A new family of ladder operators for macroscopic systems, with applications

TL;DR

This paper introduces a novel family of ladder operators for macroscopic systems that simplifies analytical solutions beyond quadratic Hamiltonians, demonstrated through ecological and social models.

Contribution

It proposes an alternative ladder operator framework enabling easier analytical solutions for complex Hamiltonians in macroscopic systems.

Findings

New ladder operators facilitate analytical solutions for non-quadratic Hamiltonians.

Applications include predator-prey models and decision-making scenarios.

The approach simplifies computations in macroscopic quantum-like systems.

Abstract

In a series of recent scientific contributions the role of bosonic and fermionic ladder operators in a macroscopic realm has been investigated. Creation, annihilation and number operators have been used in very different contexts, all sharing the same common main feature, i.e. the relevance of {\em discrete changes} in the description of the system. The main problem when using this approach is that computations are easy for Hamiltonians which are quadratic in the ladder operators, but become very complicated, both at the analytical and at the numerical level, when the Hamiltonian is not quadratic. In this paper we propose a possible alternative approach, again based on some sort of ladder operators, but for which an analytic solution can often be deduced without particular difficulties. We describe our proposal with few applications, mostly related to different versions of a predator-prey model, and to love affairs (from a decision-making point of view).