Renormalization Condition on Self-Energy at Two-Loop Level for Trapped Atomic Gas

雅彦 奥村, Y. Yamanaka

Masahiko Okumura, Y. Yamanaka

Soheil Baharian, Gordon Baym

We study the stability and dynamics of an ultracold bosonic gas trapped in a toroidal geometry and driven by rotation in the absence of dissipation. We first delineate, via the Bogoliubov mode expansion, the regions of stability and the nature of instabilities of the system for both repulsive and attractive interaction strengths. To study the response of the system to variations in the rotation rate, we introduce a ``disorder'' potential, breaking the rotational symmetry. We demonstrate the breakdown of adiabaticity as the rotation rate is slowly varied and find forced tunneling between the system's eigenstates. The nonadiabaticity is signaled by the appearance of a swallow-tail loop in the lowest-energy level, a general sign of hysteresis. Then, we show that this system is in one-to-one correspondence with a trapped gas in a double-well potential and thus exhibits macroscopic quantum self-trapping. Finally, we show that self-trapping is a direct manifestation of the behavior of the lowest-energy level.

Yukiro Kuwahara, Yusuke Nakamura, Y. Yamanaka

We study the thermal processes for the system of cold neutral atomic gas in the framework of nonequilibrium Thermo Field Dynamics (TFD) which is a real-time canonical formalism of quantum field theory for thermal situations [1]. The system is suitable for testing quantum many-body theories in nonequilibrium situations because temporal changes in thermal processes are so slow that various nonequilibrium phenomena can be observed experimentally. In nonequilibrium TFD, the quantum transport equation, which is the equation for a time-dependent number distribution introduced as an unknown parameter, is derived from the self-consistent renormalization condition on the self-energy [2]. The correction on the excitation energy is important both physically and in the renormalization of quantum field theory. Recently we have proposed the new self-consistent renormalization method in nonequilibrium TFD, in which the on-shell self-energy in time-dependent case is introduced as a generalization of the ordinary on-shell self-energy in stationary case and the renormalization conditions on it yields the quantum transport equation and the diagonal correction of the quasiparticle energy in a unified manner [2]. In this work, the renormalization condition is extended to the imaginary and off-diagonal parts of the self-energy. In our previous work [3], we applied nonequilibrium TFD to the one dimensional system of confined cold neutral atomic Bose gas. There the nonequilibrium situation was set up by a sudden displacement of the confining potential and a sudden switch-on of the interparticle interaction. We investigated the thermal process for the system by solving the quantum transport equation, but neglecting the correction of the quasiparticle energy. Then it was found that in some particular parameter region it gives rise to an unphysical result, namely the negative number distribution. Here we take account of the correction of the quasiparticle energy and solve the quantum transport equation again. The correction affects drastically the thermal relaxation process and resolves the difficulty in some parameter region, as will be shown.

雅彦 奥村, Y. Yamanaka

Yusuke Nakamura, Tomoka Sunaga, M. Mine +2 more

The non-Markoffian transport equations for the systems of cold Bose atoms confined by a external potential both without and with a Bose-Einstein condensate are derived in the framework of nonequilibrium thermal filed theory (Thermo Field Dynamics). Our key elements are an explicit particle representation and a self-consistent renormalization condition which are essential in thermal field theory. The non-Markoffian transport equation for the non-condensed system, derived at the two-loop level, is reduced in the Markoffian limit to the ordinary quantum Boltzmann equation derived in the other methods. For the condensed system, we derive a new transport equation with an additional collision term which becomes important in the Landau instability.