Momenta spacing distributions in anharmonic oscillators and the higher order finite temperature Airy kernel
| Autor: | Thomas Bothner, Mattia Cafasso, Sofia Tarricone |
|---|---|
| Přispěvatelé: | University of Bristol [Bristol], Laboratoire Angevin de Recherche en Mathématiques (LAREMA), Université d'Angers (UA)-Centre National de la Recherche Scientifique (CNRS), Concordia University [Montreal], Tarricone, Sofia |
| Jazyk: | angličtina |
| Rok vydání: | 2021 |
| Předmět: |
Statistics and Probability
Statistical Mechanics (cond-mat.stat-mech) Nonlinear Sciences - Exactly Solvable and Integrable Systems Probability (math.PR) FOS: Physical sciences Mathematical Physics (math-ph) [MATH] Mathematics [math] Nonlinear Sciences::Exactly Solvable and Integrable Systems Quantum Gases (cond-mat.quant-gas) FOS: Mathematics Primary 45J05 Secondary 30E25 42A38 35J10 81V70 Statistics Probability and Uncertainty Exactly Solvable and Integrable Systems (nlin.SI) [MATH]Mathematics [math] Condensed Matter - Quantum Gases Mathematical Physics Condensed Matter - Statistical Mechanics Mathematics - Probability |
| Zdroj: | Bothner, T, Cafasso, M & Tarricone, S 2022, ' Momenta spacing distributions in anharmonic oscillators and the higher order finite temperature Airy kernel ', Annales de l'Institut Henri Poincaré (B) Probabilités et Statistiques, vol. 58, no. 3, pp. 1505–1546 . https://doi.org/10.1214/21-AIHP1211 |
| DOI: | 10.1214/21-AIHP1211 |
| Popis: | We rigorously compute the integrable system for the limiting $(N\rightarrow\infty)$ distribution function of the extreme momentum of $N$ noninteracting fermions when confined to an anharmonic trap $V(q)=q^{2n}$ for $n\in\mathbb{Z}_{\geq 1}$ at positive temperature. More precisely, the edge momentum statistics in the harmonic trap $n=1$ are known to obey the weak asymmetric KPZ crossover law which is realized via the finite temperature Airy kernel determinant or equivalently via a Painlev\'e-II integro-differential transcendent, cf. \cite{LW,ACQ}. For general $n\geq 2$, a novel higher order finite temperature Airy kernel has recently emerged in physics literature \cite{DMS} and we show that the corresponding edge law in momentum space is now governed by a distinguished Painlev\'e-II integro-differential hierarchy. Our analysis is based on operator-valued Riemann-Hilbert techniques which produce a Lax pair for an operator-valued Painlev\'e-II ODE system that naturally encodes the aforementioned hierarchy. As byproduct, we establish a connection of the integro-differential Painlev\'e-II hierarchy to a novel integro-differential mKdV hierarchy. Comment: 40 pages, 3 figures. Version 2 updates literature |
| Databáze: | OpenAIRE |
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