Methods of Statistical Physics by A. I. Akhiezer

By A. I. Akhiezer

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3 ) w i l l be t r u e . Furthermore, i f has t h e f o r m o f a G a u s s i a n c u r v e , n o t o n l y t h e t h i r d b u t a l l

4 . 29) and, c o n s e q u e n t l y , V r e p r e s e n t s the d i f f u s i o n c o e f f i c i e n t o f the Brownian p a r t i c l e s . 25) and u s i n g ( 1 . 4 . 23) f o r f j x . v . 30) We see t h a t t h e d i s t r i b u t i o n f u n c t i o n o f Brownian p a r t i c l e s a t time t i s determined by t h e p a r t i c l e d e n s i t y a t t i m e t - l / 2 y . 29), However, according to the diffusion the q u a n t i t y n ( x , t - l / 2 y ) may be e x p r e s s e d i n t e r m s o f t h e d e n s i t y n ( x , t ) o f B r o w n i a n p a r t i c l e s and i t s s p a t i a l d e r i v a t i v e s a t time t: 00 T h e r e f o r e the d i s t r i b u t i o n f u n c t i o n f j x .

T h i s e q u a t i o n i s c a l l e d t h e Smoluchovski equation. 39) T h u s , i n t h e p r e s e n c e o f an e x t e r n a l f o r c e f i e l d t h e c u r r e n t c o n s i s t s o f two c o m p o n e n t s ; t h e d i f f u s i o n current 42 K i n e t i c E q u a t i o n s f o r C l a s s i c a l Systems PVn and the c u r r e n t caused by t h e . 3. the p a r t i c l e d i s t r i b u t i o n 1 K n . The t o t a l c u r r e n t a p p a r e n t l y is Boltzmannian. The T h e o r y o f N e u t r o n M o d e r a t i o n Another important task of p h y s i c s i n which the Fokker-Planck equation p l a y s a r o l e is neutron moderation i n m a t t e r .

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