We analyze analytically the effect of congestion costs within a physically relevant, yet exactly solvable, network model featuring central hubs. These costs lead to a competition between centralized and decentralized transport pathways. In stark contrast to conventional no-cost networks, there now exists an optimal number of connections to the central hub in order to minimize the shortest path. Our results shed light on an open problem in biology, informatics, and sociology, concerning the extent to which decentralized versus centralized design benefits real-world complex networks.
We show that abrupt structural transitions can arise in functionally optimal networks, driven by small changes in the level of transport congestion. Our results offer an explanation as to why so many diverse species of network structure arise in Nature (e.g. fungal systems) under essentially the same environmental conditions. Our findings are based on an exactly solvable model system which mimics a variety of biological and social networks. We then extend our analysis by introducing a novel renormalization scheme involving cost motifs, to describe analytically the average shortest path across multiple-ring-and-hub networks. As a consequence, we uncover a 'skin effect' whereby the structure of the inner multi-ring core can cease to play any role in terms of determining the average shortest path across the network.
Birds are exposed to Pb by oral ingestion of spent Pb shot as grit. A paucity of data exists for retention and clearance of these particles in the bird gastrointestinal tract. In the current study, northern bobwhite quail (Colinus virginianus) were orally gavaged with 1, 5, or 10 Pb shot pellets, of 2-mm diameter, and radiographically followed over time. Blood Pb levels and other measures of toxicity were collected, to correlate with pellet retention. Quail dosed with either 5 or 10 pellets exhibited morbidity between weeks 1 and 2 and were removed from further study. Most of the Pb pellets were absorbed or excreted within 14 d of gavage, independent of dose. Pellet size in the ventriculus decreased over time in radiographs, suggesting dissolution caused by the acidic pH. Birds dosed with one pellet showed mean blood Pb levels that exceeded 1,300 µg/dl at week 1, further supporting dissolution in the gastrointestinal tract. Limited signs of toxicity were seen in the one-pellet birds; however, plasma δ-aminolevulinic acid dehydratase (d-ALAD) activity was persistently depressed, suggesting possible impaired hematological function.
Information about quantum phase transitions in conventional condensed matter systems, must be sought by probing the matter system itself. By contrast, we show that mixed matter-light systems offer a distinct advantage in that the photon field carries clear signatures of the associated quantum critical phenomena. Having derived an accurate, size-consistent Hamiltonian for the photonic field in the well-known Dicke model, we predict striking behavior of the optical squeezing and photon statistics near the phase transition. The corresponding dynamics resemble those of a degenerate parametric amplifier. Our findings boost the motivation for exploring exotic quantum phase transition phenomena in atom-cavity, nanostructure-cavity, and nanostructure-photonic-band-gap systems.PACS numbers: 42.50.Fx, 32.80.t, 75.10.Nr There are several theoretical models which are currently attracting attention, based on the possible insights that they offer into the nature of Quantum Phase Transitions (QPTs). One of these is the Dicke model which was originally developed in quantum optics, together with its recent generalizations [1,2,3]. In practice, such exotic quantum phenomena can only be studied experimentally if the system's many-body quantum state can be probed in some way [4]. Unfortunately in condensed matter systems, such probing is typically indirect since one cannot 'see' many-body quantum spin states.Here we predict that in light-matter systems approximating to the Dicke model -such as atom-cavity and nanostructure-cavity systems [1, 2, 3, 4] -the statistical properties of the photon field offer direct and striking signatures of the quantum critical phenomena underlying a QPT. Our results are based on an accurate, size-consistent calculation of the statistical properties of the photon field in the Dicke model, and help motivate the exploration of such exotic quantum phenomena in atom-cavity, nanostructure-cavity, and nanostructure-photonic-band-gap systems [1,2,3,4]. In addition to the results themselves, our theoretical approach presents a number of distinct features over previous works [1, 2, 3, 4]: (1) we avoid using canonical perturbation schemes and projection methods, which can suffer from inconsistent size-dependencies as one approaches the thermodynamic limit [5]. Instead we adopt a similar renormalization-like scheme to Ref. [3], but take the opposite viewpoint by renormalizing the dynamics of the photon field as opposed to the matter system.(2) Our approach shows the direct connection between the Dicke model and a degenerate parametric optical amplifier. (3) In addition to explicitly reproducing the correct scaling near the critical point, we are able to show that striking signatures arise in a number of key statistical properties associated with the photon field. (4) We are able to show the optical manifestation of a quasi-integrable to quantum chaotic transition near the QPT.The Dicke model describes the interaction between a single-mode photon field and N non-interacting two-level systems [1,3]:whereare the c...
Recent advances in nanostructure fabrication and optical control, suggest that it will soon be possible to prepare collections of interacting two-level systems (i.e. qubits) within an optical cavity. Here we show theoretically that such systems could exhibit novel phase transition phenomena involving spin-glass phases. By contrast with traditional realizations using magnetic solids, these phase transition phenomena are associated with both matter and radiation subsystems. Moreover the various phase transitions should be tunable simply by varying the matter-radiation coupling strength.PACS numbers: 42.50. Fx, 75.10.Nr, Condensed matter physicists are keen to identify experimental realizations of Ising-like Hamiltonians involving populations of interacting two-level objects (i.e. spins) [1]. Exotic phases such as a spin-glass are of particular interest [2]. Experimental studies of spin-glasses have focused on solids containing arrays of magnetic ions [1]. However the laws of Nature limit the range of exotic behaviors that such solids can exhibit, since it is very hard to engineer the magnitude, anisotropy, range and/or disorder of the spin-spin interaction in such systems. In the seemingly unrelated fields of atomic, nanostructure and optical physics, there have been rapid advances in the fabrication and manipulation of effective two-level systems (more commonly referred to as qubits) using atoms, semiconductor quantum dots, and superconducting nanostructures [4,5,6, 7,8,9]. In particular, controlled qubit-cavity coupling has been demonstrated experimentally between such systems and a surrounding optical cavity [4,5,6, 7,8,9,10]. In quantum dots systems, in particular, the effective spin-spin (i.e. qubitqubit) interaction can in principle be tailored by adjusting the quantum dots' size, shape, separation, orientation and the background electrostatic screening. Furthermore, the interaction's anisotropy can be engineered by choosing asymmetric dot shapes. Disorder in the qubitqubit interactions will arise naturally for self-assembled dots, or can be introduced artificially by varying the individual dot positions during fabrication [9,11].Motivated by these recent experimental advances, we study the phase transitions which could arise in such multi-qubit-cavity systems. We uncover novel realizations of spin-glasses [2] in which the phase transition phenomena are associated with the spin (i.e. matter) and boson (i.e. photon) subsystems. The resulting phase diagrams can be explored experimentally by varying the qubit-cavity coupling strength λ, e.g. by re-positioning the center of the cavity around the nanostructure array, changing its orientation, or tuning the cavity Q-factor [7]. In addition to opening up the study of these important condensed matter systems to the nano-optical community, our results help strengthen the theoretical connection which seems to be emerging between multiqubit-cavity systems and spin-spin systems [12,13]. Given the above experimental considerations, we will introduce a generalization of t...
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