A new description of motion of the Fermionic SO(2N+2) top in the classical limit under the quasi-anticommutation relation approximation

The boson images of fermion SO(2N+1) Lie operators have been given together with those of SO(2N+2) ones. The SO(2N+1) Lie operators are generators of rotation in the (2N+1)-dimensional Euclidian space (N: number of single-particle states of the fermions). The images of fermion annihilation-creation operators must satisfy the canonical anti-commutation relations, when they operate on a spinor subspace. In the regular representation space we use a boson Hamiltonian with Lagrange multipliers to select out the spinor subspace. Based on these facts, a new description of a fermionic SO(2N+2) top is proposed. From the Heisenberg equations of motions for the boson operators, we get the SO(2N+1) self-consistent field (SCF) Hartree-Bogoliubov (HB) equation for the classical stationary motion of the fermion top. Decomposing an SO(2N+1) matrix into matrices describing paired and unpaired modes of fermions, we obtain a new form of the SO(2N+1) SCF equation with respect to the paired-mode amplitudes. To demonstrate the effectiveness of the new description based on the bosonization theory, the extended HB eigenvalue equation is applied to a superconducting toy-model which consists of a particle-hole plus BCS type interaction. It is solved to reach an interesting and exciting solution which is not found in the traditional HB eigenvalue equation, due to the unpaired-mode effects. To complete the new description, the Lagrange multipliers must be determined in the classical limit. For this aim a quasi anti-commutation-relation approximation is proposed. Only if a certain relation between an SO(2N+1) parameter z and the N is satisfied, unknown parameters k and l in the Lagrange multipliers can be determined withuout any inconcistency.Comment: 36 pages, no figures, typos corrected, published versio

Can the frequency-dependent specific heat be measured by thermal effusion methods?

It has recently been shown that plane-plate heat effusion methods devised for wide-frequency specific-heat spectroscopy do not give the isobaric specific heat, but rather the so-called longitudinal specific heat. Here it is shown that heat effusion in a spherical symmetric geometry also involves the longitudinal specific heat.Comment: Paper presented at the Fifth International Workshop on Complex Systems (Sendai, September, 2007), to appear in AIP Conference Proceeding

Large scale kinematics and dynamical modelling of the Milky Way nuclear star cluster

Within the central 10pc of our Galaxy lies a dense nuclear star cluster (NSC), and similar NSCs are found in most nearby galaxies. Studying the structure and kinematics of NSCs reveals the history of mass accretion of galaxy nuclei. Because the Milky Way (MW) NSC is at a distance of only 8kpc, we can spatially resolve the MWNSC on sub-pc scales. This makes the MWNSC a reference object for understanding the formation of all NSCs. We have used the NIR long-slit spectrograph ISAAC (VLT) in a drift-scan to construct an integral-field spectroscopic map of the central 9.5 x 8pc of our Galaxy. We use this data set to extract stellar kinematics both of individual stars and from the unresolved integrated light spectrum. We present a velocity and dispersion map from the integrated light and model these kinematics using kinemetry and axisymmetric Jeans models. We also measure CO bandhead strengths of 1,375 spectra from individual stars. We find kinematic complexity in the NSCs radial velocity map including a misalignment of the kinematic position angle by 9 degree counterclockwise relative to the Galactic plane, and indications for a rotating substructure perpendicular to the Galactic plane at a radius of 20" or 0.8pc. We determine the mass of the NSC within r = 4.2pc to 1.4 x 10^7 Msun. We also show that our kinematic data results in a significant underestimation of the supermassive black hole (SMBH) mass. The kinematic substructure and position angle misalignment may hint at distinct accretion events. This indicates that the MWNSC grew at least partly by the mergers of massive star clusters. Compared to other NSCs, the MWNSC is on the compact side of the r_eff - M_NSC relation. The underestimation of the SMBH mass might be caused by the kinematic misalignment and a stellar population gradient. But it is also possible that there is a bias in SMBH mass measurements obtained with integrated light.Comment: 20 pages, 19 Figures, Accepted for publication in A&

High resolution observations of Cen A: Yellow and red supergiants in a region of jet-induced star formation?

We present the analysis of near infrared (NIR), adaptive optics (AO) Subaru and archived HST imaging data of a region near the northern middle lobe (NML) of the Centaurus A (Cen A) jet, at a distance of $\sim15$ kpc north-east (NE) from the center of NGC5128. Low-pass filtering of the NIR images reveals strong -- $>3\sigma$ above the background mean -- signal at the expected position of the brightest star in the equivalent HST field. Statistical analysis of the NIR background noise suggests that the probability to observe $>3\sigma$ signal at the same position, in three independent measurements due to stochastic background fluctuations alone is negligible ($\leq10^{-7}\%$) and, therefore, that this signal should reflect the detection of the NIR counterparts of the brightest HST star. An extensive photometric analysis of this star yields $V-I$, visual-NIR, and NIR colors expected from a yellow supergiant (YSG) with an estimated age $\sim10^{+4}_{-3}$ Myr. Furthermore, the second and third brighter HST stars are, likely, also supergiants in Cen A, with estimated ages $\sim16^{+6}_{-3}$ Myr and $\sim25^{+15}_{-9}$ Myr, respectively. The ages of these three supergiants are in good agreement with the ages of the young massive stars that were previously found in the vicinity and are thought to have formed during the later phases of the jet-HI cloud interaction that appears to drive the star formation (SF) in the region for the past $\sim100$ Myr.Comment: 11 pages, 6 figures, 2 tables, accepted for publication in Ap