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We use the Matsubara functional renormalization group (FRG) to describe electronic correlations within the single impurity Anderson model. In contrast to standard FRG calculations, we account for the frequency-dependence of the two-particle…
We propose a Truncated Gaussian Basis Approach (TGBA) for simulating the dynamics of quantum many-body systems. The approach constructs an effective Hamiltonian within a reduced subspace, spanned by fermionic Gaussian states, and…
This paper develops near-optimal sustainable harvesting strategies for the predator in a predator-prey system. The objective function is of long-run average per unit time type. To date, ecological systems under environmental noise are…
We present an algorithm for measurement of the Green's function in the hybridization expansion continuous-time quantum Monte-Carlo based on continuous estimators. Compared to the standard method, the present algorithm has similar or better…
In the framework of the many-electron s-d exchange model and Hubbard model, self-consistent equations are derived for the one-particle retarded Green's function in the many-electron Hubbard X-operator representation. We analyze the general…
Theoretical descriptions of non equilibrium dynamics of quantum many-body systems essentially employ either (i) explicit treatments, relying on truncation of the expansion of the many-body wave function, (ii) compressed representations of…
I review the application of self-consistent Green's functions methods to study the properties of infinite nuclear systems. Improvements over the last decade, including the consistent treatment of three-nucleon forces and the development of…
We consider two approaches to balanced truncation of stochastic linear systems, which follow from different generalizations of the reachability Gramian of deterministic systems. Both preserve mean-square asymptotic stability, but only the…
Recent advances in both theoretical and computational methods have enabled large-scale, precision calculations of the properties of atomic nuclei. With the growing complexity of modern nuclear theory, however, also comes the need for novel…
An approach for particle-hole correlation functions, based on the so-called SCRPA, is developed. This leads to a fully self-consistent RPA-like theory which satisfies the $f$-sum rule and several other theorems. As a first step, a simpler…
I review the quantum theory of the electron moving in a random environment. First, the quantum mechanics of individual particles scattered on a random potential is discussed. The quantum-mechanical description is extended to many-body…
When the state space of a discrete state space positive recurrent Markov chain is infinite or very large, it becomes necessary to truncate the state space in order to facilitate numerical computation of the stationary distribution. This…
In this work we present and analyze two tensor network-based influence functional approaches for simulating the real-time dynamics of quantum impurity models such as the Anderson model. Via comparison with recent numerically exact…
We develop a causal optimization method that ensures causality in numerical calculations of Green's functions in interacting electron systems. Our method removes noncausality of numerical data by finding causal functions closest to the…
Many-body Green's functions encode all the properties and excitations of interacting electrons. While these are challenging to be evaluated accurately on a classical computer, recent efforts have been directed towards finding quantum…
We improved the decoupling approximation of the double-time Green's function theory, and applied it to study the spin-${1\over 2}$ two-dimensional antiferromagnetic Heisenberg model with broken bonds at finite temperature. Our decoupling…
We discuss some topics concerning rational approximations in Quantum Chromodynamics, especially those related with the mathematical theory of Pad\'e Approximants. We focus on two kind of problems: the first one related with meromorphic…
Here we present a detailed account of the fundamental problems one encounters in projection theory when non-orthogonal basis sets are used for representation of the operators. In particular, we re-examine the use of projection operators in…
We present a real-space formulation for coarse-graining Kohn-Sham Density Functional Theory that significantly speeds up the analysis of material defects without appreciable loss of accuracy. The approximation scheme consists of two steps.…
We apply the projective truncation technique to the tensor renormalization group (TRG) algorithm in order to reduce the computational cost from $O(\chi^6)$ to $O(\chi^5)$, where $\chi$ is the bond dimension, and propose three kinds of…