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

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 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 a few applications, mostly related to different versions of a predator-prey model and to love affairs (from a decision-making point of view). This article is part of the theme issue 'Quantum theory and topology in models of decision making (Part 2)'.