Bound states of infinite curved polymer chains

TL;DR

This paper studies bound states in infinite curved polymer chains modeled as point interactions, showing that non-linear asymptotically straight curves can support multiple bound states, with the number potentially unbounded.

Contribution

It introduces a model of infinite curved chains with point interactions and proves the existence of bound states for non-linear asymptotically straight curves, including cases with arbitrarily many bound states.

Findings

Bound states exist for non-linear asymptotically straight curves.

The number of bound states can be made arbitrarily large.

Supports the modeling of curved polymer chains with multiple bound states.

Abstract

We investigate an infinite array of point interactions of the same strength in R^d, d=2,3, situated at vertices of a polygonal curve with a fixed edge length. We demonstrate that if the curve is not a line, but it is asymptotically straight in a suitable sense, the corresponding Hamiltonian has bound states. Example is given in which the number of these bound states can exceed any positive integer.