Bose-Einstein condensation and gauge symmetry breaking

Yukalov, V. I.

doi:10.1002/lapl.200710029

Cited by 75 publications

(136 citation statements)

References 66 publications

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“…This demonstrates the natural gauge symmetry exhibited by all the physical equations of the fermionic fields. Hence, making an explicit choice for the value of the phase, in turn order parameter, corresponds to a formal breaking of the gauge symmetry which is guaranteed to be the necessary and sufficient condition [87,88] for the occurrence of BEC in bosonic fields. We will reveal its significance to their fermionic counterpart in due course, but, before that, several remarks are in order:…”

Section: Fermionic Order Parametermentioning

confidence: 99%

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Born-Kothari Condensation for Fermions

Ghosh

2017

Entropy

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Abstract:In the spirit of Bose-Einstein condensation, we present a detailed account of the statistical description of the condensation phenomena for a Fermi-Dirac gas following the works of Born and Kothari. For bosons, while the condensed phase below a certain critical temperature, permits macroscopic occupation at the lowest energy single particle state, for fermions, due to Pauli exclusion principle, the condensed phase occurs only in the form of a single occupancy dense modes at the highest energy state. In spite of these rudimentary differences, our recent findings [Ghosh and Ray, 2017] identify the foregoing phenomenon as condensation-like coherence among fermions in an analogous way to Bose-Einstein condensate which is collectively described by a coherent matter wave. To reach the above conclusion, we employ the close relationship between the statistical methods of bosonic and fermionic fields pioneered by Cahill and Glauber. In addition to our previous results, we described in this mini-review that the highest momentum (energy) for individual fermions, prerequisite for the condensation process, can be specified in terms of the natural length and energy scales of the problem. The existence of such condensed phases, which are of obvious significance in the context of elementary particles, have also been scrutinized.

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Section: Fermionic Order Parametermentioning

confidence: 99%

“…The phase factor to the state |α produces a different state altogether. This observation has a very fundamental consequence because the existence of BEC is always accompanied by spontaneous breaking of such symmetry [87,88].…”

mentioning

confidence: 99%

Born-Kothari Condensation for Fermions

Ghosh

2017

Entropy

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“…Interestingly, this category can be further divided into two subgroups as the quasi-degeneracy has two different origins: (i) The quasi-degeneracy of the quantum energy levels is caused by the large volume size of the system. The gas-solid transition mentioned above [11,12] and the Bose-Einstein condensation of ideal gas [15] are typical examples of this case. The degree of degeneracy in this subgroup is usually infinite.…”

Section: Effective Ground State and Spontaneous Symmetry Breakingmentioning

confidence: 99%

Extended two-site Bose–Hubbard model with pair tunneling: spontaneous symmetry breaking, effective ground state and fragmentation

Zhu

Zhang

2015

J. Phys. B: At. Mol. Opt. Phys.

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The extended Bose-Hubbard model for a double-well potential with pair tunneling is studied through both exact diagonalization and mean field theory (MFT). When pair tunneling is strong enough, the ground state wavefunction predicted by the MFT is complex and doubly degenerate while the quantum ground state wavefunction is always real and unique. The time reversal symmetry is spontaneously broken when the system transfers from the quantum ground state into one of the mean field ground states upon a small perturbation. As the gap between the lowest two levels decreases exponentially with particle number, the required perturbation inducing the spontaneous symmetry breaking (SSB) is infinitesimal for particle number of typical cold atom systems. The quantum ground state is further analyzed with the Penrose-Onsager criterion, and is found to be a fragmented condensate. The state also develops the pair correlation and has non-vanishing pair order parameter instead of the conventional single particle order parameter. When this model is generalized to optical lattice, a pair superfluid can be generated. The mean field ground state can be regarded as effective ground state in this simple model. The detailed computation for this model enables us to offer an in-depth discussion of the relation between SSB and effective ground state, giving a glimpse on how nonlinearity arises in the SSB of a quantum system.

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“…Many works contain the statement that, though symmetry breaking helps describing BEC's, the latter, in principle, does not require any symmetry breaking. This is, however, not correct: spontaneous breaking of symmetry is a necessary and sufficient condition for Bose-Einstein condensation [3][4][5].…”

Section: Introductionmentioning

confidence: 99%

Bose–Einstein condensation and symmetry breaking of a complex charged scalar field

Matos¹,

Castellanos²,

Suárez³

2017

Eur. Phys. J. C

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In this work the Klein-Gordon equation for a complex scalar field with U (1) symmetry endowed in a mexican-hat scalar field potential with thermal and electromagnetic contributions is written as a Gross-Pitaevskii (GP)-like equation. This equation is interpreted as a charged generalization of the GP equation at finite temperatures found in previous works. Its hydrodynamical representation is obtained and the corresponding thermodynamical properties are derived and related to measurable quantities. The condensation temperature in the non-relativistic regime associated with the aforementioned system within the semiclassical approximation is calculated. Also, a generalized equation for the conservation of energy for a charged bosonic gas is found when electromagnetic fields are introduced, and it is studied how under certain circumstances its breaking of symmetry can give some insight on the phase transition of the system not just into the condensed phase but also on other related systems

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Bose-Einstein condensation and gauge symmetry breaking

Cited by 75 publications

References 66 publications

Born-Kothari Condensation for Fermions

Born-Kothari Condensation for Fermions

Extended two-site Bose–Hubbard model with pair tunneling: spontaneous symmetry breaking, effective ground state and fragmentation

Bose–Einstein condensation and symmetry breaking of a complex charged scalar field

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