A quest for perspectives: selected works of S. by S. Chandrasekhar, Kameshwar C. Wali

By S. Chandrasekhar, Kameshwar C. Wali

This worthy paintings offers chosen papers of S. Chandrasekhar, co-winner of the Nobel Prize for Physics in 1983 and a systematic enormous popular for his prolific and enormous contributions to astrophysics, physics and utilized arithmetic. The reader will locate the following so much of Chandrasekhar's articles that ended in significant advancements in a variety of components of physics and astrophysics. There also are articles of a well-liked and old nature, in addition to a few hitherto unpublished fabric in line with Chandrasekhar's talks at meetings. each one component of the e-book includes annotations through the editor.

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9 On Physique statistique des fluides classiques 20 Janvier 2006 Cl. A. 2. 17) dont chacune d’entre elles d´emarre comme suit : 1 φn (t) = 1 − σn2 t2 + . . 18) PN apparaˆıt alors sous la forme d’une int´egrale de Fourier : PN (X) = 1 2π N dt e−itX φn (t) = n=1 N 1 2π dt e−itX n=1 1 1 − σn2 t2 + . . 2 . 19) En d´eveloppant le produit et en n’´ecrivant que les termes en t2 au plus, il vient11 : PN (X) = 1 2π dt e−itX 1 − t2 2 N σn2 + O(t3 ) . 20) n=1 Il s’agit maintenant de trouver√la forme asymptotique de PN quand N 1.

A. 1. REPONSE D’UN SYSTEME A 39 Il s’agit maintenant de trouver la valeur moyenne d’une certaine grandeur A, A , en pr´esence du champ : A e−βH . 4), W = −FC. Comme la perturbation W est suppos´ee petite, on fait un d´eveloppement en puissances de W : e−βH ≡ e−β(H0 +W ) = e−βH0 (1 − βW + . ) . 9) e−βH0 . En ne gardant que les termes en O(W ) : W 0) = A 0 0 0 + βF ( AC 0 − A 0 C 0) . 11) ou encore : δ A ≡ A − A 0 = −β( AW 0 − A 0 W 0 ) = βF ( AC 0 − A 0 Dans ces ´equations, l’indice 0 rappelle que la moyenne est prise avec H0 , qui d´efinit l’´etat d’´equilibre en l’absence de champ perturbateur.

52) ` nouveau, l’int´egrand est une fonction d’autocorr´elation. 39) : P (N ) = P ( N ) e−(N− N )2 /[2kB T (∂ N /∂µ)V,T ] . 53) On peut multiplier les exemples montrant la relation directe qui existe entre stabilit´e et positivit´e des fluctuations. Ainsi, consid´erant un syst`eme isotherme – isobare (dont le potentiel est G) et pour lequel le volume V est une grandeur interne, les fluctuations de volume, ∆V 2 , sont donn´ees par : ∆V 2 = (kB T )2 ∂ 2 ln Y ∂P 2 ≡ −kB T T ,N ∂2G ∂P 2 . 50), il vient finalement (voir ausssi [2] p.

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