Covariant statistical mechanics and the stress-energy tensor

After recapitulating the covariant formalism of equilibrium statistical mechanics in special relativity and extending it to the case of a non-vanishing spin tensor, we show that the relativistic stress-energy tensor at thermodynamical equilibrium can be obtained from a functional derivative of the partition function with respect to the inverse temperature four-vector \beta. For usual thermodynamical equilibrium, the stress-energy tensor turns out to be the derivative of the relativistic thermodynamic potential current with respect to the four-vector \beta, i.e. T^{\mu \nu} = - \partial \Phi^\mu/\partial \beta_\nu. This formula establishes a relation between stress-energy tensor and entropy current at equilibrium possibly extendable to non-equilibrium hydrodynamics.Comment: 4 pages. Final version accepted for publication in Phys. Rev. Let

Agglomeration externalities, innovation and regional growth: Theoretical perspectives and meta-analysis

Technological change and innovation and are central to the quest for regional development. In the globally-connected knowledge-driven economy, the relevance of agglomeration forces that rely on proximity continues to increase, paradoxically despite declining real costs of information, communication and transportation. Globally, the proportion of the population living in cities continues to grow and sprawling cities remain the engines of regional economic transformation. The growth of cities results from a complex chain that starts with scale, density and geography, which then combine with industrial structure characterised by its extent of specialisation, competition and diversity, to yield innovation and productivity growth that encourages employment expansion, and further urban growth through inward migration. This paper revisits the central part of this virtuous circle, namely the Marshall-Arrow-Romer externalities (specialisation), Jacobs externalities (diversity) and Porter externalities (competition) that have provided alternative explanations for innovation and urban growth. The paper evaluates the statistical robustness of evidence for such externalities presented in 31 scientific articles, all building on the seminal work of Glaeser et al. (1992). We aim to explain variation in estimation results using study characteristics by means of ordered probit analysis. Among the results, we find that the impact of diversity depends on how it is measured and that diversity is important for the high-tech sector. High population density increases the chance of finding positive effects of specialisation on growth. More recent data find more positive results for both specialization and diversity, suggesting that agglomeration externalities become more important over time. Finally, primary study results depend on whether or not the externalities are considered jointly and on other features of the regression model specification

Synthesis and viscosity behavior of poly(γ-p-biphenylmethyl-L-glutamate) in benzene/dichloroacetic acid mixtures, a comparison with poly(γ-benzyl-L-glutamate)

The synthesis of poly(γ-p-biphenylmethyl-L-glutamate), PBPLG, (poly{L-imino-1-[2-(4-biphenylylmethoxycarbonyl)ethyl]-2-oxoethylene}), (1d) is described. The viscosity behavior of this polymer in benzene/dichloroacetic acid mixtures (c=0,2.10 -3 - 1,4.10 -3 g/cm3) at 25°CC is investigated. The results are compared with measurements on poly(γ-benzyl-L-glutamate), PBLG, (poly[L-imino-1-(2-benzyloxycarbonylethyl)-2-oxoethylene]), (1c) under the same conditions. A transition from a rigid hydrogen bonded helix to a random solvated coil occurs in two stages for both: PBPLG (first stage 0-55%, second stage 55-100% dichloroacetic acid) and PBLG (first stage 0-70%, second stage 70-100% dichloroacetic acid). \ud Therefore, the introduction of a p-phenyl substituent in PBLG leads to a less stable helix in benzene/dichloroacetic acid mixtures. \ud The stability and viscosity behavior of PBLG in benzene/dichloroacetic acid mixtures (c=0,2.10 - 3 - 1,4.10 - 3g/cm3) is quite similar to the behavior of PBLG in m-cresol/dichloroacetic acid mixtures (c=1,0.10 - 3 - 4,0.10 - 3 g/cm3)

Nonpolar resistive switching in Cu/SiC/Au non-volatile resistive memory devices

Amorphous silicon carbide (a-SiC) based resistive memory (RM) Cu/a-SiC/Au devices were fabricated and their resistive switching characteristics investigated. All four possible modes of nonpolar resistive switching were achieved with ON/OFF ratio in the range 10 6-10 8. Detailed current-voltage I-V characteristics analysis suggests that the conduction mechanism in low resistance state is due to the formation of metallic filaments. Schottky emission is proven to be the dominant conduction mechanism in high resistance state which results from the Schottky contacts between the metal electrodes and SiC. ON/OFF ratios exceeding 10 7 over 10 years were also predicted from state retention characterizations. These results suggest promising application potentials for Cu/a-SiC/Au RM

Speed limits for quantum gates in multi-qubit systems

We use analytical and numerical calculations to obtain speed limits for various unitary quantum operations in multiqubit systems under typical experimental conditions. The operations that we consider include single-, two-, and three-qubit gates, as well as quantum-state transfer in a chain of qubits. We find in particular that simple methods for implementing two-qubit gates generally provide the fastest possible implementations of these gates. We also find that the three-qubit Toffoli gate time varies greatly depending on the type of interactions and the system's geometry, taking only slightly longer than a two-qubit controlled-NOT (CNOT) gate for a triangle geometry. The speed limit for quantum-state transfer across a qubit chain is set by the maximum spin-wave speed in the chain.Comment: 7 pages (two-column), 2 figures, 2 table

Relativistic viscoelastic fluid mechanics

A detailed study is carried out for the relativistic theory of viscoelasticity which was recently constructed on the basis of Onsager's linear nonequilibrium thermodynamics. After rederiving the theory using a local argument with the entropy current, we show that this theory universally reduces to the standard relativistic Navier-Stokes fluid mechanics in the long time limit. Since effects of elasticity are taken into account, the dynamics at short time scales is modified from that given by the Navier-Stokes equations, so that acausal problems intrinsic to relativistic Navier-Stokes fluids are significantly remedied. We in particular show that the wave equations for the propagation of disturbance around a hydrostatic equilibrium in Minkowski spacetime become symmetric hyperbolic for some range of parameters, so that the model is free of acausality problems. This observation suggests that the relativistic viscoelastic model with such parameters can be regarded as a causal completion of relativistic Navier-Stokes fluid mechanics. By adjusting parameters to various values, this theory can treat a wide variety of materials including elastic materials, Maxwell materials, Kelvin-Voigt materials, and (a nonlinearly generalized version of) simplified Israel-Stewart fluids, and thus we expect the theory to be the most universal description of single-component relativistic continuum materials. We also show that the presence of strains and the corresponding change in temperature are naturally unified through the Tolman law in a generally covariant description of continuum mechanics.Comment: 52pages, 11figures; v2: minor corrections; v3: minor corrections, to appear in Physical Review E; v4: minor change