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Annals of Physics

Derivation of non-Markovian transport equations for trapped cold atoms in nonequilibrium thermal field theory

Yusuke Nakamura, Tomoka Sunaga, M. Mine, Masahiko Okumura, Y. Yamanaka

Published Sep 26, 2009• 6 citations
Publisher
DOI
10.1016/j.aop.2009.09.014

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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.
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.
The nonequilibrium dynamics of an homogeneous scalar field is studied using Langevin equations. Microscopic derivations based on quantum field theory methods can lead to complicated nonlocal equations of motion. Here we study, numerically, the results obtained by appropriately approximating these equations in a local form (the Markovian approximation) and compare with results obtained with suitable prescriptions for accounting for the nonlocal terms, i.e. the non-Markovian form. We use a prescription for the nonlocal equations motivated by the results obtained from previous derivations using nonequilibrium quantum field theory methods.