Entanglement dynamics via semiclassical propagators in systems of two spins

We analyze the dynamical generation of entanglement in systems of two interacting spins initially prepared in a product of spin coherent states. For arbitrary time-independent Hamiltonians, we derive a semiclassical expression for the purity of the reduced density matrix as function of time. The final formula, subsidiary to the linear entropy, shows that the short-time dynamics of entanglement depends exclusively on the stability of trajectories governed by the underlying classical Hamiltonian. Also, this semiclassical measure is shown to reproduce the general properties of its quantum counterpart and give the expected result in the large spin limit. The accuracy of the semiclassical formula is further illustrated in a problem of phase exchange for two particles of spin $j$.Comment: 10 page

Rural to Urban Population Density Scaling of Crime and Property Transactions in English and Welsh Parliamentary Constituencies

Urban population scaling of resource use, creativity metrics, and human behaviors has been widely studied. These studies have not looked in detail at the full range of human environments which represent a continuum from the most rural to heavily urban. We examined monthly police crime reports and property transaction values across all 573 Parliamentary Constituencies in England and Wales, finding that scaling models based on population density provided a far superior framework to traditional population scaling. We found four types of scaling: i ) non-urban scaling in which a single power law explained the relationship between the metrics and population density from the most rural to heavily urban environments, ii ) accelerated scaling in which high population density was associated with an increase in the power-law exponent, iii ) inhibited scaling where the urban environment resulted in a reduction in the power-law exponent but remained positive, and iv ) collapsed scaling where transition to the high density environment resulted in a negative scaling exponent. Urban scaling transitions, when observed, took place universally between 10 and 70 people per hectare. This study significantly refines our understanding of urban scaling, making clear that some of what has been previously ascribed to urban environments may simply be the high density portion of non-urban scaling. It also makes clear that some metrics undergo specific transitions in urban environments and these transitions can include negative scaling exponents indicative of collapse. This study gives promise of far more sophisticated scale adjusted metrics and indicates that studies of urban scaling represent a high density subsection of overall scaling relationships which continue into rural environments

Regge-like quark-antiquark excitations in the effective-action formalism

Radial excitations of the quark-antiquark string sweeping the Wilson-loop area are considered in the framework of the effective-action formalism. Identifying these excitations with the daughter Regge trajectories, we find corrections which they produce to the constituent quark mass. The energy of the quark-antiquark pair turns out to be mostly saturated by the constituent quark masses, rather than by the elongation of the quark-antiquark string. Specifically, while the constituent quark mass turns out to increase as the square root of the radial-excitation quantum number, the energy of the string increases only as the fourth root of that number.Comment: 11 pages, 2 figures, talk given at the International Workshop on QCD Green's Functions, Confinement and Phenomenology, 5-9 September 2011, Trento, Ital

The Electronic States of Two Oppositely doped Mott Insulators Bilayers

We study the effect of Coulomb interaction between two oppositely doped low-dimensional tJ model systems. We exactly show that, in the one-dimensional case, an arbitrarily weak interaction leads to the formation of charge neutral electron-hole pairs. We then use two different mean-field theories to address the two-dimensional case, where inter-layer excitons also form and condense. We propose that this results in new features which have no analog in single layers, such as the emergence of an insulating spin liquid phase. Our simple bilayer model might have relevance to the physics of doped Mott insulator interfaces and of the new four layer Ba2CaCu4O8 compound.Comment: 4 pages, 1 figur

Finite energy spectral function of an anisotropic 2D system of coupled Hubbard chains

We study the crossover from the one-dimensional to the two-dimensional Hubbard model in the photoemission spectra of weakly coupled chains. The chains with on-site repulsion are treated using the spin-charge factorized wave function, that is known to provide an essentially exact description of the chain in the strong coupling limit. The hoppings between the chains are considered as a perturbation. We calculate the dynamical spectral function at all energies in the random-phase approximation, by resuming an infinite set of diagrams. Even though the hoppings drive the system from a fractionalized Luttinger-liquid-like system to a Fermi-liquid-like system at low energies, significant characteristics of the one-dimensional system remain in the two-dimensional system. Furthermore, we find that introducing (frustrating) hoppings beyond the nearest neighbor one, the interference effects increase the energy and momentum range of the one--dimensional character.Comment: 22 pages, 10 figure

Nonlinear gyrofluid computation of edge localised ideal ballooning modes

Three dimensional electromagnetic gyrofluid simulations of the ideal ballooning mode blowout scenario for tokamak edge localized modes (ELMs) are presented. Special emphasis is placed on energetic diagnosis, examining changes in the growth rate in the linear, overshoot, and decay phases. The saturation process is energy transfer to self generated edge turbulence which exhibits an ion temperature gradient (ITG) mode structure. Convergence in the decay phase is found only if the spectrum reaches the ion gyroradius. The equilibrium is a self consistent background whose evolution is taken into account. Approximately two thirds of the total energy in the edge layer is liberated in the blowout. Parameter dependence with respect to plasma pressure and the ion gyroradius is studied. Despite the violent nature of the short-lived process, the transition to nonlinearity is very similar to that found in generic tokamak edge turbulence.Comment: The following article has been submitted to Physics of Plasmas. After it is published, it will be found at http://pop.aip.org