scholarly journals Ground state energy of a dilute two-dimensional Bose gas from the Bogoliubov free energy functional

2019 ◽  
Vol 60 (7) ◽  
pp. 071903 ◽  
Author(s):  
Søren Fournais ◽  
Marcin Napiórkowski ◽  
Robin Reuvers ◽  
Jan Philip Solovej
Keyword(s):  
Free Energy ◽  
Ground State Energy ◽  
Ground State ◽  
State Energy ◽  
Energy Functional ◽  
Bose Gas ◽  
Two Dimensional ◽  
Free Energy Functional

scholarly journals TWO-DIMENSIONAL BOSE GAS AT LOW DENSITY

1993 ◽  
Vol 07 (15) ◽  
pp. 1029-1038 ◽  
Author(s):  
A.A. OVCHINNIKOV
Keyword(s):  
Ground State Energy ◽  
Ground State ◽  
State Energy ◽  
Scattering Length ◽  
Three Dimensional ◽  
Bose Gas ◽  
Dimensional System ◽  
Two Dimensional ◽  
Zero Temperature ◽  
Three Dimensional System

We propose a new method to describe the interacting bose gas at zero temperature. For three-dimensional system, the correction to the ground state energy in density is reproduced. For the two-dimensional dilute bose gas, the ground state energy in the leading order in the parameter | ln α2ρ|−1, where α is a two-dimensional scattering length, is obtained.

scholarly journals On the Kirchhoff-Love Hypothesis (Revised and Vindicated)

2021 ◽  
Author(s):  
Olivier Ozenda ◽  
Epifanio G. Virga
Keyword(s):  
Free Energy ◽  
Dimension Reduction ◽  
Three Dimensional ◽  
Energy Functional ◽  
The Other ◽  
Variational Model ◽  
Two Dimensional ◽  
Elastic Plates ◽  
Kinematic Constraint ◽  
Free Energy Functional

AbstractThe Kirchhoff-Love hypothesis expresses a kinematic constraint that is assumed to be valid for the deformations of a three-dimensional body when one of its dimensions is much smaller than the other two, as is the case for plates. This hypothesis has a long history checkered with the vicissitudes of life: even its paternity has been questioned, and recent rigorous dimension-reduction tools (based on standard $\varGamma $ Γ -convergence) have proven to be incompatible with it. We find that an appropriately revised version of the Kirchhoff-Love hypothesis is a valuable means to derive a two-dimensional variational model for elastic plates from a three-dimensional nonlinear free-energy functional. The bending energies thus obtained for a number of materials also show to contain measures of stretching of the plate’s mid surface (alongside the expected measures of bending). The incompatibility with standard $\varGamma $ Γ -convergence also appears to be removed in the cases where contact with that method and ours can be made.

scholarly journals The Second-Order Correction to the Ground State Energy of the Dilute Bose Gas

2020 ◽  
Vol 21 (2) ◽  
pp. 571-626 ◽  
Author(s):  
Birger Brietzke ◽  
Jan Philip Solovej
Keyword(s):  
Ground State Energy ◽  
Ground State ◽  
State Energy ◽  
Bose Gas ◽  
Second Order ◽  
Order Correction ◽  
Dilute Bose Gas

The ground state energy and entropy of the two-dimensional t–J model

2002 ◽  
Vol 63 (6-8) ◽  
pp. 1419-1422
Author(s):  
Takashi Koretsune ◽  
Masao Ogata
Keyword(s):  
Ground State Energy ◽  
Ground State ◽  
State Energy ◽  
Two Dimensional
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