Skeleton Diagrams Research Articles

Self-consistent Keldysh approach to quenches in the weakly interacting Bose-Hubbard model

We present a non-equilibrium Green's functional approach to study the dynamics following a quench in weakly interacting Bose Hubbard model (BHM). The technique is based on the self-consistent solution of a set of equations which represents a particular case of the most general set of Hedin's equations for the interacting single-particle Green's function. We use the ladder approximation as a skeleton diagram for the two-particle scattering amplitude useful, through the self-energy in the Dyson equation, for finding the interacting single-particle Green's function. This scheme is then implemented numerically by a parallelized code. We exploit this approach to study the correlation propagation after a quench in the interaction parameter, for one (1D) and two (2D) dimensions. In particular, we show how our approach is able to recover the crossover from ballistic to diffusive regime by increasing the boson-boson interaction. Finally we also discuss the role of a thermal initial state on the dynamics both for 1D and 2D Bose Hubbard models, finding that surprisingly at high temperature a ballistic evolution is restored.

Algebraic Lattices in QFT Renormalization

The structure of overlapping subdivergences, which appear in the perturbative expansions of quantum field theory, is analyzed using algebraic lattice theory. It is shown that for specific QFTs the sets of subdivergences of Feynman diagrams form algebraic lattices. This class of QFTs includes the Standard model. In kinematic renormalization schemes, in which tadpole diagrams vanish, these lattices are semimodular. This implies that the Hopf algebra of Feynman diagrams is graded by the coradical degree or equivalently that every maximal forest has the same length in the scope of BPHZ renormalization. As an application of this framework a formula for the counter terms in zero-dimensional QFT is given together with some examples of the enumeration of primitive or skeleton diagrams.

Some finite terms from ladder diagrams in three and four loop maximal supergravity

We consider the finite part of the leading local interactions in the low energy expansion of the four graviton amplitude from the ladder skeleton diagrams in maximal supergravity on T 2, at three and four loops. At three loops, we express the and amplitudes as integrals over the moduli space of an underlying auxiliary geometry. These amplitudes are evaluated exactly for special values of the the moduli of the auxiliary geometry, where the integrand simplifies. We also perform a similar analysis for the amplitude at four loops that arise from the ladder skeleton diagrams for a special value of a parameter in the moduli space of the auxiliary geometry. While the dependence of the amplitudes on the volume of the T 2 is very simple, the dependence on the complex structure of the T 2 is quite intricate. In some of the cases, the amplitude consists of terms each of which factorizes into a product of two invariant modular forms. While one of the factors is a non-holomorphic Eisenstein series, the other factor splits into a sum of modular forms each of which satisfies a Poisson equation on moduli space with source terms that are bilinear in the Eisenstein series. This leads to several possible perturbative contributions unto genus 5 in type II string theory on S1. Unlike the one and two loop supergravity analysis, these amplitudes also receive non-perturbative contributions from bound states of three D-(anti)instantons in the IIB theory.

High-order terms in the renormalized perturbation theory for the Anderson impurity model

We study the renormalized perturbation theory of the single-impurity Anderson model, particularly the high-order terms in the expansion of the self-energy in powers of the renormalized coupling $\tilde{U}$. Though the presence of counter-terms in the renormalized theory may appear to complicate the diagrammatics, we show how these can be seamlessly accommodated by carrying out the calculation order-by-order in terms of skeleton diagrams. We describe how the diagrams pertinent to the renormalized self-energy and four-vertex can be automatically generated, translated into integrals and numerically integrated. To maximize the efficiency of our approach we introduce a generalized $k$-particle/hole propagator, which is used to analytically simplify the resultant integrals and reduce the dimensionality of the integration. We present results for the self-energy and spectral density to fifth order in $\tilde{U}$, for various values of the model asymmetry, and compare them to a Numerical Renormalization Group calculation.

