Elementary Properties of Composite Systems in Quantum Mechanics

A. Khvedelidze, I. Rogojin, I. Rogozhin

The issue of the dichotomy between the elementary and composite nature of a finite-dimensional quantum system is discussed within the framework of the generalized Stratonovich–Weyl formulation of quantum mechanics. Performing numerical studies, we demonstrate how information on the possibility of realizing a virtual 2-level subsystem is encoded in the properties of the Wigner function of a total 4-level system.

Shigeru Machida, Akio Motoyoshi

John P. Lowe

A. Khvedelidze, I. Rogozhin

Abstract The issue of the dichotomy between the elementary and composite nature of a finite-dimensional quantum system is discussed within the framework of the generalized Stratonovich–Weyl formulation of quantum mechanics. Performing numerical studies, we demonstrate how information on the possibility of realizing a virtual 2-level subsystem is encoded in the properties of the Wigner function of a total 4-level system.

László B. Szabados

Abstract The spin geometry theorem of Penrose is extended from SU(2) to E(3) (Euclidean) invariant elementary quantum mechanical systems. Using the natural decomposition of the total angular momentum into its spin and orbital parts, the distance between the centre-of-mass lines of the elementary subsystems of a classical composite system can be recovered from their relative orbital angular momenta by E(3)-invariant classical observables. Motivated by this observation, an expression for the ‘empirical distance’ between the elementary subsystems of a composite quantum mechanical system, given in terms of E(3)-invariant quantum observables, is suggested. It is shown that, in the classical limit, this expression reproduces the a priori Euclidean distance between the subsystems, though at the quantum level it has a discrete character. ‘Empirical’ angles and 3-volume elements are also considered.

John P. Lowe