Pure States, Mixed States and Hawking Problem in Generalized Quantum Mechanics

This paper is the continuation of a study into the information paradox problem started by the author in his earlier works. As previously, the key instrument is a deformed density matrix in quantum mechanics of the early universe. It is assumed that the latter represents quantum mechanics with fundamental length. It is demonstrated that the obtained results agree well with the canonical viewpoint that in the processes involving black holes pure states go to the mixed ones in the assumption that all measurements are performed by the observer in a well-known quantum mechanics. Also it is shown that high entropy for Planck remnants of black holes appearing in the assumption of the Generalized Uncertainty Relations may be explained within the scope of the density matrix entropy introduced by the author previously. It is noted that the suggested paradigm is consistent with the Holographic Principle. Because of this, a conjecture is made about the possibility for obtaining the Generalized Uncertainty Relations from the covariant entropy bound at high energies in the same way as R. Bousso has derived Heisenberg uncertainty principle for the flat space.Comment: 12 pages,no figures,some corrections,new reference

The Universe as a Nonuniform Lattice in the Finite-Dimensional Hypercube II.Simple Cases of Symmetry Breakdown and Restoration

This paper continues a study of field theories specified for the nonuniform lattice in the finite-dimensional hypercube with the use of the earlier described deformation parameters. The paper is devoted to spontaneous breakdown and restoration of symmetry in simple quantum-field theories with scalar fields. It is demonstrated that an appropriate deformation opens up new possibilities for symmetry breakdown and restoration. To illustrate, at low energies it offers high-accuracy reproducibility of the same results as with a nondeformed theory. In case of transition from low to higher energies and vice versa it gives description for new types of symmetry breakdown and restoration depending on the rate of the deformation parameter variation in time, and indicates the critical points of the previously described lattice associated with a symmetry restoration. Besides, such a deformation enables one to find important constraints on the initial model parameters having an explicit physical meaning.Comment: 9 pages,Revte

#Bigbirds never die: Understanding social dynamics of emergent hashtag

We examine the growth, survival, and context of 256 novel hashtags during the 2012 U.S. presidential debates. Our analysis reveals the trajectories of hashtag use fall into two distinct classes: “winners” that emerge more quickly and are sustained for longer periods of time than other “also-rans” hashtags. We propose a “conversational vibrancy” framework to capture dynamics of hashtags based on their topicality, interactivity, diversity, and prominence. Statistical analyses of the growth and persistence of hashtags reveal novel relationships between features of this framework and the relative success of hashtags. Specifically, retweets always contribute to faster hashtag adoption, replies extend the life of “winners” while having no effect on “also-rans.” This is the first study on the lifecycle of hashtag adoption and use in response to purely exogenous shocks. We draw on theories of uses and gratification, organizational ecology, and language evolution to discuss these findings and their implications for understanding social influence and collective action in social media more generally

Quantum Mechanics at Planck's scale and Density Matrix

In this paper Quantum Mechanics with Fundamental Length is chosen as Quantum Mechanics at Planck's scale. This is possible due to the presence in the theory of General Uncertainty Relations. Here Quantum Mechanics with Fundamental Length is obtained as a deformation of Quantum Mechanics. The distinguishing feature of the proposed approach in comparison with previous ones, lies on the fact that here density matrix subjects to deformation whereas so far commutators have been deformed. The density matrix obtained by deformation of quantum-mechanical density one is named throughout this paper density pro-matrix. Within our approach two main features of Quantum Mechanics are conserved: the probabilistic interpretation of the theory and the well-known measuring procedure corresponding to that interpretation. The proposed approach allows to describe dynamics. In particular, the explicit form of deformed Liouville's equation and the deformed Shr\"odinger's picture are given. Some implications of obtained results are discussed. In particular, the problem of singularity, the hypothesis of cosmic censorship, a possible improvement of the definition of statistical entropy and the problem of information loss in black holes are considered. It is shown that obtained results allow to deduce in a simple and natural way the Bekenstein-Hawking's formula for black hole entropy in semiclassical approximation.Comment: 18 pages,Latex,new reference

Mechanism of Modifying Ballistic Properties of Propellant Formulations by Fast-Burning Inclusions

The combustion characteristics of binary compositions of fast-burning energetic materials (FBEM) with main composite propellant components like ammonium perchlorate (AP) and polymeric binders have been studied in a constant pressure bomb, and combustion mechanism has been proposed. Combustion behaviour of composite propellants containing granulated FBEM of different particle sizes has been investigated. FBEM additives as high as 40 per cent of fine particle size to a composite propellant have not been shown to influence markedly the burning rate, whereas incorporation of FBEM grains of 500 micrometer particle size allows not only a considerable increase in the burning rate but also modifies the burning rate-pressure dependence. A mechanism of combustion of propellant compositions containing FBEM grains has been evolved that allows criteria for FBEM performance and combustion stability

Superaging correlation function and ergodicity breaking for Brownian motion in logarithmic potentials

We consider an overdamped Brownian particle moving in a confining asymptotically logarithmic potential, which supports a normalized Boltzmann equilibrium density. We derive analytical expressions for the two-time correlation function and the fluctuations of the time-averaged position of the particle for large but finite times. We characterize the occurrence of aging and nonergodic behavior as a function of the depth of the potential, and support our predictions with extensive Langevin simulations. While the Boltzmann measure is used to obtain stationary correlation functions, we show how the non-normalizable infinite covariant density is related to the super-aging behavior.Comment: 16 pages, 6 figure