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In this paper, we present a theoretical analysis of the model reduction algorithm for linear switched systems. This algorithm is a reminiscence of the balanced truncation method for linear parameter varying systems. Specifically in this…
In a previous work (N. H. Tong, Phys. Rev. B 92, 165126 (2015)), an equation-of-motion based series expansion formalism was used to do the second-order strong-coupling expansion for the single-particle Green function of the Anderson…
We present a quantum-classical hybrid implementation of the Liouvillian recursion method to compute many-body Green's functions using a quantum computer. From an approximate ground state preparation circuit, this algorithm produces the…
The standard nonperturbative approaches of renormalization group for tensor models are generally focused on a purely local potential approximation (i.e. involving only generalized traces and product of them) and are showed to strongly…
In this paper we consider approximations to the popular Pitman-Yor process obtained by truncating the stick-breaking representation. The truncation is determined by a random stopping rule that achieves an almost sure control on the…
I introduce several simplified schemes for the approximation of the self-consistency condition of the dynamical cluster approximation. The applicability of the schemes is tested numerically using the fluctuation-exchange approximation as a…
The ill-posed analytic continuation problem for Green's functions and self-energies is investigated by revisiting the Pad\'{e} approximants technique. We propose to remedy the well-known problems of the Pad\'{e} approximants by performing…
Kernel approximation with exponentials is useful in many problems with convolution quadrature and particle interactions such as integral-differential equations, molecular dynamics and machine learning. This paper proposes a weighted…
The self-energy method for quantum impurity models expresses the correlation part of the self-energy in terms of the ratio of two Green's functions and allows for a more accurate calculation of equilibrium spectral functions than is…
Practical methods to compute dipole strengths for a three-body system by using a discretized continuum are analyzed. New techniques involving Green's function are developed, either by correcting the tail of the approximate wave function in…
The basic mathematical properties of Green's functions used in statistical mechanics as well as the equations defining these functions and the techniques of solving these equations are reviewed. An approach is presented called the…
Acoustic room modes and the Green's function mode expansion are well-known for rectangular rooms with perfectly reflecting walls. First-order approximations also exist for nearly rigid boundaries; however, current analytical methods fail to…
In the first part of this paper we introduced an algorithm that uses reachable set approximation to approximate the minimum time function of linear control problems. To illustrate the error estimates and to demonstrate differences to other…
The main objective of the work is to provide sharp two-sided estimates of $\lambda$-Green function of hyperbolic Brownian motion of a half-space. We strongly rely on recent results obtained by K. Bogus and J. Malecki [3], regarding precise…
We present a symmetry-enabled direct quantum protocol for computing many-body Green's functions, a central tool for studying strongly correlated quantum systems. Our protocol relies only on native time evolution and straightforward…
The impurity Green function and dynamical susceptibilties for the two-channel Anderson impurity model are calculated. An exact expression for the self-energy of the impurity Green function is derived. The imaginary part of the self-energy…
A new non-perturbative framework for many-body correlated systems is formulated by extending the operator projection method (OPM). This method offers a systematic expansion which enables us to project into the low-energy structure after…
We derive equations of motion for Green's functions of the multi-orbital Anderson impurity model by differentiating symmetrically with respect to all time arguments. The resulting equations relate the one- and two-particle Green's function…
We generalize the Green-Kubo approach, previously applied to bulk systems of spherically symmetric active particles [J. Chem. Phys. 145, 161101 (2016)], to include spatially inhomogeneous activity. The method is applied to predict the…
The Green's function plays a crucial role when studying the nature of quantum many-body systems, especially strongly-correlated systems. Although the development of quantum computers in the near future may enable us to compute energy…