Estimating the work in integer partitioning

Andreas, April K.; Beichl, Isabel

doi:10.1109/mcise.2003.1166552

Cited by 1 publication

(1 citation statement)

References 7 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…It was then shown that this probability distribution does not become Gaussian, and it adopts its limiting distribution shape if n > 10 10 , which itself is a remarkable fact. Here we only mention that the same combinatorial problem arises in many different branches of mathematical physics, such as lattice animals in statistical physics (Lima and de Menezes, 2001;Wu et al, 1996), numerical analysis on combinatorial optimisation (Andreas and Beichl, 2003;Bauke et al, 2003;Majumdar and Krapivsky, 2002;Mertens, 1998) and also in the description of the low-energy excitations of a one dimensional fermion-system as bosonic degrees of freedom (bosonisation) (Schönhammer and Meden, 1996).…”

Section: E Statistical Physicsmentioning

confidence: 99%

Colloquium: Physics of the Riemann hypothesis

2011

View full text Add to dashboard Cite

Physicists become acquainted with special functions early in their studies. Consider our perennial model, the harmonic oscillator, for which we need Hermite functions, or the Laguerre functions in quantum mechanics. Here we choose a particular number theoretical function, the Riemann zeta function and examine its influence in the realm of physics and also how physics may be suggestive for the resolution of one of mathematics' most famous unconfirmed conjectures, the Riemann Hypothesis. Does physics hold an essential key to the solution for this more than hundred-year-old problem? In this work we examine numerous models from different branches of physics, from classical mechanics to statistical physics, where this function plays an integral role. We also see how this function is related to quantum chaos and how its pole-structure encodes when particles can undergo Bose-Einstein condensation at low temperature. Throughout these examinations we highlight how physics can perhaps shed light on the Riemann Hypothesis. Naturally, our aim could not be to be comprehensive, rather we focus on the major models and aim to give an informed starting point for the interested Reader.

show abstract