Systems with Many Particles

K. Kong Wan

A general physical system is a compound system consisting of many constituents. A constituent may be made up of more than one particle, e.g., a molecule is made of atoms which themselves are made up of many particles. In a superconductor at low temperatures the electrons form pairs. 1 Each pair can be treated as a constituent of a superconducting current. For convenience we also call these constituents particles . A general physical system is referred to as a many-particle system. The theory for many-particle systems can be built up from one-particle theory. The situation can be complicated since there are different types of many-particle systems: A compound system may consists of a definite number of particles, i.e., the number of particles in the system remains the same for all time. Such a system may consist of distinguishable particles, or identical, i.e., indistinguishable, particles. 560 A compound system may consists of an indefinite number of particles, i.e., the number of particles in the system may change in time due to interactions. The particles involved may or may not be identical.

Walter E Thirring

Tingwei Zhou

Entanglement of the wave–particle duality of particles has attracted enormous attention as one of fundamental feature of quantum mechanics. Herein, we systematically studied the wave–particle entanglement of the particle system composed of N particles. The results indicate that the particle system has the wave–particle entanglement after the interaction, when the wave function of any one of the system can be obtained by using same basis vectors before the interaction. Moreover, a construction method of the wave–particle entanglement state is found for the particle system. Finally, the photons can show the wave–particle entanglement in the previous experimental work, which was further confirmed by the construction method. The results provide a new understanding for the entanglement of the wave–particle duality.

Eugen Fick, Günter Sauermann

M. Tomaselli, L C Liu, T K hl +3 more

The structure and dynamics of an n -particle system are described with coupled nonlinear Heisenberg commutator equations where the nonlinear terms are generated by the two-body interaction that excites the reference vacuum via particle–particle and particle–hole excitations. Nonperturbative solutions of the system are obtained with the use of the dynamic linearization approximation and cluster transformation coefficients. The dynamic linearization approximation converts the commutator chain into an eigenvalue problem. The cluster coefficients factorize the matrix elements of the ( n ) particles or particle–hole systems in terms of the matrix elements of the ( n − 1)-systems coupled to particle–particle, particle–hole and hole–hole bosons. Group properties of the particle–particle, particle–hole and hole–hole permutation groups simplify the calculation of these coefficients. The particle–particle vacuum excitations generate superconductive diagrams in the dynamics of three-quark systems. Applications of the model to fermionic and bosonic systems are discussed.

Russell K. Hobbie, Bradley John Roth