obtained by proving first that at low enough temperatures macroscopic permutation cycles appear in the system, and then showing that this implies BEC. We find also that in the limit of zero temperature the infinite cycles cover the whole system, while BEC remains partial. For… 

References

SHOWING 1-10 OF 122 REFERENCES

Infrared bounds, phase transitions and continuous symmetry breaking

We present a new method for rigorously proving the existence of phase transitions. In particular, we prove that phase transitions occur in (φ·φ)32 quantum field theories and classical, isotropic

Thermodynamic Limit and Proof of Condensation for Trapped Bosons

We study condensation of trapped bosons in the limit when the number of particles tends to infinity. For the noninteracting gas we prove that there is no phase transition in any dimension, but in any

Long Cycles in a Perturbed Mean Field Model of a Boson Gas

In this paper we give a precise mathematical formulation of the relation between Bose condensation and long cycles and prove its validity for the perturbed mean field model of a Bose gas. We

Path integrals in the theory of condensed helium

One of Feynman`s early applications of path integrals was to superfluid {sup 4}He. He showed that the thermodynamic properties of Bose systems are exactly equivalent to those of a peculiar type of

The thermodynamic limit for an imperfect Boson gas

We give a rigorous treatment in the infinite volume limit of a model Hamiltonian representing an imperfect Boson gas. In particular we obtain the exact expression for the mean particle density in the

The λ-Phenomenon of Liquid Helium and the Bose-Einstein Degeneracy

IN a recent paper1 Fröhlich has tried to interpret the λ-phenomenon of liquid helium as an order–disorder transition between n holes and n helium atoms in a body-centred cubic lattice of 2n places.

Percolation transition in the Bose gas

The canonical partition function of a Bose gas gives rise to a probability distribution over the permutations of N particles. The author studies the probability and mean value of the cycle lengths in

Equivalence of Bose-Einstein condensation and symmetry breaking.

It is shown that, whenever Bogoliubov's approximation, that is, the replacement of a( 0) and a*(0) by complex numbers in the Hamiltonian, asymptotically yields the right pressure, it also implies the asymPTotic equality of |a(0)|(2)/V and a-0)/V in symmetry breaking fields, irrespective of the existence or absence of Bose-Einstein condensation.

Slippery Wave Functions

Superfluids and superconductors show a very surprising behavior at low temperatures. As their temperature is reduced, materials of both kinds can abruptly fall into a state in which they will support

Bose-Einstein condensation and symmetry breaking

Adding a gauge symmetry breaking field − ν √ V ( a 0 + a ∗ 0 ) to the Hamiltonian of some simplified models of an interacting Bose gas we compute the condensate density and the symmetry breaking order
...