scholarly journals Quantum corrections to the ground-state energy of a trapped Bose-Einstein condensate: A diffusion Monte Carlo calculation

2001 ◽  
Vol 63 (6) ◽  
Author(s):  
D. Blume ◽  
Chris H. Greene
Keyword(s):  
Monte Carlo ◽  
Ground State Energy ◽  
Ground State ◽  
State Energy ◽  
Monte Carlo Calculation ◽  
Einstein Condensate ◽  
Quantum Corrections ◽  
Diffusion Monte Carlo ◽  
Bose Einstein Condensate ◽  
Bose Einstein

Monte Carlo calculation of the ground-state energy of an optical polaron

1983 ◽  
Vol 28 (10) ◽  
pp. 5735-5738 ◽  
Author(s):  
W. Becker ◽  
B. Gerlach ◽  
H. Schliffke
Keyword(s):  
Monte Carlo ◽  
Ground State Energy ◽  
Ground State ◽  
State Energy ◽  
Monte Carlo Calculation

scholarly journals Dynamical collapse of cylindrical symmetric dipolar Bose–Einstein condensates

2021 ◽  
Vol 60 (6) ◽  
Author(s):  
Jacopo Bellazzini ◽  
Luigi Forcella
Keyword(s):  
Ground State ◽  
State Energy ◽  
Symmetric Functions ◽  
Riesz Transform ◽  
Einstein Condensate ◽  
Pitaevskii Equation ◽  
General Integral ◽  
Bose Einstein Condensate ◽  
Bose Einstein

AbstractWe study the formation of singularities for cylindrical symmetric solutions to the Gross–Pitaevskii equation describing a dipolar Bose–Einstein condensate. We prove that solutions arising from initial data with energy below the energy of the Ground State and that do not scatter collapse in finite time. The main tools to prove our result are the variational characterization of the Ground State energy, suitable localized virial identities for cylindrical symmetric functions, and general integral and pointwise estimates for operators involving powers of the Riesz transform.

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