Two Particle States in an Asymmetric Box
Xin Li, Chuan Liu
TL;DR
This paper generalizes L"uscher's finite-volume formulas to asymmetric boxes, relating two-particle energy levels to scattering phases, and discusses applications in extracting scattering lengths from finite-volume spectra.
Contribution
It extends the finite-volume energy spectrum analysis to asymmetric boxes, providing new relations between energy shifts and scattering parameters.
Findings
Derived exact energy eigenstates in asymmetric boxes.
Established relations between energy shifts and scattering phases.
Discussed potential applications in scattering length determination.
Abstract
The exact two-particle energy eigenstates in an asymmetric rectangular box with periodic boundary conditions in all three directions are studied. Their relation with the elastic scattering phases of the two particles in the continuum are obtained. These results can be viewed as a generalization of the corresponding formulae in a cubic box obtained by L\"uscher before. In particular, the s-wave scattering length is related to the energy shift in the finite box. Possible applications of these formulae are also discussed.
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