Nonlocal coherent states in an infinite array of boson sites

TL;DR

This paper develops a rigorous mathematical framework for constructing nonlocal coherent states in an infinite array of boson sites, extending the concept of coherent states beyond finite systems using advanced analysis and number theory.

Contribution

It introduces a novel construction of nonlocal coherent states for infinite boson arrays, addressing a significant gap in quantum state theory.

Findings

Successfully constructs nonlocal coherent states in infinite arrays

Uses Dirichlet series and number theory for the construction

Provides a rigorous mathematical foundation for infinite boson systems

Abstract

A regular coherent state (CS) is a special type of quantum state for boson particles placed in a single site. The defining feature of the CS is that it is an eigenmode of the annihilation operator. The construction easily generalizes to the case of a finite number of sites. However, the challenge is altogether different when one considers an infinite array of sites. In this work we demonstrate a mathematically rigorous construction that resolves the latter case. The resulting nonlocal coherent states (NCS) are simultaneous eigenmodes for all of the infinitely many annihilation operators acting in the infinite array's Fock space. Our construction fundamentally relies on Dirichlet series-based analysis and number theoretic arguments.