Effective Field Theory for Bound State Reflection

TL;DR

This paper develops an effective field theory to analyze how shallow quantum bound states, like dimers, reflect from hard surfaces, providing insights into their structure and compressibility across different dimensions.

Contribution

It introduces a general effective field theory framework for shallow dimer reflection and calculates reflection lengths up to second order, validated by numerical lattice results in 1D, 2D, and 3D.

Findings

Effective field theory accurately predicts reflection scattering lengths.

Numerical lattice results agree with theoretical calculations.

Analysis of alpha particle compressibility on a lattice.

Abstract

Elastic quantum bound-state reflection from a hard-wall boundary provides direct information regarding the structure and compressibility of quantum bound states. We discuss elastic quantum bound-state reflection and derive a general theory for elastic reflection of shallow dimers from hard-wall surfaces using effective field theory. We show that there is a small expansion parameter for analytic calculations of the reflection scattering length. We present a calculation up to second order in the effective Hamiltonian in one, two, and three dimensions. We also provide numerical lattice results for all three cases as a comparison with our effective field theory results. Finally, we provide an analysis of the compressibility of the alpha particle confined to a cubic lattice with vanishing Dirichlet boundaries.