One-directional quantum mechanical dynamics and an application to decision making

Abstract

In recent works we have used quantum tools in the analysis of the time evolution of several macroscopic systems. The main ingredient in our approach is the self-adjoint Hamiltonian H of the system S. This Hamiltonian quite often, and in particular for systems with a finite number of degrees of freedom, gives rise to reversible and oscillatory dynamics. Sometimes this is not what physical reasons suggest. We discuss here how to use non self-adjoint Hamiltonians to overcome this difficulty: the time evolution we obtain out of them show a preferable arrow of time, and it is not reversible. Several applications are constructed, in particular in connection to information dynamics.

Modeling epidemics through ladder operators

“…It is clear that the analytic form of H could be enriched, for instance by adding extra terms, by requiring some explicit time dependence in the Hamiltonian itself, or also by relaxing the assumption that H should be Hermitian [22] , [23] . We could also refine our analysis by assuming that some external rule acts on the system, as proposed in [24] .…”

Spreading of Competing Information in a Network

“…The Hamiltonian H contains all the operators describing the interactions occurring between the different agents of the system, in particular the diffusion of fake and good news, and the ability to modify the nature of news from good to fake and vice versa. We stress that the use of operational methods has proven successful in describing the dynamics of several macroscopic systems arising in decision making, [ 5 ], population dynamics, [ 6 ], basic cancer cell dynamics, [ 7 , 8 ], biological aspects of the bacterial dynamics, [ 9 ], and epigenetic evolution, [ 10 ] (see [ 11 , 12 ] for other fields of application).…”