An effective hand vein feature extraction method

As a new authentication method developed years ago, vein recognition technology features the unique advantage of bioassay. This paper studies the specific procedure for the extraction of hand back vein characteristics. There are different positions used in the collecting process, so that a suitable intravenous regional orientation method is put forward, allowing the positioning area to be the same for all hand positions. In addition, to eliminate the pseudo vein area, the valley regional shape extraction operator can be improved and combined with multiple segmentation algorithms. The images should be segmented step by step, making the vein texture to appear clear and accurate. Lastly, the segmented images should be filtered, eroded, and refined. This process helps to filter the most of the pseudo vein information. Finally, a clear vein skeleton diagram is obtained, demonstrating the effectiveness of the algorithm. This paper presents a hand back vein region location method. This makes it possible to rotate and correct the image by working out the inclination degree of contour at the side of hand back.

A real-time thermal field theoretical analysis of Kubo-type shear viscosity: Numerical understanding with simple examples

A real-time thermal field theoretical calculation of shear viscosity has been described in the Kubo formalism for bosonic and fermionic medium. The two-point function of viscous-stress tensor in the lowest order provides one-loop skeleton diagram of boson or fermion field for bosonic or fermionic matter. According to the traditional diagrammatic technique of transport coefficients, the finite thermal width of boson or fermion is introduced in their internal lines during the evaluation of boson–boson or fermion–fermion loop diagram. These thermal widths of ϕ boson and ψ fermion are respectively obtained from the imaginary part of self-energy for ϕΦ and ψΦ loops, where interactions of higher mass Φ boson with ϕ and ψ are governed by the simple ϕϕΦ and [Formula: see text] interaction Lagrangian densities. A two-loop diagram, having same power of coupling constant as in the one-loop diagram, is deduced and its contribution appears much lower than the one-loop values of shear viscosity. Therefore, the one-loop results of Kubo-type shear viscosity may be considered as leading order results for this simple ϕϕΦ and [Formula: see text] interactions. This approximation is valid for any values of coupling constant and at the temperatures greater than the mass of constituent particles of the medium.

秦岭火地塘林区油松和华山松林乔木层净生产力与气候因子的关系

以秦岭火地塘林区油松(<em>Pinus tabulaeformis</em>)和华山松(<em>Pinus armandi</em>)林为研究对象,以其生物量及树高-胸径模型为基础,运用树木年轮宽度方法推算出1973年至2011年生物量和生产力年际动态,并通过相关分析和多元逐步回归分析探讨了油松和华山松林乔木层净生产力与温度、降水之间的关系.结果显示,该林区油松林和华山松林乔木层生物量39a间增长迅速,分别从1973年的15.32 t/hm²和7.53 t/hm²增长到2011年的175.97 t/hm²和130.98 t/hm²,平均年净生产力分别为4.18 t hm^-2 a^-1和3.20 t hm^-2 a^-1,油松林乔木层生物量和生产力均高于华山松林;气候分析表明年净生产力与降水关系不明显,与温度关系较为密切,随气温升高呈波动上升趋势:单月气候因子中上年7月温度、当年7月温度与油松林乔木层净生产力显著正相关,上年7月温度与华山松林乔木层净生产力显著正相关;油松林乔木层净生产力动态变化主要受1-7月平均温度影响,华山松林主要受5-7月平均温度影响;油松林生产力与温度因子的相关性高于华山松林.两种林型的生物量和生产力差异是由油松和华山松生物学特性所致.;The Qinling Mountains have some of the best sites for research on impact of climate change on forest growth in China. We selected two main forest types in the mountains, <em>Pinus tabulaeformis</em> and <em>Pinus armandi</em> forests, to explore relationships between net primary productivity (NPP) of the tree layer and climatic factors in order to understand response of the growth to climate change. Nine plots of <em>P. tabulaeformis</em> and fifteen plots of <em>P. armandi</em> forests were established at the Huoditang forest region in the Qinling Mountains. More than 20 cross increment cores were extracted from different trees at each plot. After being cross dated by the skeleton diagram method, tree ring widths of increment cores were measured with WINDENDRO tree ring system. Annual diameters of sample trees were calculated using tree ring widths. Regression equations between diameter at breast height (DBH) and height of <em>P. tabulaeformis</em> and <em>P. armandi</em> forests at the Huoditang forest region were used to estimate the annual biomass and NPP from 1973 to 2011. Then correlations were analyzed between NPP and climatic factors including monthly and seasonal temperature and precipitation. Multiple stepwise regression analysis was used to select the climatic factors with the most impact on the annual NPP of the two forest types. A relatively consistent dynamic trend was found in the biomass and NPP of the two stands. The biomass of <em>P. tabulaeformis</em> and <em>P. armandi</em> forests increased dramatically in the past 39 years from 15.32 t/hm² and 7.53 t/hm² to 175.97 t/hm² and 130.98 t/hm², respectively, and the mean annual NPP were 4.18 t hm^-2 a^-1 and 3.20 t hm^-2 a^-1 respectively. Higher biomass and NPP of the tree layers were found in<em> P. tabulaeformis </em>compared to <em>P. armandi</em> forests. No significant correlation was observed between the NPP and monthly and seasonal precipitation; in contrast the NPP was closely correlated with the monthly and seasonal temperature. Among the monthly temperature factors, the temperature in July of the previous year correlated positively with NPP for <em>P. tabulaeformis</em> and <em>P. armandi </em>forests. Also the temperature in the current July correlated with NPP in the same year in <em>P. tabulaeformis</em> forests. Among the seasonal temperature factors, a significant coefficient was observed between the NPP of <em>P. tabulaeformis</em> forests and the mean temperature from January to July. A significant coefficient was observed between the NPP of <em>P. armandi</em> forests and the mean temperature from May to July; higher coefficients were found between the NPP of and climatic factors in <em>P. tabulaeformis</em> forests than that in <em>P. armandi</em> ones. The difference in the biomass and productivity between two kinds of forest types are due to their different biological characteristics.

