Off-topic for aiqbench

This story was gathered from a source we follow but falls outside AI and quantum coverage, so there is no aiqbench take for it.

Multivariable Painleve'-II equation: connection formulas for asymptotic solutions

arXivAugust 25, 20261 min read

arXiv:2603.22470v4 Announce Type: replace-cross Abstract: For an integrable generalization of the Painleve'-II equation (P-II) to a system of coupled equations with symmetry breaking terms, an asymptotically exact WKB analysis is applied to obtain connection formulas for solutions at different infinities. The analysis relies on an exact solution of the quantum mechanical Demkov--Osherov model (DOM), revealing a possible deeper relation between classical integrable systems and solvable multistate Landau--Zener models. An application of the connection formulas to the problem of unstable vacuum decay during a second-order phase transition provides precise scaling of the number of excitations, including subdominant contributions.

Abstract:For an integrable generalization of the Painleve'-II equation (P-II) to a system of coupled equations with symmetry breaking terms, an asymptotically exact WKB analysis is applied to obtain connection formulas for solutions at different infinities. The analysis relies on an exact solution of the quantum mechanical Demkov--Osherov model (DOM), revealing a possible deeper relation between classical integrable systems and solvable multistate Landau--Zener models. An application of the connection formulas to the problem of unstable vacuum decay during a second-order phase transition provides precise scaling of the number of excitations, including subdominant contributions.

Mathematical Physics (math-ph); General Relativity and Quantum Cosmology (gr-qc); Exactly Solvable and Integrable Systems (nlin.SI); Quantum Physics (quant-ph)

arXiv:2603.22470 [math-ph]

(or arXiv:2603.22470v4 [math-ph] for this version)

Full text under the publisher's open licence · 118 words

Read at arXiv ↗Ask about this article