Schrödinger equation approach to Statistical Mechanics of interacting strings: Exact results

Abstract

In this work, we consider a pair of interacting strings that may thermally fluctuate around some line-reference. We assume that the two strings interact via a q-deformed Morse potential that reproduces well the features of the real interaction. Using the Transfer Matrix Method, based on the resolution of a Schrödinger equation, we first exactly determine their solutions that were found to be bound states. Second, from the exact expression of the ground state, we compute the contact probability that is the probability to find two interacting strings at a (finite) distance apart, and obtain its exact scaling form and the associated contact exponents. The main conclusion is that, the analytical studies reveal that the q-deformed Morse potential is a good candidate for the investigation of the statistical properties of fluctuating strings.