Non-unitary evolution of quantum logical structure

M. LOSADA; S. FORTIN; F. HOLIK

Stuttgart

Congreso; PHHQP17: Non-Hermitian Hamiltonians in Physics: Theory and Experiment; 2017

Universität Stuttgart

In this presentation, we argue that the description of the classical limit in terms of theSchrödinger picture -in which states evolve in time, while observables and physicalproperties are constant- is not completely adequate, because it cannot explain thequantum-to-classical transition of the logical structure of physical properties. lf aquantum system undergoes a physical process such that its behavior becomesclassic, then the logical structure of its properties should undergo a transition from aquantum logic to a classical logic, i.e. its lattice structure should become distributive.In order to give an adequate description of the logic structure transition, we proposeto study the classical limit in terms of the Heisenberg picture, in which observablesand physical properties evolve in time. This perspective allows considering the timeevolution of the whole lattice of properties. On this basis, we will study theclassical limit from a logical point of view, by describing the manner in which thestructure of properties becomes a Boolean lattice.lt should be noted that, according to Schrödinger equation, a closed system alwaysevolves unitarily. Therefore, even in the Heisenberg picture, if two observables areincompatible at one time, they will remain incompatible in any time. For thatreason, for describing the quantum-to-classical transition of the logic of a physicalsystem, we will need to consider non-unitary time evolutions, generated by nonHermitianHamiltonians.