Physics – Condensed Matter – Statistical Mechanics
Scientific paper
2004-03-11
Physica A 341, 586 (2004)
Physics
Condensed Matter
Statistical Mechanics
17 pages, 7 figures, RevTeX
Scientific paper
10.1016/j.physa.2004.05.047
The problem to express a natural number N as a product of natural numbers without regard to order corresponds to a thermally isolated non-interacting Bose gas in a one-dimensional potential with logarithmic energy eigenvalues. This correspondence is used for characterising the probability distribution which governs the number of factors in a randomly selected factorisation of an asymptotically large N. Asymptotic upper bounds on both the skewness and the excess of this distribution, and on the total number of factorisations, are conjectured. The asymptotic formulas are checked against exact numerical data obtained with the help of recursion relations. It is also demonstrated that for large numbers which are the product of different primes the probability distribution approaches a Gaussian, while identical prime factors give rise to non-Gaussian statistics.
Holthaus Martin
Page Steffen
Weiss Christoph
No associations
LandOfFree
Factorising numbers with a Bose-Einstein condensate does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with Factorising numbers with a Bose-Einstein condensate, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Factorising numbers with a Bose-Einstein condensate will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-452126