Efficiency on the stage of vehicle operation: environmental and economic aspects

The paper proposes a method for evaluating the effectiveness of the vehicle during its operation with the inclusion of environmental factors in the study. The skeleton diagram of the production program of the company which aims to identify key indicators to improve performance of a vehicle during its operation.

Stationary property of the thermodynamic potential of the Hubbard model in strong coupling diagrammatic approach for superconducting state

Diagrammatic analysis for normal state of Hubbard model proposed in our previous paper is generalized and used to investigate superconducting state of this model. We use the notion of charge quantum number to describe the irreducible Green's function of the superconducting state. As in the previous paper we introduce the notion of tunneling Green's function and of its mass operator. This last quantity turns out to be equal to correlation function of the system. We proved the existence of exact relation between renormalized one-particle propagator and thermodynamic potential which includes integration over auxiliary interaction constant. The notion of skeleton diagrams of propagator and vacuum kinds were introduced. These diagrams are constructed from irreducible Green's functions and tunneling lines. Identity of this functional to the thermodynamic potential has been proved and the stationarity with respect to variation of the mass operator has been demonstrated.

Critical exponents from the two-particle irreducible1/Nexpansion

We calculate the critical exponent $\ensuremath{\nu}$ of the $O(N)$ symmetric ${\ensuremath{\varphi}}^{4}$ model within the $1/N$ expansion of the two-particle-irreducible effective action, which provides us with a self-consistent approximation scheme for the correlation function. The exponent $\ensuremath{\nu}$ controls the behavior of a two-point function $⟨\ensuremath{\varphi}\ensuremath{\varphi}⟩$ near the critical point $T\ensuremath{\ne}{T}_{c}$ through the correlation length $\ensuremath{\xi}\ensuremath{\sim}|T\ensuremath{-}{T}_{c}{|}^{\ensuremath{-}\ensuremath{\nu}}$, but we notice that it appears also in the scaling form of the three-point vertex function ${\ensuremath{\Gamma}}^{(2,1)}\ensuremath{\sim}⟨\ensuremath{\varphi}\ensuremath{\varphi}{\ensuremath{\varphi}}^{2}⟩$ at the critical point $T={T}_{c}$; in the momentum space, ${\ensuremath{\Gamma}}^{(2,1)}\ensuremath{\sim}{k}^{2\ensuremath{-}\ensuremath{\eta}\ensuremath{-}1/\ensuremath{\nu}}$. We derive a self-consistent equation for ${\ensuremath{\Gamma}}^{(2,1)}$ from the two-particle-irreducible effective action including the skeleton diagrams up to the next-leading-order in the $1/N$ expansion, and solve it to the leading-log accuracy (i.e., keeping the leading $\mathrm{ln}k$ terms) to obtain $\ensuremath{\nu}$. Our results turn out to improve those obtained in the standard one-particle-irreducible calculation at the next-leading-order.

