On the Kirkwood-Salsburg and Mayer-Montroll equations and their solutions for many-body interactions

✍ Scribed by H. Moraal

• Publisher: Elsevier Science
• Year: 1981
• Tongue: English
• Weight: 354 KB
• Volume: 105
• Category: Article
• ISSN: 0378-4371
• DOI: 10.1016/0378-4371(81)90077-7

✦ Synopsis

The Kirkwood-Salsburg and the Mayer-Montroll equations for an arbitrary stable interaction are derived for the case of an exponentially integrable external potential (of which a finite volume is a special case). It is shown that the Mayer-Montroll equation has at least one solution (the equilibrium state) if the activity z is such that the grand canonical partition function -~(z) is nonzero; also, there is at least one eigenvector with eigenvalue 1 for z such that -~(z)= 0. The difference with the Kirkwood-Salsburg equation lies in the possibility of more solutions, as is shown by an example.