Coherent states in quantum billiards constructed in the basis of the continued eigenfunctions

Abstract:In the article a new approach to construction of generalized coherent states in quantum billiards is proposed. The coherent states are defined as the projections of a Gaussian wave function on the basis of the eigenstates of the quantum billiard, continued outside. The continuation is built as the solution of the equivalent Balian--Bloch equation, defined on the entire $\mathbb{R}^2$ and the projection operator is built using the resolvent of the Balian--Bloch equation. In the case of the one--dimensional potential well and billiards, belonging to the Coxeter group, the wave functions of the coherent states were expressed analytically via the Jacobi and Riemann theta functions.

Chaotic Dynamics (nlin.CD); Quantum Physics (quant-ph)

arXiv:2608.20302 [nlin.CD]

(or arXiv:2608.20302v1 [nlin.CD] for this version)

https://doi.org/10.48550/arXiv.2608.20302 Focus to learn more arXiv-issued DOI via DataCite (pending registration)

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