Quantum dynamical semigroups for diffusion models with Hartree interaction

We consider a class of evolution equations in Lindblad form, which model the dynamics of dissipative quantum mechanical systems with mean-field interaction. Particularly, this class includes the so-called Quantum Fokker-Planck-Poisson model. The existence and uniqueness of global-in-time, mass preserving solutions is proved, thus establishing the existence of a nonlinear conservative quantum dynamical semigroup. The mathematical difficulties stem from combining an unbounded Lindblad generator with the Hartree nonlinearity.Comment: 30 pages; Introduction changed, title changed, easier and shorter proofs due to new energy norm. to appear in Comm. Math. Phy

OB Stars in the Solar Neighborhood I: Analysis of their Spatial Distribution

We present a newly-developed, three-dimensional spatial classification method, designed to analyze the spatial distribution of early type stars within the 1 kpc sphere around the Sun. We propose a distribution model formed by two intersecting disks -the Gould Belt (GB) and the Local Galactic Disk (LGD)- defined by their fundamental geometric parameters. Then, using a sample of about 550 stars of spectral types earlier than B6 and luminosity classes between III and V, with precise photometric distances of less than 1 kpc, we estimate for some spectral groups the parameters of our model, as well as single membership probabilities of GB and LGD stars, thus drawing a picture of the spatial distribution of young stars in the vicinity of the Sun.Comment: 28 pages including 9 Postscript figures, one of them in color. Accepted for publication in The Astronomical Journal, 30 January 200

Giant Molecular Clouds are More Concentrated to Spiral Arms than Smaller Clouds

From our catalog of Milky Way molecular clouds, created using a temperature thresholding algorithm on the Bell Laboratories 13CO Survey, we have extracted two subsets:(1) Giant Molecular Clouds (GMCs), clouds that are definitely larger than 10^5 solar masses, even if they are at their `near distance', and (2) clouds that are definitely smaller than 10^5 solar masses, even if they are at their `far distance'. The positions and velocities of these clouds are compared to the loci of spiral arms in (l, v) space. The velocity separation of each cloud from the nearest spiral arm is introduced as a `concentration statistic'. Almost all of the GMCs are found near spiral arms. The density of smaller clouds is enhanced near spiral arms, but some clouds (~10%) are unassociated with any spiral arm. The median velocity separation between a GMC and the nearest spiral arm is 3.4+-0.6 km/s, whereas the median separation between smaller clouds and the nearest spiral arm is 5.5+-0.2 km/s.Comment: 11 pages, 3 figure

The Nature of the Gould Belt from a Fractal Analysis of its Stellar Population

The Gould Belt (GB) is a system of gas and young, bright stars distributed along a plane that is inclined with respect to the main plane of the Milky Way. Observational evidence suggests that the GB is our closest star formation complex, but its true nature and origin remain rather controversial. In this work we analyze the fractal structure of the stellar component of the GB. In order to do this, we tailor and apply an algorithm that estimates the fractal dimension in a precise and accurate way, avoiding both boundary and small data set problems. We find that early OB stars (of spectral types earlier than B4) in the GB have a fractal dimension very similar to that of the gas clouds in our Galaxy. On the contrary, stars in the GB of later spectral types show a larger fractal dimension, similar to that found for OB stars of both age groups in the local Galactic disk (LGD). This result seems to indicate that while the younger OB stars in the GB preserve the memory of the spatial structure of the cloud where they were born, older stars are distributed following a similar morphology as that found for the LGD stars. The possible causes for these differences are discussed.Comment: 20 pages including 7 figures and 1 table. ApJ (in press

Cloning by positive maps in von Neumann algebras

We investigate cloning in the general operator algebra framework in arbitrary dimension assuming only positivity instead of strong positivity of the cloning operation, generalizing thus results obtained so far under that stronger assumption. The weaker positivity assumption turns out quite natural when considering cloning in the general C∗-algebra framework

Chandra observation of the central galaxies in A1060 cluster of galaxies

Chandra observation of the central region of the A1060 cluster of galaxies resolved X-ray emission from two giant elliptical galaxies, NGC 3311 and NGC 3309. The emission from these galaxies consists of two components, namely the hot interstellar medium (ISM) and the low-mass X-ray binaries (LMXBs). We found the spatial extent of the ISM component was much smaller than that of stars for both galaxies, while the ratios of X-ray to optical blue-band luminosities were rather low but within the general scatter for elliptical galaxies. After subtracting the LMXB component, the ISM is shown to be in pressure balance with the intracluster medium of A1060 at the outer boundary of the ISM. These results imply that the hot gas supplied from stellar mass loss is confined by the external pressure of the intracluster medium, with the thermal conduction likely to be suppressed. The cD galaxy NGC 3311 does not exhibit the extended potential structure which is commonly seen in bright elliptical galaxies, and we discuss the possible evolution history of the very isothermal cluster A1060.Comment: 12 pages, 7 figures, Latex2e(emulateapj5), accepted in Ap

Environment Induced Entanglement in Markovian Dissipative Dynamics

We show that two, non interacting 2-level systems, immersed in a common bath, can become mutually entangled when evolving according to a Markovian, completely positive reduced dynamics.Comment: 4 pages, LaTex, no figures, added reference

Completely positive maps with memory

The prevailing description for dissipative quantum dynamics is given by the Lindblad form of a Markovian master equation, used under the assumption that memory effects are negligible. However, in certain physical situations, the master equation is essentially of a non-Markovian nature. This paper examines master equations that possess a memory kernel, leading to a replacement of white noise by colored noise. The conditions under which this leads to a completely positive, trace-preserving map are discussed for an exponential memory kernel. A physical model that possesses such an exponential memory kernel is presented. This model contains a classical, fluctuating environment based on random telegraph signal stochastic variables.Comment: 4 page

Symplectic evolution of Wigner functions in markovian open systems

The Wigner function is known to evolve classically under the exclusive action of a quadratic hamiltonian. If the system does interact with the environment through Lindblad operators that are linear functions of position and momentum, we show that the general evolution is the convolution of the classically evolving Wigner function with a phase space gaussian that broadens in time. We analyze the three generic cases of elliptic, hyperbolic and parabolic Hamiltonians. The Wigner function always becomes positive in a definite time, which is shortest in the hyperbolic case. We also derive an exact formula for the evolving linear entropy as the average of a narrowing gaussian taken over a probability distribution that depends only on the initial state. This leads to a long time asymptotic formula for the growth of linear entropy.Comment: this new version treats the dissipative cas