scholarly journals Scrutinizing GW-Based Methods Using the Hubbard Dimer

2021 ◽  
Vol 9 ◽  
Author(s):  
S. Di Sabatino ◽  
P.-F. Loos ◽  
P. Romaniello
Keyword(s):  
Excitation Spectrum ◽  
Trace Formula ◽  
Electron Interaction ◽  
Excitation Energies ◽  
Fluctuation Dissipation ◽  
Fluctuation Dissipation Theorem ◽  
Wide Range ◽  
Self Consistent ◽  
Approximate Nature ◽  
Self Consistency

Using the simple (symmetric) Hubbard dimer, we analyze some important features of the GW approximation. We show that the problem of the existence of multiple quasiparticle solutions in the (perturbative) one-shot GW method and its partially self-consistent version is solved by full self-consistency. We also analyze the neutral excitation spectrum using the Bethe-Salpeter equation (BSE) formalism within the standard GW approximation and find, in particular, that 1) some neutral excitation energies become complex when the electron-electron interaction U increases, which can be traced back to the approximate nature of the GW quasiparticle energies; 2) the BSE formalism yields accurate correlation energies over a wide range of U when the trace (or plasmon) formula is employed; 3) the trace formula is sensitive to the occurrence of complex excitation energies (especially singlet), while the expression obtained from the adiabatic-connection fluctuation-dissipation theorem (ACFDT) is more stable (yet less accurate); 4) the trace formula has the correct behavior for weak (i.e., small U) interaction, unlike the ACFDT expression.

scholarly journals A Self-Consistent Treatment of Damped Motion for Stable and Unstable Collective Modes

1998 ◽  
Vol 07 (02) ◽  
pp. 243-274 ◽  
Author(s):  
H. Hofmann ◽  
D. Kiderlen
Keyword(s):  
Harmonic Approximation ◽  
Linear Response Theory ◽  
Collective Modes ◽  
Fluctuation Dissipation ◽  
Second Moments ◽  
Fluctuation Dissipation Theorem ◽  
Dissipative Tunneling ◽  
Self Consistent ◽  
Path Approximation ◽  
Consistent Treatment

We address the dynamics of damped collective modes in terms of first and second moments. The modes are introduced in a self-consistent fashion with the help of a suitable application of linear response theory. Quantum effects in the fluctuations are governed by diffusion coefficients Dμν. The latter are obtained through a fluctuation dissipation theorem generalized to allow for a treatment of unstable modes. Numerical evaluations of the Dμν are presented. We discuss briefly how this picture may be used to describe global motion within a locally harmonic approximation. Relations to other methods are discussed, like "dissipative tunneling", RPA at finite temperature and generalizations of the "Static Path Approximation".

scholarly journals Modelling thermal fluctuations in non-ideal fluids with the lattice Boltzmann method

2011 ◽  
Vol 369 (1944) ◽  
pp. 2274-2282 ◽  
Author(s):  
M. Gross ◽  
R. Adhikari ◽  
M. E. Cates ◽  
F. Varnik
Keyword(s):  
Ideal Fluid ◽  
Lattice Boltzmann ◽  
Exact Result ◽  
Thermal Fluctuations ◽  
Ideal Gas ◽  
Fluctuation Dissipation ◽  
Fluctuation Dissipation Theorem ◽  
Wide Range ◽  
Ideal Fluids ◽  
Boltzmann Method

Recently, we proposed a theoretical framework to include thermal fluctuations into the Lattice Boltzmann (LB) method for non-ideal fluids. Here, we apply a variant thereof to a certain class of force-based non-ideal fluid LB models. We find that ideal-gas-like noise is an exact result of the fluctuation–dissipation theorem in the hydrodynamic regime. It is shown that satisfactory equilibration of the density and fluid momentum can be obtained in a simulation over a wide range of length scales.

scholarly journals Entropic measure unveils country competitiveness and product specialization in the World trade web

2021 ◽  
Vol 11 (1) ◽  
Author(s):  
Gianluca Teza ◽  
Michele Caraglio ◽  
Attilio L. Stella
Keyword(s):  
Iterative Scheme ◽  
Entropy Function ◽  
Bipartite Networks ◽  
Complexity Measures ◽  
Wide Range ◽  
Self Consistent ◽  
Set Up ◽  
Technical Features ◽  
Country Competitiveness ◽  
Entropic Measure

AbstractWe show how the Shannon entropy function can be used as a basis to set up complexity measures weighting the economic efficiency of countries and the specialization of products beyond bare diversification. This entropy function guarantees the existence of a fixed point which is rapidly reached by an iterative scheme converging to our self-consistent measures. Our approach naturally allows to decompose into inter-sectorial and intra-sectorial contributions the country competitivity measure if products are partitioned into larger categories. Besides outlining the technical features and advantages of the method, we describe a wide range of results arising from the analysis of the obtained rankings and we benchmark these observations against those established with other economical parameters. These comparisons allow to partition countries and products into various main typologies, with well-revealed characterizing features. Our methods have wide applicability to general problems of ranking in bipartite networks.

scholarly journals The Response to Stratospheric Forcing and Its Dependence on the State of the Troposphere

2009 ◽  
Vol 66 (7) ◽  
pp. 2107-2115 ◽  
Author(s):  
Cegeon J. Chan ◽  
R. Alan Plumb
Keyword(s):  
Time Scale ◽  
Equilibrium Temperature ◽  
Intrinsic Variability ◽  
Winter Solstice ◽  
Fluctuation Dissipation ◽  
Fluctuation Dissipation Theorem ◽  
Order Of Magnitude ◽  
Leading Mode ◽  
Set Up ◽  
Hemisphere Winter

Abstract In simple GCMs, the time scale associated with the persistence of one particular phase of the model’s leading mode of variability can often be unrealistically large. In a particularly extreme example, the time scale in the Polvani–Kushner model is about an order of magnitude larger than the observed atmosphere. From the fluctuation–dissipation theorem, one implication of these simple models is that responses are exaggerated, since such setups are overly sensitive to any external forcing. Although the model’s equilibrium temperature is set up to represent perpetual Southern Hemisphere winter solstice, it is found that the tropospheric eddy-driven jet has a preference for two distinct regions: the subtropics and midlatitudes. Because of this bimodality, the jet persists in one region for thousands of days before “switching” to another. As a result, the time scale associated with the intrinsic variability is unrealistic. In this paper, the authors systematically vary the model’s tropospheric equilibrium temperature profile, one configuration being identical to that of Polvani and Kushner. Modest changes to the tropospheric state to either side of the parameter space removed the bimodality in the zonal-mean zonal jet’s spatial distribution and significantly reduced the time scale associated with the model’s internal mode. Consequently, the tropospheric response to the same stratospheric forcing is significantly weaker than in the Polvani and Kushner case.

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