Interdimensional degeneracies for a quantum NN-body system in DD dimensions

Complete spectrum of exact interdimensional degeneracies for a quantum $N$-body system in $D$-dimensions is presented by the method of generalized spherical harmonic polynomials. In an $N$-body system all the states with angular momentum $[\mu+n]$ in $(D-2n)$ dimensions are degenerate where $[\mu]$ and $D$ are given and $n$ is an arbitrary integer if the representation $[\mu+n]$ exists for the SO($D-2n$) group and $D-2n\geq N$. There is an exceptional interdimensional degeneracy for an $N$-body system between the state with zero angular momentum in $D=N-1$ dimensions and the state with zero angular momentum in $D=N+1$ dimensions.Comment: 8 pages, no figure, RevTex, Accepted by EuroPhys.Let

Quantum four-body system in D dimensions

By the method of generalized spherical harmonic polynomials, the Schr\"{o}dinger equation for a four-body system in $D$-dimensional space is reduced to the generalized radial equations where only six internal variables are involved. The problem on separating the rotational degrees of freedom from the internal ones for a quantum $N$-body system in $D$ dimensions is generally discussed.Comment: 19 pages, no figure, RevTex, Submitted to J. Math. Phy

The universal "heartbeat" oscillations in black hole systems accross the mass-scale

The hyperluminous X-ray source (HLX-1, the peak X-ray luminosity $\sim 10^{42}\rm erg\ s^{-1}$) near the spiral galaxy ESO 243-49 is possibly the best candidate for intermediate mass black hole (IMBH), which underwent recurrent outbursts with a period of $\sim 400$ days. The physical reason for this quasi-periodic variability is still unclear. We explore the possibility of radiation-pressure instability in accretion disk by modeling the light curve of HLX-1, and find that it can roughly reproduce the duration, period and amplitude of the recurrent outbursts HLX-1 with an IMBH of ~10^5Msun. Our result provides a possible mechanism to explain the recurrent outbursts in HLX-1. We further find a universal correlation between the outburst duration and the bolometric luminosity for the BH sources with a very broad mass range (e.g., X-ray binaries, XRBs, HLX-1 and active galactic nuclei, AGNs), which is roughly consistent with the prediction of radiation-pressure instability of the accretion disk. These results imply that "heartbeat" oscillations triggered by radiation-pressure instability may appears in different-scale BH systems.Comment: ApJ in press; 15 pages, 5 Figure