Momentum-space analysis of multipartite entanglement at quantum phase transitions

We investigate entanglement properties at quantum phase transitions of an integrable extended Hubbard model in the momentum space representation. Two elementary subsystems are recognized: the single mode of an electron, and the pair of modes (electrons coupled through the eta-pairing mechanism). We first detect the two/multi-partite nature of each quantum phase transition by a comparative study of the singularities of Von Neumann entropy and quantum mutual information. We establish the existing relations between the correlations in the momentum representation and those exhibited in the complementary picture: the direct lattice representation. The presence of multipartite entanglement is then investigated in detail through the Q-measure, namely a generalization of the Meyer-Wallach measure of entanglement. Such a measure becomes increasingly sensitive to correlations of a multipartite nature increasing the size of the reduced density matrix. In momentum space, we succeed in obtaining the latter for our system at arbitrary size and we relate its behaviour to the nature of the various QPTs.Comment: 8 pages, 4 figure

An intercomparison of two turbulence closure schemes and four parameterizations for stochastic dispersion models

Two Lagrangian particle models, developed by Luhar and Britter (Atmos. Environ., 23 (1989) 1191) and Weil (J. Atmos. Sci., 47 (1990) 501), satisfying the “well-mixed” condition as prescribed by Thomson (J. Fluid. Mech., 180 (1987) 529), are compared. They differ in the closure scheme used in calculating the probability density function of the random forcing in a convective boundary layer. Four different turbulent parameterizations were used as input to both models. Their performances are evaluated against one of the well-known Willis and Deardorff water tank experiments (Atmos. Environ., 12 (1978) 1305). Predicted and measured ground-level concentrations (g.l.c.), maximum g.l.c. distance, mean plume height and plume vertical spread are presented and discussed

Structure of quantum correlations in momentum space and off diagonal long range order in eta pairing and BCS states

The quantum states built with the eta paring mechanism i.e., eta pairing states, were first introduced in the context of high temperature superconductivity where they were recognized as important example of states allowing for off-diagonal long-range order (ODLRO). In this paper we describe the structure of the correlations present in these states when considered in their momentum representation and we explore the relations between the quantum bipartite/multipartite correlations exhibited in k space and the direct lattice superconducting correlations. In particular, we show how the negativity between paired momentum modes is directly related to the ODLRO. Moreover, we investigate the dependence of the block entanglement on the choice of the modes forming the block and on the ODLRO; consequently we determine the multipartite content of the entanglement through the evaluation of the generalized "Meyer Wallach" measure in the direct and reciprocal lattice. The determination of the persistency of entanglement shows how the network of correlations depicted exhibits a self-similar structure which is robust with respect to "local" measurements. Finally, we recognize how a relation between the momentum-space quantum correlations and the ODLRO can be established even in the case of BCS states.Comment: 11 pages, 3 figure

MICROSPRAY SIMULATION OF DENSE GAS DISPERSION IN COMPLEX TERRAIN

An extended validation of the new Lagrangian particle model MicroSpray version for dense gas simulation is proposed. MicroSpray simulates the dense gas dispersion in situations characterized by the presence of buildings, other obstacles, complex terrain, and possible occurrence of low wind speed conditions. Its performances are compared to a chlorine railway accident (Macdona), to a field experiment (Kit Fox) and to an atmospheric CFD model

A model based on Heisenberg’s theory for the eddy diffusivity in decaying turbulence applied to the residual layer

The problemof the theoretical derivation of a parameterization for the eddy diffusivity in decaying turbulence is addressed. This derivation makes use of the dynamical equation for the energy spectrum density and the classical statistical diffusion theory. The starting point is Heisenberg’s elementary decaying turbulence theory. The main assumption is related to the identification of a frequency, lying in the inertial subrange, characterizing the inertial energy transfer among eddies of different size. The resulting eddy diffusivity parameterization is then applied to the decay of convective turbulence in the residual layer. Besides the intrinsic scientific interest, this topic has relevance for mesoscale transport and diffusion simulations. The resulting expression for the eddy diffusivity cannot be solved analytically. For this reason an algebraic approximated formulation, giving nearly the same results as the exact expression, is also proposed

Estimation of emission rate from experimental data

The estimation of the source pollutant strength is a relevant issue for atmospheric environment. This characterizes an inverse problem in the atmospheric pollution dispersion studies. In the inverse analysis, a time-dependent pollutant source is considered, where the location of such source term is assumed known. The inverse problem is formulated as a non-linear optimization approach, whose objective function is given by the least-square difference between the measured and simulated by the mathematical model, pollutant concentration, associated with a regularization operator. The forward problem is addressed by a Lagrangian model, and a quasi-Newton method is employed for minimizing the objective function. The second-order Tikhonov regularization is applied and the regularization parameter is computed by using the L-curve scheme. The inverse-problem methodology is verified with data from the tracer Copenhagen experiment

Symmetry breaking effects upon bipartite and multipartite entanglement in the XY model

We analyze the bipartite and multipartite entanglement for the ground state of the one-dimensional XY model in a transverse magnetic field in the thermodynamical limit. We explicitly take into account the spontaneous symmetry breaking in order to explore the relation between entanglement and quantum phase transitions. As a result we show that while both bipartite and multipartite entanglement can be enhanced by spontaneous symmetry breaking deep into the ferromagnetic phase, only the latter is affected by it in the vicinity of the critical point. This result adds to the evidence that multipartite, and not bipartite, entanglement is the fundamental indicator of long range correlations in quantum phase transitions.Comment: 13 pages, 19 figures, comments welcome. V2: small changes, published versio