تقرير
Hamiltonian and exclusion statistics approach to discrete forward-moving paths
| العنوان: | Hamiltonian and exclusion statistics approach to discrete forward-moving paths |
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| المؤلفون: | Ouvry, Stéphane, Polychronakos, Alexios P. |
| المصدر: | Phys. Rev. E 104, 014143 (2021) |
| سنة النشر: | 2021 |
| المجموعة: | Mathematics Condensed Matter High Energy Physics - Theory Mathematical Physics |
| مصطلحات موضوعية: | Mathematical Physics, Condensed Matter - Statistical Mechanics, High Energy Physics - Theory, Mathematics - Combinatorics |
| الوصف: | We use a Hamiltonian (transition matrix) description of height-restricted Dyck paths on the plane in which generating functions for the paths arise as matrix elements of the propagator to evaluate the length and area generating function for paths with arbitrary starting and ending points, expressing it as a rational combination of determinants. Exploiting a connection between random walks and quantum exclusion statistics that we previously established, we express this generating function in terms of grand partition functions for exclusion particles in a finite harmonic spectrum and present an alternative, simpler form for its logarithm that makes its polynomial structure explicit. Comment: Updated and expanded version to appear in Phys Rev E |
| نوع الوثيقة: | Working Paper |
| DOI: | 10.1103/PhysRevE.104.014143 |
| URL الوصول: | http://arxiv.org/abs/2103.15827 |
| رقم الأكسشن: | edsarx.2103.15827 |
| قاعدة البيانات: | arXiv |
| DOI: | 10.1103/PhysRevE.104.014143 |
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