Effect of the Zero-Mode on the Response of a Trapped Bose-Condensed Gas

The dynamical response of a trapped Bose-Einstein condensate (BEC) is formulated consistently with quantum field theory and is numerically evaluated. We regard the BEC as a manifestation of the breaking of the global phase symmetry. Then, the Goldstone theorem implies the existence of a zero energy excitation mode (the zero-mode). We calculate the effect of the zero-mode on the response frequency and show that the contribution of the zero-mode to the first excitation mode is not so important in the parameter set realized in the existing experiment. This is the reason that experimental results can be described using the Bogoliubov prescription, although it breaks the consistency of the description in quantum field theory.Comment: 18 pages, 3 figure

Condition for emergence of complex eigenvalues in the Bogoliubov-de Gennes equations

The condition for the appearance of dynamical instability of the Bose-condensed system, characterized by the emergence of complex eigenvalues in the Bogoliubov-de Gennes equations, is studied analytically. We perturbatively expand both the Gross-Pitaevskii and Bogoliubov-de Gennes equations with respect to the coupling constant. It is concluded that the degeneracy between a positive-norm eigenmode and a negative-norm one is essential for the emergence of complex modes. Based on the conclusion, we justify the two-mode approximation applied in our previous work [E. Fukuyama \textit{et al}., Phys. Rev. A {\bf 76}, 043608 (2007)], in which we analytically studied the condition for the existence of complex modes when the condensate has a highly quantized vortex.Comment: 7page

Quantum Field Theoretical Analysis on Unstable Behavior of Bose-Einstein Condensates in Optical Lattices

We study the dynamics of Bose-Einstein condensates flowing in optical lattices on the basis of quantum field theory. For such a system, a Bose-Einstein condensate shows a unstable behavior which is called the dynamical instability. The unstable system is characterized by the appearance of modes with complex eigenvalues. Expanding the field operator in terms of excitation modes including complex ones, we attempt to diagonalize the unperturbative Hamiltonian and to find its eigenstates. It turns out that although the unperturbed Hamiltonian is not diagonalizable in the conventional bosonic representation the appropriate choice of physical states leads to a consistent formulation. Then we analyze the dynamics of the system in the regime of the linear response theory. Its numerical results are consitent with as those given by the discrete nonlinear Schrodinger equation.Comment: 16pages, 4figure

Condition for the Existence of Complex Modes in a Trapped Bose--Einstein Condensate with a Highly Quantized Vortex

We consider a trapped Bose--Einstein condensate (BEC) with a highly quantized vortex. For the BEC with a doubly, triply or quadruply quantized vortex, the numerical calculations have shown that the Bogoliubov--de Gennes equations, which describe the fluctuation of the condensate, have complex eigenvalues. In this paper, we obtain the analytic expression of the condition for the existence of complex modes, using the method developed by Rossignoli and Kowalski [R. Rossignoli and A. M. Kowalski, Phys. Rev. A 72, 032101 (2005)] for the small coupling constant. To derive it, we make the two-mode approximation. With the derived analytic formula, we can identify the quantum number of the complex modes for each winding number of the vortex. Our result is consistent with those obtained by the numerical calculation in the case that the winding number is two, three or four. We prove that the complex modes always exist when the condensate has a highly quantized vortex

Gamma Irradiation on Growth and Development of Amorphophallus Muelleri Blume.

Iles-iles (Amorphophallus muelleri Blume) produces apomictic seeds lead to low genetic variation. In order to induce genetic variation, germinated seeds were exposed to Gamma irradiation (Co-60) at doses of 10 to 100 Gy. Seed irradiation was conducted at Center for the Application of Isotope and Irradiation Technology -National Nuclear Energy Agency (CAIRT), Indonesia. Morphology and yield of M1 generation were observed. Results showed that irradiation at a dose of 10 Gy close to LD50 with survival rate 56%. Gamma irradiation at a dose of 10 Gy delayed seeds germination. Germination rates gradually increased and reached maximum at 4 weeks after planting (WAP) for control plants, and 14 WAP of irradiated plants. At 16 WAP, germination rate of 10 Gy irradiated plants was 56% and 84% for those of control plants. Irradiation induced chimera as indicated by short petiole, variegated and abnornal shape of leaflets. Some irradiated plants entered dormancy at 8-10 weeks later than control ones. Prolong vegetative periode lead the plants to produce heavier corms. This study revealed the possibility to induce variation of A. muelleri by using gamma irradition. Keywords: Amorphophallus muelleri, gamma irradiation (Co-60), morphological variation, mutation breedin

Fermi surface in BaNi2_2P2_2

We report measurements of the de Haas-van Alphen (dHvA) oscillation and a band structure calculation for the pnictide superconductor BaNi$_2$P$_2$, which is isostructural to BaFe$_2$As$_2$, the mother compound of the iron-pnictide high-$T_c$ superconductor (Ba$_{1-x}$K$_x$)Fe$_2$As$_2$. Six dHvA-frequency branches with frequencies up to $\sim$8 kT were observed, and they are in excellent agreement with results of the band-structure calculation. The determined Fermi surface is large, enclosing about one electron and hole per formula unit, and three-dimensional. This is in contrast to the small two-dimensional Fermi surface expected for the iron-pnictide high-$T_c$ superconductors. The mass enhancement is about two.Comment: To appear in J. Phys. Soc. Jpn., Vol. 78, No.