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The formation and evolution mechanism of fullerenes in the planetary nebula or in the interstellar medium are still not understood. Here we present the study on the cluster formation and the relative reactivity of fullerene cations (from smaller to larger, C$_{44}$ to C$_{70}$) with anthracene molecule (C$_{14}$H$_{10}$). The experiment is performed in the apparatus that combines a quadrupole ion trap with a time-of-flight mass spectrometer. By using a 355 nm laser beam to irradiate the trapped fullerenes cations (C$_{60}$$^+$ or C$_{70}$$^+$), smaller fullerene cations C$_{(60-2n)}$$^+$, n=1-8 or C$_{(70-2m)}$$^+$, m=1-11 are generated, respectively. Then reacting with anthracene molecules, series of fullerene/anthracene cluster cations are newly formed (e.g., (C$_{14}$H$_{10}$)C$_{(60-2n)}$$^+$, n=1-8 and (C$_{14}$H$_{10}$)C$_{(70-2m)}$$^+$, m=1-11), and slight difference of the reactivity within the smaller fullerene cations are observed. Nevertheless, smaller fullerenes show obviously higher reactivity when comparing to fullerene C$_{60}$$^+$ and C$_{70}$$^+$. A successive loss of C$_2$ fragments mechanism is suggested to account for the formation of smaller fullerene cations, which then undergo addition reaction with anthracene molecules to form the fullerene-anthracene cluster cations. It is found that the higher laser energy and longer irradiation time are key factors that affect the formation of smaller fullerene cations. This may indicate that in the strong radiation field environment (such as photon-dominated regions) in space, fullerenes are expected to follow the top-down evolution route, and then form small grain dust (e.g., clusters) through collision reaction with co-existing molecules, here, smaller PAHs.

We study the one-dimensional Fermionic Hubbard model with SU(N) spin symmetry in the incommensurate filling case. The basic properties of Green's function, momentum distribution and tunneling density of states of the system at low temperature are studied in the frame work of Luttinger liquid theory combined with Bethe Ansatz solutions for arbitrary interaction. In the strong interacting case, the system enters the spin-incoherent regime at intermediate temperature Espin < T < Ec and we obtain the Green's function and tunneling density of states by generalizing the path integral approach for the SU(2) case to the SU(N) case in this regime. The theoretical results we obtained agree qualitatively with the experiments on the one-dimensional alkaline earth atomic system with SU(N) spin symmetry. The similarities and difference between the one-dimensional SU(N) Fermionic Hubbard system at large N and the one-dimensional spinless Bosonic system are also investigated., Comment: 10 pages

We investigate the magnetic properties of a repulsive fermionic SU($3$) Hubbard model on the Lieb lattice from weak to strong interaction by means of the mean-field approximation. To validate the method we employed, we first discuss the SU($2$) Hubbard model at the mean-field level, and find that our results are consistent with known rigorous theorems. We then extend the calculation to the case of SU($3$) symmetry. We find that, at $4/9$ filling, the SU$(3)$ symmetry spontaneously breaks into the SU$(2)\times$U$(1)$ symmetry in the ground state, leading to a staggered ferromagnetic state for any repulsive $U$ at zero temperature. We then investigate the stability of the ferromagnetic state by relaxing the filling away from $4/9$, and conclude that the ferromagnetic state is sensitive but robust to fillings, as it can persist within a certain filling regime. We also apply the mean-field approximation to finite temperature to calculate the critical temperature and the critical entropy of the ferromagnetic state. As the resulting critical entropy per particle is significantly greater than that can be realized in experiments, we expect some quasi-long-range-ordered features of such a ferromagnetic state can be realized and observed with fermionic alkaline-earth-metal(-like) atoms loaded into optical lattices., Comment: 11 pages, 10 figures

In this letter we consider a magnetic impurity in a one-dimensional spin-$1/2$ Fermi gas with infinitely strong repulsive interaction between fermions. We rigorously prove that, independent of whether the magnetic coupling between impurity and fermions is ferromagnetic or anti-ferromagnetic, the ground state is always a fully polarized ferromagnetic state for the itinerant fermions. This ferromagnetism can be understood as a cooperative effect of avoiding frustration of magnetic coupling during fermion hopping and the large spin degeneracy of a fermion Tonks gas. By numerically diagonalizing a finite size system, we show that the spin gap first increases linearly with magnetic coupling strength in the weak coupling regime, while decreases in the strong coupling regime. Our results show that a magnetic impurity in a strongly correlated gas can exhibit effect different from the Kondo effect as in a weakly correlated Fermi liquid., Comment: Similar results have been obtained by Phys.Rev.B. 50,9577(1994)

Alkali-earth atoms have a long-lived electronic excited state, which can be localized in the Fermi sea of ground state atoms by an external potential and serve as magnetic impurities, due to the spin-exchange interaction between the excited and the ground state atoms. This can give rise to the Kondo effect. However, in order to achieve this effect in current atomic gas experiment, it requires the Kondo temperature to be increased to a sizable portion of the Fermi temperature. In this letter we propose that the spin-exchange interaction can be strongly enhanced by utilizing the confinement-induced resonance (CIR). We analyze this system by the renormalization group approach, and we show that nearby a CIR, the Kondo temperature can indeed be increased to the regime attainable by current experiments., Comment: 9 pages, 7 figures