scholarly journals Non-existence of Bose–Einstein condensation in Bose–Hubbard model in dimensions 1 and 2

2020 ◽  
Vol 61 (11) ◽  
pp. 113303
Author(s):  
Piotr Stachura ◽  
Wiesław Pusz ◽  
Jacek Wojtkiewicz
Keyword(s):  
Hubbard Model ◽  
Einstein Condensation ◽  
Bose Einstein Condensation ◽  
Bose Einstein

scholarly journals Bose–Einstein Condensation Processes with Nontrivial Geometric Multiplicities Realized via 𝒫𝒯−Symmetric and Exactly Solvable Linear-Bose–Hubbard Building Blocks

2021 ◽  
Vol 3 (3) ◽  
pp. 517-533
Author(s):  
Miloslav Znojil
Keyword(s):  
Hubbard Model ◽  
Building Blocks ◽  
Exceptional Point ◽  
Einstein Condensation ◽  
Real Spectrum ◽  
Geometric Multiplicity ◽  
Bose Einstein Condensation ◽  
Exactly Solvable ◽  
Linear Version ◽  
Bose Einstein

It is well known that, using the conventional non-Hermitian but PT−symmetric Bose–Hubbard Hamiltonian with real spectrum, one can realize the Bose–Einstein condensation (BEC) process in an exceptional-point limit of order N. Such an exactly solvable simulation of the BEC-type phase transition is, unfortunately, incomplete because the standard version of the model only offers an extreme form of the limit, characterized by a minimal geometric multiplicity K = 1. In our paper, we describe a rescaled and partitioned direct-sum modification of the linear version of the Bose–Hubbard model, which remains exactly solvable while admitting any value of K≥1. It offers a complete menu of benchmark models numbered by a specific combinatorial scheme. In this manner, an exhaustive classification of the general BEC patterns with any geometric multiplicity is obtained and realized in terms of an exactly solvable generalized Bose–Hubbard model.

scholarly journals TOWARDS BOSE–EINSTEIN CONDENSATION OF ELECTRON PAIRS: ROLE OF SCHWINGER BOSONS

1999 ◽  
Vol 13 (08) ◽  
pp. 925-937 ◽  
Author(s):  
GANG SU ◽  
MASUO SUZUKI
Keyword(s):  
Hilbert Space ◽  
Hubbard Model ◽  
Strong Coupling ◽  
Einstein Condensation ◽  
Electron Pairs ◽  
Bose Einstein Condensation ◽  
Attractive Hubbard Model ◽  
Hilbert Subspace ◽  
Bose Einstein

It can be shown that the bosonic degree of freedom of the tightly bound on-site electron pairs could be separated as Schwinger bosons. This is implemented by projecting the whole Hilbert space into the Hilbert subspace spanned by states of two kinds of Schwinger bosons (to be called binon and vacanon) subject to a constraint that these two kinds of bosonic quasiparticles cannot occupy the same site. We argue that a binon is actually a kind of quantum fluctuations of electron pairs, and a vacanon corresponds to a vacant state. These two bosonic quasiparticles may be responsible for the Bose–Einstein condensation (BEC) of the system associated with electron pairs. These concepts are also applied to the attractive Hubbard model with strong coupling, showing that it is quite useful. The relevance of the present arguments to the existing theories associated with the BEC of electron pairs is briefly commented.

Systems with Condensates and Pairing

2018 ◽  
Author(s):  
Klaus Morawetz
Keyword(s):  
Critical Parameters ◽  
Einstein Condensation ◽  
Cooper Pairs ◽  
Pair Breaking ◽  
Systematic Theory ◽  
Bose Einstein Condensation ◽  
T Matrix ◽  
The Stability ◽  
Bose Einstein

The Bose–Einstein condensation and appearance of superfluidity and superconductivity are introduced from basic phenomena. A systematic theory based on the asymmetric expansion of chapter 11 is shown to correct the T-matrix from unphysical multiple-scattering events. The resulting generalised Soven scheme provides the Beliaev equations for Boson’s and the Nambu–Gorkov equations for fermions without the usage of anomalous and non-conserving propagators. This systematic theory allows calculating the fluctuations above and below the critical parameters. Gap equations and Bogoliubov–DeGennes equations are derived from this theory. Interacting Bose systems with finite temperatures are discussed with successively better approximations ranging from Bogoliubov and Popov up to corrected T-matrices. For superconductivity, the asymmetric theory leading to the corrected T-matrix allows for establishing the stability of the condensate and decides correctly about the pair-breaking mechanisms in contrast to conventional approaches. The relation between the correlated density from nonlocal kinetic theory and the density of Cooper pairs is shown.

scholarly journals Bose Einstein condensation in a magnetic double-well potential

2003 ◽  
Vol 5 (2) ◽  
pp. S119-S123 ◽  
Author(s):  
T G Tiecke ◽  
M Kemmann ◽  
Ch Buggle ◽  
I Shvarchuck ◽  
W von Klitzing ◽  
...  
Keyword(s):  
Einstein Condensation ◽  
Bose Einstein Condensation ◽  
Bose Einstein ◽  
Double Well Potential
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