Related papers: Stability of self-consistent solutions for the Hub…
A two-particle self-consistency is rarely part of mean-field theories. It is, however, essential for avoiding spurious critical transitions and unphysical behavior. We present a general scheme for constructing analytically controllable…
A self-consistent theory for two-particle fluctuations with renormalized irreducible vertices is proposed. Using the Parquet formalism, we construct the fully antisymmetric full vertex in terms of the two-particle fluctuations in the…
We analyze behavior of correlated electrons described by Hubbard-like models at intermediate and strong coupling. We show that with increasing interaction a pole in a generic two-particle Green function is approached. The pole signals…
In this thesis, I present a non-perturbative approach to the single-band attractive Hubard model which is an extension of previous work by Vilk and Tremblay on the repulsive model. Exact results are derived in the general context of…
Single-band Hubbard model at criticality of the metal-insulator transition is studied using approximations derived from parquet theory. It is argued that only the electron-hole and interaction two-particle channels in the parquet algebra…
We present a general method to study weak-coupling instabilities of a large class of interacting electron models in a controlled and unbiased way. Quite generally, the electron gas is unstable towards a superconducting state even in the…
We study a two-state quantum system with a non linearity intended to describe interactions with a complex environment, arising through a non local coupling term. We study the stability of particular solutions, obtained as constrained…
In a Hilbert space setting, we study the stability properties of the regularized continuous Newton method with two potentials, which aims at solving inclusions governed by structured monotone operators. The Levenberg-Marquardt…
We apply the recently introduced Hubbard model approach to quantitatively describe the experimental charge stability diagram and tunnel coupling of silicon double quantum dot systems. The results calculated from both the generalized Hubbard…
We show how the stability conditions for a system of interacting fermions that conventionally involve variations of thermodynamic potentials can be rewritten in terms of one- and two-particle correlators. We illustrate the applicability of…
In a generic random system, the coexistence of extended and localized states can be evidenced by the subextensive width of energy distribution of a physical initial state in, for example, the quantum quenches which involving the local…
The development of numerical methods capable of simulating realistic materials with strongly correlated electrons, with controllable errors, is a central challenge in quantum many-body physics. Here we describe how a hybrid between…
The Hubbard model is the simplest model that is believed to exhibit superconductivity arising from purely repulsive interactions, and has been extensively applied to explore a variety of unconventional superconducting systems. Here we study…
Two-particle generalized susceptibilities and their irreducible vertex functions play a prominent role in the quantum many-body theory for correlated electron systems. They act as basic building blocks in the parquet formalism which…
This paper investigates equilibrium points and stability in two synchronous machine configurations: (i) a single generator with an impedance load and (ii) two interconnected machines with co-located loads. We consider both abc and dq…
We study instabilities occurring in the electron system whose Fermi surface has flat regions on its opposite sides. Such a Fermi surface resembles Fermi surfaces of some high-$T_c$ superconductors. In the framework of the parquet…
One way of improving the behavior of finite element schemes for classical, time-dependent Maxwell's equations, is to render them from their hyperbolic character to elliptic form. This paper is devoted to the study of the stabilized linear…
We present a method to perform stability analysis of nonequilibrium fixed points appearing in self-consistent electron transport calculations. The nonequilibrium fixed points are given by the self-consistent solution of stationary,…
We consider the stability analysis of a large class of linear 1-D PDEs with polynomial data. This class of PDEs contains, as examples, parabolic and hyperbolic PDEs, PDEs with boundary feedback and systems of in-domain/boundary coupled…
The parquet equations are a self-consistent set of equations for the effective two-particle vertex of an interacting many-fermion system. The application of these equations to bulk models is, however, demanding due to the complex emergent…