scholarly journals Kramers equation for a charged Brownian particle: The exact solution

2005 ◽  
Vol 355 (2-4) ◽  
pp. 274-282 ◽  
Author(s):  
Tania P. Simões ◽  
Roberto E. Lagos
Keyword(s):  
Exact Solution ◽  
Brownian Particle ◽  
Kramers Equation

On the Convergence of Karhunen-Loeve Series Expansion for a Brownian Particle

1993 ◽  
Vol 60 (3) ◽  
pp. 783-784
Author(s):  
W. G. Paff ◽  
G. Ahmadi
Keyword(s):  
Exact Solution ◽  
Series Expansion ◽  
Particle Velocity ◽  
Langevin Equation ◽  
Brownian Particle ◽  
Equation Of Motion ◽  
Mean Square ◽  
The Mean

A linear Langevin equation for the velocity of a Brownian particle is considered. The equation of motion is solved and the Karhunen-Loeve expansion for the particle velocity is derived. The mean-square velocity as obtained by the truncated Karhunen-Loeve expansion is compared with the exact solution. It is shown, as the number of terms in the series increases, the result approaches that of the exact solution asymptotically.

Exact solution of a four-site crystal model for an intermediate-valence system

1986 ◽  
Vol 47 (6) ◽  
pp. 1029-1034 ◽  
Author(s):  
J.C. Parlebas ◽  
R.H. Victora ◽  
L.M. Falicov
Keyword(s):  
Exact Solution ◽  
Intermediate Valence ◽  
Crystal Model
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