scholarly journals On the Poisson Structure of the Time-Dependent Mean-Field Equations For Systems of Bosons out of Equilibrium

1998 ◽  
Vol 264 (1) ◽  
pp. 1-12 ◽  
Author(s):  
Mohamed Benarous
Keyword(s):  
Poisson Structure ◽  
Mean Field ◽  
Time Dependent ◽  
Field Equations ◽  
Mean Field Equations

scholarly journals Derivation of the time dependent Gross–Pitaevskii equation with external fields

2015 ◽  
Vol 27 (01) ◽  
pp. 1550003 ◽  
Author(s):  
Peter Pickl
Keyword(s):  
Mean Field ◽  
Hartree Equation ◽  
Time Dependent ◽  
Pitaevskii Equation ◽  
External Fields ◽  
Interacting Particles ◽  
Field Equations ◽  
Positivity Condition ◽  
Mean Field Equations ◽  
Singular Interactions

Using a new method [19], it is possible to derive mean field equations from the microscopic N body Schrödinger evolution of interacting particles without using BBGKY hierarchies. This method also allows for error estimates and can be generalized to systems with external fields, of which both points are relevant from a physics perspective. Recently, this method was used to derive the Hartree equation for singular interactions [11] and the Gross–Pitaevskii equation without positivity condition on the interaction [17] where one had to restrict the scaling behavior of the interaction. Assuming positivity of the interaction, this paper deals with more general scalings including the so-called Gross–Pitaevskii scaling.

Precipitation in small systems—II. Mean field equations more effective than population balance

1996 ◽  
Vol 51 (19) ◽  
pp. 4423-4436 ◽  
Author(s):  
S. Manjunath ◽  
K.S. Gandhi ◽  
R. Kumar ◽  
Doraiswami Ramkrishna
Keyword(s):  
Mean Field ◽  
Population Balance ◽  
Field Equations ◽  
Small Systems ◽  
Mean Field Equations

Solution of the mean field equations for spontaneous fission

1987 ◽  
Vol 35 (3) ◽  
pp. 1007-1027 ◽  
Author(s):  
G. Puddu ◽  
J. W. Negele
Keyword(s):  
Spontaneous Fission ◽  
Mean Field ◽  
Field Equations ◽  
Mean Field Equations ◽  
The Mean
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