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This research presents a novel mathematical framework for constructing coherent states in quantum billiards by extending solutions beyond physical boundaries using the Balian-Bloch equation. By leveraging Jacobi and Riemann theta functions, the method provides analytical expressions for complex geometries like Coxeter shapes while avoiding computationally intensive eigenstate calculations. This advancement offers a more efficient route to describing particle dynamics in irregular quantum systems without relying on traditional approximations.

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Hse University Proposes New Coherent State Construction for Billiards

Quantum ZeitgeistSeptember 4, 20264 min read

Coherent states in complex systems have traditionally demanded extensive computation or relied upon approximations that struggle with irregular boundaries. Now, a new mathematical technique offers an alternative by constructing these states without explicitly calculating eigenstates for certain geometries. This allows analytical solutions, utilising established functions like those of Jacobi and Riemann, for quantum billiards including one-dimensional wells and Coxeter shapes.

A new technique constructs generalised coherent states within quantum billiards, wave functions resembling Gaussian shapes even at the edges of the billiard. This approach defines such states by projecting a Gaussian wave function onto continued eigenstates, solutions to the Balian, Bloch equation extending beyond the billiard’s boundaries. A new method defines coherent states, representations of particle motion, within quantum billiards. The technique defines these…

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