Time-Dependent Variational Approach for Boson Systems

Arthur K. Kerman, Paolo Tommasini

A. Kuriyama, Constança Providência, João da Providência +2 more

Various aspects of the deformed boson scheme are investigated with the aim of applying it to the time-dependent variational method for many-boson systems. The case of the multiboson states is also discussed. In analogy with the time-dependent Hartree-Fock theory in many-fermion systems, the classical aspect of the deformed boson is discussed.

M. C. Cambiaggio, G.G. Dussel, J. A. Ramirez

Arthur K. Kerman, Paolo Tommasini

We investigate the Dirac time-dependent variational method using a Gaussian trial functional for an infinite one-dimensional system of bosons interacting through a repulsive contact interaction. The method produces a set of nonlinear time-dependent equations for the variational parameters. By solving the static equations we have calculated the ground state energy per particle. We have also considered small oscillations about the equilibrium and obtain mode equations which lead us to a gapless dispersion relation. The existence of an exact numerical solution for the ground-state energy and excitations obtained by Lieb allow us to compare with the Gaussian results. We can also, as the system becomes less dilute, see the improvement of the results as compared with the Bogoliubov scheme.

Philipp O. J. Scherer

A. Kuriyama, Constança Providência, João da Providência +2 more

Basic idea presented in Parts (I) and (II) for the deformed boson scheme is applied to the case of the su(2,1)-algebra for describing many-body systems consisting of three kinds of boson operators. A possible form of the coherent state for the su(2,1)-algebra is generalized and the deformed su(2,1)-algebra is presented. As an application, the time-evolution of the statistically mixed state in a certain boson system, which has been already investigated by the present authors, is reinvestigated.