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Performance of wave function and Green's function methods for non-equilibrium many-body dynamics
Theoretical descriptions of the non-equilibrium dynamics of quantum many-body systems essentially employ either (i) explicit treatments, relying on the truncation of the expansion of the many-body wave function, (ii) compressed representations of the many-body wave function, or (iii) evolution of an effective (downfolded) representation through Green's functions. In this work, we select representative cases of each of the methods and address how these complementary approaches capture the dynamics driven by intense field perturbations to non-equilibrium states. Under strong driving, the systems are characterized by strong entanglement of the single-particle density matrix and natural populations approaching those of a strongly interacting equilibrium system. We generate a representative set of results that are numerically exact and form a basis for a critical comparison of the distinct families of methods. We demonstrate that the compressed formulation based on similarity-transformed Hamiltonians (coupled-cluster approach) is practically exact in weak fields and, hence, weakly or moderately correlated systems. Coupled cluster, however, struggles for strong driving fields, under which the system exhibits strongly correlated behavior, as measured by the von Neumann entropy of the single-particle density matrix. The dynamics predicted by Green's functions in the (widely popular) G W approximation are less accurate, but improve significantly upon the mean-field results in the strongly driven regime. Published by the American Physical Society 2025
Corrigendum to “Topological invariant in terms of the Green functions for the Quantum Hall Effect in the presence of varying magnetic field” [Ann. Phys., NY 418 (2020) 168179]
We correct misprints found in the text of the paper.
Green functions of currents in the odd-intrinsic parity sector of QCD
The independent operator basis of the most important resonances in the odd-intrinsic parity sector of QCD allows us to construct Lagrangians for corresponding Feynman diagrams of several types of interaction channels of the mesons and resonances. Here, we will discuss all three-point current correlators non-trivial for this sector. We briefly summarize their basic properties and high energy behaviour via the operator product expansion (OPE) framework. We also show that the vector field formalism is not compatible with the OPE, and for this reason the antisymmetric field formalism is a more suitable choice. We also briefly introduce some fundamental phenomological aspects that could be useful in the next studies.
An SYK-inspired model with density–density interactions: Spectral & wave function statistics, Green’s function and phase diagram
The Sachdev–Ye–Kitaev (SYK) model is a rare example of a strongly-interacting system that is analytically tractable. Tractability arises because the model is largely structureless by design and therefore artificial: while the interaction is restricted to two-body terms, interaction matrix elements are “randomized” and therefore the corresponding interaction operator does not commute with the local density. Unlike conventional density–density-type interactions, the SYK-interaction is, in this sense, not integrable. We here investigate a variant of the (complex) SYK model, which restores this integrability. It features a randomized single-body term and a density–density-type interaction. We present numerical investigations suggesting that the model exhibits two integrable phases separated by several intermediate phases including a chaotic one. The chaotic phase carries several characteristic SYK-signatures including in the spectral statistics and the frequency scaling of the Green’s function and therefore should be adiabatically connected to the non-Fermi liquid phase of the original SYK model. Thus, our model Hamiltonian provides a bridge from the SYK-model towards microscopic realism.
Green function approach to R-matrix theory and applications to light nuclear reactions [Slides]
Abstract not provided.
Numerical algorithms developed for carrier transport in nanoelectronic devices: recursive green functions, NEGF, and multiple sequential scattering
Quantitative simulations of carrier transport in physical systems that are of the size of a few nanometers require the use of quantum mechanical models at a very fundamental level.