Incorporating dynamic mean-field theory into diagrammatic Monte Carlo

The bold diagrammatic Monte Carlo (BDMC) method performs an unbiased sampling of Feynman's diagrammatic series using skeleton diagrams. For lattice models the efficiency of BDMC can be dramatically improved by incorporating dynamical mean-field theory (DMFT) solutions into renormalized propagators. From the DMFT perspective, combining it with BDMC leads to an unbiased method with well-defined accuracy. We illustrate the power of this approach by computing the single-particle propagator (and thus the density of states) in the non-perturbative regime of the Anderson localization problem, where a gain of the order of ${10}^{4}$ is achieved with respect to conventional BDMC in terms of convergence to the exact answer.

Techniques forn-particle irreducible effective theories

In this paper we show that the skeleton diagrams in the $m$-Loop $n\mathrm{PI}$ effective action correspond to an infinite resummation of perturbative diagrams which is void of double counting at the $m$-Loop level. We also show that the variational equations of motion produced by the $n$-Loop $n\mathrm{PI}$ effective theory are equivalent to the Schwinger-Dyson equations, up to the order at which they are consistent with the underlying symmetries of the original theory. We use a diagrammatic technique to obtain the 5-Loop 5PI effective action for a scalar theory with cubic and quartic interactions, and verify that the result satisfies these two statements.

Diagrammatic theory for periodic anderson model

Diagrammatic theory for Periodic Anderson Model has been developed, supposing the Coulomb repulsion of f — localized electrons as a main parameter of the theory. f-Electrons are strongly correlated and c-conduction electrons are uncorrelated. Correlation function for f- and mass operator for c-electrons are determined. The Dyson equation for c- and Dyson-type equation for f-electrons are formulated for their propagators. The skeleton diagrams are defined for correlation function and thermodynamic functional. The stationary property of renormalized thermodynamic potential with respect to, the variation of the mass operator is established. The result is appropriate both for the normal and for the superconducting states of the system.

Diagrammatic analysis of the Hubbard model: Stationary property of the thermodynamic potential

Diagrammatic approach proposed many years ago for strong correlated Hubbard model is developed for analyzing of the thermodynamic potential properties. The new exact relation between such renormalized quantities as thermodynamic potential, one-particle propagator and correlation function is established. This relation contains additional integration of the one-particle propagator by the auxiliary constant. The vacuum skeleton diagrams constructed from irreducible Green’s functions and tunneling propagator lines are determined and special functional is introduced. The properties of such functional are investigated and its relation to the thermodynamic potential is established. The stationary properties of this functional with respect to first order changing of the correlation function is demonstrated and as a consequence the stationary properties of the thermodynamic potential is proved.

Diagram analysis of the Hubbard model: Stationarity property of the thermodynamic potential

The diagram approach proposed many years ago for the strongly correlated Hubbard model is developed with the aim to analyze the thermodynamic potential properties. A new exact relation between renormalized quantities such as the thermodynamic potential, the one-particle propagator, and the correlation function is established. This relation contains an additional integration of the one-particle propagator with respect to an auxiliary constant. The vacuum skeleton diagrams constructed from the irreducible Green’s functions and tunneling propagator lines are determined and a special functional is introduced. The properties of this functional are investigated and its relation to the thermodynamic potential is established. The stationarity property of this functional with respect to first-order variations of the correlation function is demonstrated; as a consequence, the stationarity property of the thermodynamic potential is proved.

