Sonic analog of gravitational black holes in Bose-Einstein condensates

It is shown that, in dilute-gas Bose-Einstein condensates, there exist both dynamically stable and unstable configurations which, in the hydrodynamic limit, exhibit a behavior resembling that of gravitational black holes. The dynamical instabilities involve creation of quasiparticle pairs in positive and negative energy states, as in the well-known suggested mechanism for black hole evaporation. We propose a scheme to generate a stable sonic black hole in a ring trap.Comment: RevTeX 3.1, 1 figure, 4 page

Deformed Density Matrix and Generalized Uncertainty Relation in Thermodynamics

A generalization of the thermodynamic uncertainty relations is proposed. It is done by introducing of an additional term proportional to the interior energy into the standard thermodynamic uncertainty relation that leads to existence of the lower limit of inverse temperature. The authors are of the opinion that the approach proposed may lead to proof of these relations. To this end, the statistical mechanics deformation at Planck scale. The statistical mechanics deformation is constructed by analogy to the earlier quantum mechanical results. As previously, the primary object is a density matrix, but now the statistical one. The obtained deformed object is referred to as a statistical density pro-matrix. This object is explicitly described, and it is demonstrated that there is a complete analogy in the construction and properties of quantum mechanics and statistical density matrices at Plank scale (i.e. density pro-matrices). It is shown that an ordinary statistical density matrix occurs in the low-temperature limit at temperatures much lower than the Plank's. The associated deformation of a canonical Gibbs distribution is given explicitly.Comment: 15 pages,no figure

Large Solar Neutrino Mixing in an Extended Zee Model

The Zee model, which employs the standard Higgs scalar ($\phi$) with its duplicate ($\phi^\prime$) and a singly charged scalar ($h^+$), can utilize two global symmetries associated with the conservation of the numbers of $\phi$ and $\phi^\prime$, $N_{\phi,\phi^\prime}$, where $N_\phi+N_{\phi^\prime}$ coincides with the hypercharge while $N_\phi-N_{\phi^\prime}$ ($\equiv X$) is a new conserved charge, which is identical to $L_e-L_\mu-L_\tau$ for the left-handed leptons. Charged leptons turn out to have $e$-$\mu$ and $e$-$\tau$ mixing masses, which are found to be crucial for the large solar neutrino mixing. In an extended version of the Zee model with an extra triplet Higgs scalar (s), neutrino oscillations are described by three steps: 1) the maximal atmospheric mixing is induced by democratic mass terms supplied by $s$ with $X$=2 that can initiate the type II seesaw mechanism for the smallness of these masses; 2) the maximal solar neutrino mixing is triggered by the creation of radiative masses by $h^+$ with $X$ = 0; 3) the large solar neutrino mixing is finally induced by a $\nu_\mu$-$\nu_\tau$ mixing arising from the rotation of the radiative mass terms as a result of the diagonalization that converts $e$-$\mu$ and $e$-$\tau$ mixing masses into the electron mass.Comment: RevTex, 10 pages including one figure page, to be published in Int. J. Mod. Phys. A (2002

CO and CH3OH observations of the BHR71 outflows with APEX

Context : Highly-collimated outflows are believed to be the earliest stage in outflow evolution, so their study is essential for understanding the processes driving outflows. The BHR71 Bok globule is known to harbour such a highly-collimated outflow, which is powered by a protostar belonging to a protobinary system. Aims : We aimed at investigating the interaction of collimated outflows with the ambient molecular cloud by using molecular tracers. Methods : We mapped the BHR71 highly-collimated outflow in CO(3-2) with the APEX telescope, and observed several bright points of the outflow in the molecular transitions CO(4-3), 13CO(3-2), C18O(3-2), and CH3OH(7-6). We use an LVG code to characterise the temperature enhancements in these regions. Results : In our CO(3-2) map, the second outflow driven by IRS2, which is the second source of the binary system, is completely revealed and shown to be bipolar. We also measure temperature enhancements in the lobes. The CO and methanol LVG modelling points to temperatures between 30 and 50K in the IRS1 outflow, while the IRS2 outflow seems to be warmer (up to 300K).Comment: 4 pages, 5 Figures, accepted by A&A Letters, to appear in the APEX First results special issu

Exact bounds for distributed graph colouring

We prove exact bounds on the time complexity of distributed graph colouring. If we are given a directed path that is properly coloured with $n$ colours, by prior work it is known that we can find a proper 3-colouring in $\frac{1}{2} \log^*(n) \pm O(1)$ communication rounds. We close the gap between upper and lower bounds: we show that for infinitely many $n$ the time complexity is precisely $\frac{1}{2} \log^* n$ communication rounds.Comment: 16 pages, 3 figure

Quantum evolution according to real clocks

We characterize good clocks, which are naturally subject to fluctuations, in statistical terms. We also obtain the master equation that governs the evolution of quantum systems according to these clocks and find its general solution. This master equation is diffusive and produces loss of coherence. Moreover, real clocks can be described in terms of effective interactions that are nonlocal in time. Alternatively, they can be modeled by an effective thermal bath coupled to the system.Comment: RevTeX 3.01, 6 page

Sonic black holes in dilute Bose-Einstein condensates

The sonic analog of a gravitational black hole in dilute-gas Bose-Einstein condensates is investigated. It is shown that there exist both dynamically stable and unstable configurations which, in the hydrodynamic limit, exhibit behaviors completely analogous to that of gravitational black holes. The dynamical instabilities involve the creation of quasiparticle pairs in positive and negative energy states. We illustrate these features in two qualitatively different one-dimensional models, namely, a long, thin condensate with an outcoupler laser beam providing an "atom sink" and a tight ring-shaped condensate. We also simulate the creation of a stable sonic black hole by solving the Gross-Pitaevskii equation numerically for a condensate subject to a trapping potential which is adiabatically deformed. A sonic black hole could, in this way, be created experimentally with state-of-the-art or planned technology

Is there a problem with quantum wormhole states in N=1 Supergravity?

The issue concerning the existence of wormhole states in locally supersymmetric minisuperspace models with matter is addressed. Wormhole states are apparently absent in models obtained from the more general theory of N=1 supergravity with supermatter. A Hartle-Hawking type solution can be found, even though some terms (which are scalar field dependent) cannot be determined in a satisfactory way. A possible cause is investigated here. As far as the wormhole situation is concerned, we argue here that the type of Lagrange multipliers and fermionic derivative ordering used can make a difference. A proposal is made for supersymmetric quantum wormholes to also be invested with a Hilbert space structure, associated with a maximal analytical extension of the corresponding minisuperspace.is concerned, we argue here that the type of Lagrange multipliers and fermionic derivative ordering used can make a difference. A proposal is made for supersymmetric quantum wormholes to also be invested with a Hilbert space structure, associated with a maximal analytical extension of the corresponding minisuperspace.Comment: 22 pages, TeX (some font problems may occur, just press Return), Based on a essay submitted to the 1995 ravity Research Foundation Awards, accepted in G.R.