Composite systems

Додин Дмитрий Валерьевич, I. G. Kovalenko, Alexander I. Lvovsky

A composite quantum system is a fundamental object in quantum informatics. A composite quantum system is considered a system whose dimension is a composite integer number whereas the prime integers may only correspond to non‐composite systems. Entanglement and the procedure of reduction to a subsystem via averaging over environment are only formulated for composite systems. In the present report we introduce a procedure of decomposition into ‘subsystems’ for a system whose dimension is an arbitrary number including a prime integer. This procedure generalizes the standard procedure of reduction. In the particular case of a non‐composite system the space of states of the decomposed system splits into direct sum of subspaces of states and the average dimension of subspaces is a fractional number. We compare the properties of the introduced procedure of decomposition and the standard separation into subsystems.

Elemér Elad Rosinger

A family of {\it quantumness spaces} is identified and precisely defined. They are spaces which characterize the difference between states given by classical compositions of systems, and on the other hand, states corresponding to their quantum compositions. Consequently, the quantum composition of systems is {\it reduced} to two classical compositions. A family of rankings is also defined for the respective family of quantumness.

Cheng-Li Wu, D.H. Feng

Based on the composite particle representation presented in the last paper (I), a method of solving the many-body problem known as the composite particle approximation is proposed. It is shown that a many-body system can be simplified to a composite particle system (plus one or more uncorrelated basic particles if any existed) if the following conditions are satisfied: 1) the binding energies of the composite particles are much larger than the excitation energies of the system; 2) there is domination of the collective mode for the composite particles. The interactions between the composite particles, as well as the interactions between composite particles and the basic particles can be evaluated from the original particle-particle interactions. Applications of this theory are indicated.

Günther Ludwig