Greens Functions for Prediction of Noise From Non-Axisymmetric Jets
No abstract available
Model independent description of FEL shot noise, amplification and saturation using Greens function
N/A
On the Landau Background Gauge Fixing and the IR Properties of YM Green Functions
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Green Functions for the Radial Electric Component of the Monopole Wake Field in a Round Resistive Chamber
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Coupled-cluster Green's function: Analysis of properties originating in the exponential parametrization of the ground-state wave function
In this paper we derive basic properties of the Green’s function matrix elements stemming from the exponential coupled cluster (CC) parametrization of the ground-state wave function. We demon- strate that all intermediates used to express retarded (or equivalently, ionized) part of the Green’s function in the ω-representation can be expressed through connected diagrams only. Similar proper- ties are also shared by the first order ω-derivatives of the retarded part of the CC Green’s function. This property can be extended to any order ω-derivatives of the Green’s function. Through the Dyson equation of CC Green’s function, the derivatives of corresponding CC self-energy can be evaluated analytically. In analogy to the CC Green’s function, the corresponding CC self-energy is expressed in terms of connected diagrams only. Moreover, the ionized part of the CC Green’s func- tion satisfies the non-homogeneous linear system of ordinary differential equations, whose solution may be represented in the exponential form. Our analysis can be easily generalized to the advanced part of the CC Green’s function.
Electromagnetic scaling functions within the Green's function Monte Carlo approach
We have studied the scaling properties of the electromagnetic response functions of 4 He and 12 C nuclei computed by the Green's function Monte Carlo approach, retaining only the one-body current contribution. Longitudinal and transverse scaling functions have been obtained in the relativistic and nonrelativistic cases and compared to experiment for various kinematics. The characteristic asymmetric shape of the scaling function exhibited by data emerges in the calculations in spite of the nonrelativistic nature of the model. The results are mostly consistent with scaling of zeroth, first, and second kinds. Our analysis reveals a direct correspondence between the scaling and the nucleon-density response functions. In conclusion, the scaling function obtained from the proton-density response displays scaling of the first kind, even more evidently than the longitudinal and transverse scaling functions
The Determination of the Large-Scale Circulation of the Pacific Ocean from Satellite Altimetry using Model Green's Functions
A Green's function method for obtaining an estimate of the ocean circulation using both a general circulation model and altimetric data is demonstrated. The fundamental assumption is that the model is so accurate that the differences between the observations and the model-estimated fields obey a linear dynamics. In the present case, the calculations are demonstrated for model/data differences occurring on very a large scale, where the linearization hypothesis appears to be a good one. A semi-automatic linearization of the Bryan/Cox general circulation model is effected by calculating the model response to a series of isolated (in both space and time) geostrophically balanced vortices. These resulting impulse responses or 'Green's functions' then provide the kernels for a linear inverse problem. The method is first demonstrated with a set of 'twin experiments' and then with real data spanning the entire model domain and a year of TOPEX/POSEIDON observations. Our present focus is on the estimate of the time-mean and annual cycle of the model. Residuals of the inversion/assimilation are largest in the western tropical Pacific, and are believed to reflect primarily geoid error. Vertical resolution diminishes with depth with 1 year of data. The model mean is modified such that the subtropical gyre is weakened by about 1 cm/s and the center of the gyre shifted southward by about 10 deg. Corrections to the flow field at the annual cycle suggest that the dynamical response is weak except in the tropics, where the estimated seasonal cycle of the low-latitude current system is of the order of 2 cm/s. The underestimation of observed fluctuations can be related to the inversion on the coarse spatial grid, which does not permit full resolution of the tropical physics. The methodology is easily extended to higher resolution, to use of spatially correlated errors, and to other data types.
Green's function studies of phonon transport across Si/Ge superlattices
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Optical spectroscopy of molecular junctions: Nonequilibrium Green’s functions perspective
We consider optical spectroscopy of molecular junctions from the quantum transport perspective when radiation field is quantized and optical response of the system is simulated as photon flux. Using exact expressions for photon and electronic fluxes derived within the nonequilibrium Green function (NEGF) methodology and utilizing fourth order diagrammatic perturbation theory (PT) in molecular coupling to radiation field, we perform simulations employing realistic parameters. Results of the simulations are compared to the bare PT which is usually employed in studies on nonlinear optical spectroscopy to classify optical processes. We show that the bare PT violates conservation laws, while flux conserving NEGF formulation mixes optical processes.