42,096 research outputs found

### Generalized Rayleigh and Jacobi processes and exceptional orthogonal polynomials

We present four types of infinitely many exactly solvable Fokker-Planck
equations, which are related to the newly discovered exceptional orthogonal
polynomials. They represent the deformed versions of the Rayleigh process and
the Jacobi process.Comment: 17 pages, 4 figure

### Two-dimensional gases of generalized statistics in a uniform magnetic field

We study the low temperature properties of two-dimensional ideal gases of
generalized statistics in a uniform magnetic field. The generalized statistics
considered here are the parafermion statistics and the exclusion statistics.
Similarity in the behaviours of the parafermion gas of finite order $p$ and the
gas with exclusion coefficient $g=1/p$ at very low temperatures is noted. These
two systems become exactly equivalent at $T=0$. Qumtum Hall effect with these
particles as charge carriers is briefly discussed.Comment: Latex file, 14 pages, 5 figures available on reques

### Condition for tripartite entanglement

We propose a scheme for classifying the entanglement of a tripartite pure
qubit state. This classification scheme consists of an ordered list of seven
elements. These elements are the Cayley hyper-determinant, and its six
associated $2 \times 2$ subdeterminants. In particular we show that this
classification provides a necessary and sufficient condition for separability.Comment: 8 pages, to appear in the Proceedings of "Quantum Theory and
Symmetries 7", Prague, Aug 7-13, 201

### Multiple Chern-Simons Fields on a Torus

Intertwined multiple Chern-Simons gauge fields induce matrix statistics among
particles. We analyse this theory on a torus, focusing on the vacuum structure
and the Hilbert space. The theory can be mimicked, although not completely, by
an effective theory with one Chern-Simons gauge field. The correspondence
between the Wilson line integrals, vacuum degeneracy and wave functions for
these two theories are discussed. Further, it is obtained in both of these
cases that the two total momenta and Hamiltonian commute only in the physical
Hilbert space.Comment: 20 pages, UMN-TH-1128/93, plain Te

### Stellar Velocity Dispersion and Black Hole Mass in the Blazar Markarian 501

The recently discovered correlation between black hole mass and stellar
velocity dispersion provides a new method to determine the masses of black
holes in active galaxies. We have obtained optical spectra of Markarian 501, a
nearby gamma-ray blazar with emission extending to TeV energies. The stellar
velocity dispersion of the host galaxy, measured from the calcium triplet lines
in a 2"x3.7" aperture, is 372 +/- 18 km/s. If Mrk 501 follows the M-sigma
correlation defined for local galaxies, then its central black hole has a mass
of (0.9-3.4)x10^9 solar masses. This is significantly larger than some previous
estimates for the central mass in Mrk 501 that have been based on models for
its nonthermal emission. The host galaxy luminosity implies a black hole of
6x10^8 solar masses, but this is not in severe conflict with the mass derived
from the M-sigma relation because the M_BH-L_bulge correlation has a large
intrinsic scatter. Using the emission-line luminosity to estimate the
bolometric luminosity of the central engine, we find that Mrk 501 radiates at
an extremely sub-Eddington level of L/L_Edd ~ 10^-4. Further applications of
the M-sigma relation to radio-loud active galactic nuclei may be useful for
interpreting unified models and understanding the relationship between radio
galaxies and BL Lac objects.Comment: To appear in ApJ Letters. 5 pages, 2 figure

### Reply to Hagen & Sudarshan's Comment

We show that the argument in Phys Rev Lett 70 (1993) 1360 is correct and
consistent, and that Hagen & Sudarshan's solution has inconsistency leading to
non-vanishing commutators of $[P^1, P^2]$ and $[P^j, H]$ even in physical
states. This proves that many of HS's statements in their Comment are based
merely on incorrect guess, but not on careful algebra.Comment: one page, UMN-TH-1245/9

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