Diagram theory for the periodic anderson model: Stationarity of the thermodynamic potential

Diagrammatic theory for Periodic Anderson Model has been developed, supposing the Coulomb repulsion of $f-$ localized electrons as a main parameter of the theory. $f-$ electrons are strongly correlated and $c-$ conduction electrons are uncorrelated. Correlation function for $f-$ and mass operator for $c-$ electrons are determined. The Dyson equation for $c-$ and Dyson-type equation for $f-$ electrons are formulated for their propagators. The skeleton diagrams are defined for correlation function and thermodynamic functional. The stationary property of renormalized thermodynamic potential about the variation of the mass operator is established. The result is appropriate as for normal and as for superconducting state of the system.

Technical Note: Extraction of Wing Venation Characteristics by Image Analysis

Wing venation characteristics, such as the wing diagram and coordinates of vein junctions, are species-specific and are usually used in studies of insect identification. Image analysis methods are quick and precise means to measure these characteristics. An image analysis method is proposed that enables extraction of the wing diagram and automatic identification of vein junctions. A color image of an insect wing is converted to a binary image of wing venation based on thresholding. A distance-to-boundary map of the complement of the binary image is computed using a distance transform function. The vein skeleton is obtained by a watershed transform. The lookup table method is applied to find coordinates of vein junctions. The proposed method is capable of producing a smooth vein skeleton diagram and can extract the coordinates of vein junctions. This approach is not limited to high-quality images and is simple because the characteristics are obtained almost simultaneously. The experimental results showed that the proposed method is repeatable and useful for wing analysis.

Dressing the post-Newtonian two-body problem and classical effective field theory

We apply a dressed perturbation theory to better organize and economize the computation of high orders of the 2-body effective action of an inspiralling Post-Newtonian gravitating binary. We use the effective field theory approach with the non-relativistic field decomposition (NRG fields). For that purpose we develop quite generally the dressing theory of a non-linear classical field theory coupled to point-like sources. We introduce dressed charges and propagators, but unlike the quantum theory there are no dressed bulk vertices. The dressed quantities are found to obey recursive integral equations which succinctly encode parts of the diagrammatic expansion, and are the classical version of the Schwinger-Dyson equations. Actually, the classical equations are somewhat stronger since they involve only finitely many quantities, unlike the quantum theory. Classical diagrams are shown to factorize exactly when they contain non-linear world-line vertices, and we classify all the possible topologies of irreducible diagrams for low loop numbers. We apply the dressing program to our Post-Newtonian case of interest. The dressed charges consist of the dressed energy-momentum tensor after a non-relativistic decomposition, and we compute all dressed charges (in the harmonic gauge) appearing up to 2PN in the 2-body effective action (and more). We determine the irreducible skeleton diagrams up to 3PN and we employ the dressed charges to compute several terms beyond 2PN.

Entropy production in 2D [formula omitted] theory in the Kadanoff–Baym approach

We study non-equilibrium quantum dynamics of the single-component scalar field theory in 1 + 1 space–time dimensions on the basis of the Kadanoff–Baym equation including the next-to-leading-order (NLO) skeleton diagrams. As an extension of the non-relativistic case, we derive relativistic kinetic entropy at the first order in the gradient expansion of the Kadanoff–Baym equations. The derived entropy satisfies the H-theorem. Next we perform numerical simulations in spatially homogeneous configurations to investigate thermalization properties of the system by evaluating the system entropy. We find that at later times the kinetic entropy increases approaching the equilibrium value, although the limited time interval in the early stage invalidates the use of it.

Shear Viscosity of Hot QED at Finite Chemical Potential from Kubo Formula

Within the framework of finite temperature feld theory this paper discusses the shear viscosity of hot QED plasma through Kubo formula at one-loop skeleton diagram level with a finite chemical potential. The effective widths (damping rates) are introduced to regulate the pinch singularities and then gives a reliable estimation of the shear viscous coefficient. The finite chemical potential contributes positively compared to the pure temperature case. The result agrees with that from the kinetics theory qualitatively.