Related papers: Chebyshev polynomial representation of imaginary t…
In this work, we present a mesh-independent, data-driven library, chebgreen, to mathematically model one-dimensional systems, possessing an associated control parameter, and whose governing partial differential equation is unknown. The…
Accurate modeling of the electronic structure of warm dense matter is a challenging problem whose solution would allow a better understanding of material properties like equation of state, opacity, and conductivity, with resulting…
Quantum computing shows promise for addressing computationally intensive problems but is constrained by the exponential resource requirements of general quantum state tomography (QST), which fully characterizes quantum states through…
We study the Green's function of the $ \nu=1/2 $ Chern-Simons system in the temporal (Weyl) gauge. We derive the Chern-Simons path integral in the temporal gauge. In order to do this, we gauge transform the path integral in the Coulomb…
Quantization of electrodynamics in curved space-time in the Lorenz gauge and with arbitrary gauge parameter makes it necessary to study Green functions of non-minimal operators with variable coefficients. Starting from the integral…
The Double Green Function Formalism has been extensively used in dealing with the thermodynamics of quantum systems which evolved in time under the action of a given self-adjoint Hamiltonian. In this work, we extend the formalism to include…
The pointwise space-time behaviors of the Green's function and the global solution to the modified Vlasov- Poisson-Boltzmann (mVPB) system in one-dimensional space are studied in this paper. It is shown that, the Green's function admits the…
In this work we have presented a rather general and easy-to-apply method for discrete Hilbert space representation of quantum mechanical Green's operators. We have shown that if in some discrete Hilbert space basis representation the…
It is shown that the non-equilibrium self-energy of an interacting lattice-fermion model has a unique Lehmann representation. Based on the construction of a suitable non-interacting effective medium, we provide an explicit and numerically…
The accurate computation of low-energy spectra of strongly correlated quantum many-body systems, typically accessed via Green's-functions, is a long-standing problem posing enormous challenges to numerical methods. When the spectral…
We present a detailed account of the GW space-time method. The method increases the size of systems whose electronic structure can be studied with a computational implementation of Hedin's GW approximation. At the heart of the method is a…
Leibniz' combinatorial formula for determinants is modified to establish a condensed and easily handled compact representation for Hessenbergians, referred to here as Leibnizian representation. Alongside, the elements of a fundamental…
In the framework of Kontsevich-Zagier periods, we derive integral representations for weight-$k$ automorphic Green's functions invariant under modular transformations in $\varGamma_0(N)$ ($N\in\mathbb Z_{\geq1} $), provided that there are…
A method for deriving quantum kinetic equations with initial correlations is developed on the basis of the nonequilibrium Green's function formalism. The method is applicable to a wide range of correlated initial states described by…
Representing spectral densities, real-frequency, and real-time Green's functions of continuous systems by a small discrete set of complex poles is an ubiquitous problem in condensed matter physics, with applications ranging from quantum…
Algorithms and underlying mathematics are presented for numerical computation with periodic functions via approximations to machine precision by trigonometric polynomials, including the solution of linear and nonlinear periodic ordinary…
The asymptotics of the equal-time one-particle Green's function for the half-filled one-dimensional Hubbard model is studied at finite temperature. We calculate its correlation length by evaluating the largest and the second largest…
We present a simple derivation of a Feynman-Kac type formula to study fermionic systems. In this approach the real time or the imaginary time dynamics is expressed in terms of the evolution of a collection of Poisson processes. A computer…
We present a flexible density-matrix renormalization group approach to calculate finite-temperature spectral functions of one-dimensional strongly correlated quantum systems. The method combines the purification of the finite-temperature…
We propose and apply the finite-element discrete variable representation to express the nonequilibrium Green's function for strongly inhomogeneous quantum systems. This method is highly favorable against a general basis approach with regard…