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

TL;DR

This paper explores using non self-adjoint Hamiltonians in quantum models to introduce an arrow of time, with applications to information dynamics and decision making.

Contribution

It introduces a novel approach employing non self-adjoint Hamiltonians to model irreversible quantum dynamics, addressing limitations of traditional reversible models.

Findings

Non self-adjoint Hamiltonians produce non-reversible, arrow-of-time dynamics.

Applications demonstrate relevance to information processing and decision making.

Reversible quantum models may not capture all physical phenomena.

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 $\Sc$. 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.