Quasi-particle excitations and the many-boson problem

Richard David Etters

M. Binder

Tai Kai Ng

Mohsen Razavy, M. Binder

For a system of many bosons, quasi-particles are defined as simple excitations having energies equal to those predicted by the Bogoliubov and Valatin–Butler theories. Scattering between these elementary excitations is caused by the residual interaction. This results in a change in the energies of quasi-particles, and a finite lifetime for the excitations. The force between two quasi-particles is determined in terms of the boson–boson potential, and the distribution function for different excitations. Perturbed single particle energies are also calculated within the framework of the reaction matrix.

Sadao Ohkido, Masahide Takahashi

In many-electron systems, particularly when it is the case that the system consists of quasi-particles having almost no interaction with each other, the approaches to considering a quasi-particle to be a basic particle are important. We propose a bosonization method of the system in which a quasi-particle consists of electron–hole pairs. Low-lying electron excited states are approximately considered as the collective motion states of the quasi-particles that correspond to the quantized normal mode oscillations, and each of these quasi-particles consists of the electron–hole pairs. We consider the fundamental model Hamiltonian, and transform this into the quasi-particle representation Hamiltonian. Then, we transform these quasi-particles into bosons by using the Dyson-type boson mapping method. The obtained Dyson-type boson Hamiltonian enables a straightforward interpretation of the low-lying electron excited states and facilitates their calculation. To confirm the usefulness of this method, we apply this to the |$\pi$|-electrons system of the ethylene molecule.

Shuichiro Yamasaki, T. Kebukawa, Sigenobu Sunakawa