Exact Partition Functions for the Primitive Droplet Nucleation Model in 2 and 3 Dimensions

نویسنده

  • H. A. Kastrup
چکیده

The grand canonical partition functions for primitive droplet nucleation models with an excess energy ǫ n = −ˆµ n + σ n 1−η , η = 1/d, for droplets of n constituents in d dimensions are calculated exactly in closed form in the cases d = 2 and 3 for all (complex) ˆ µ by exploiting the fact that the partition functions obey simple linear PDE.

برای دانلود رایگان متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

منابع مشابه

Canonical Quantum Statistics of Schwarzschild Black Holes and Ising Droplet Nucleation

Recently it was shown[1] that the imaginary part of the canonical partition function of Schwarzschild black holes with an energy spectrum En = σ √ nEP , n = 1, 2, . . . , has properties which naively interpreted leads to the expected unusual thermodynamical properties of such black holes (Hawking temperature, Bekenstein-Hawking entropy etc.). The present paper interprets the same imaginary part...

متن کامل

Schwarzschild Black Hole Quantum Statistics, Droplet Nucleation and DLCQ Matrix Theory

Generalizing previous quantum gravity results for Schwarzschild black holes from 4 to D ≥ 4 spacetime dimensions yields an energy spectrum En = n 1−1/(D−2) σ EP,D , n = 1, 2, . . . , σ = O(1) . Assuming the degeneracies dn of these levels to be given by dn = g , g > 1, leads to a partition function which is the same as that of the primitive droplet nucleation model for 1st-order phase transitio...

متن کامل

Schwarzschild Black Hole Quantum Statistics from Z(2) Orientation Degrees of Freedom and its Relations to Ising Droplet Nucleation

Generalizing previous quantum gravity results for Schwarzschild black holes from 4 to D ≥ 4 space-time dimensions yields an energy spectrum En = αn (D−3)/(D−2) EP,D , n = 1, 2, . . . , α = O(1) , where EP,D is the Planck energy in that space-time. This energy spectrum means that the quantized area AD−2(n) of the D−2 dimensional horizon has universally the form AD−2 = n aD−2, where aD−2 is essen...

متن کامل

Homogeneous nucleation of droplets from a supersaturated vapor phase

An approximate semianalytic theory is developed to describe the homogeneous nucleation of droplets from a supersaturated vapor, beginning with a partition function and including rigorously the translation and surface tension contributions. The liquid and vapor phases are treated as uniform ~step density profile! and may be described by any accurate equation of state. It is shown that the classi...

متن کامل

Monte Carlo Approach to M-Theory

We discuss supersymmetric Yang-Mills theory dimensionally reduced to zero dimensions and evaluate the SU(2) and SU(3) partition functions by Monte Carlo methods. The exactly known SU(2) results are reproduced to very high precision. Our calculations for SU(3) agree closely with an extension of a conjecture due to Green and Gutperle concerning the exact value of the SU(N) partition functions. ∗k...

متن کامل

ذخیره در منابع من


  با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید

عنوان ژورنال:

دوره   شماره 

صفحات  -

تاریخ انتشار 1998