Direct evaluation of statistical mechanical path integrals

✍ Scribed by Ludwig W. Bruch

• Publisher: Elsevier Science
• Year: 1973
• Tongue: English
• Weight: 200 KB
• Volume: 23
• Category: Article
• ISSN: 0009-2614
• DOI: 10.1016/0009-2614(73)89585-5

✦ Synopsis

The discrcrc srep Wiener inrejiral or Trotter Ibrmula approsimalion to the density operator of equilibrium slatisli. caL mechanics is cvnluared for the linear porcnrinl and for rhe h;lrmonic oscillator potcntral. Esplicic rcbultb show the speed of convrrpcncc 0T the opprosiimation.

'The formal espression for hermitian operators A and B: lim (e"hveE'!")nl = exp (A tE) N--

(1) can be used [I]** as the basis ofpsth integral formulations of quantum statisrical rmchanics. For Il?e equilibrium density matrix or thermodynamic Green's function the operators A and B arc chosen to be:

where /3 is (F;, T)-', Tis the absolute temperature, ku is Bolrzmann's constant, K is the kinetic energy operator p2/2p, and I/ is the potential energy. The subject of this paper is the evaluation of an object related to eq. ( 1):

(b(e+Hlo)l, 3 (bl(e-PKir;e-Pr"J~)NI,),