相关论文: Origin of misleading convergence in self-consisten…
For a system of correlated electrons, the Luttinger-Ward functional provides a link between static thermodynamic quantities on the one hand and single-particle excitations on the other. The functional is useful to derive several general…
The Luttinger-Ward functional (LWF) has been a starting point for conserving approximations in many-body physics for 50 years. The recent discoveries of its multivaluedness and the associated divergence of the two-particle irreducible…
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…
Perturbation theory using self-consistent Green's functions is one of the most widely used approaches to study many-body effects in condensed matter. On the basis of general considerations and by performing analytical calculations for the…
The dynamic melting of vortex lattices in type II superconductors is considered. A field-theoretic formulation of the pinning problem allows the average over the quenched disorder to be performed exactly. A self-consistent theory is…
Calculations of the ground state of inhomogeneous many-electron systems involve a solving of the Poisson equation for Coulomb potential and the Schroedinger equation for single-particle orbitals. Due to nonlinearity and complexity this set…
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…
Many-body theory is largely based on self-consistent equations that are constructed in terms of the physical quantity of interest itself, for example the density. Therefore, the calculation of important properties such as total energies or…
We consider steady solutions to the incompressible Euler equations in a two-dimensional channel with rigid walls. The flow consists of two periodic layers of constant vorticity separated by an unknown interface. Using global bifurcation…
In this work, we analyze in detail the occurrence of divergences in the irreducible vertex functions for one of the fundamental models of many-body physics: the Anderson impurity model (AIM). These divergences -- a surprising hallmark of…
We propose an efficient dual boson scheme, which extends the DMFT paradigm to collective excitations in correlated systems. The theory is fully self-consistent both on the one- and on the two-particle level, thus describing the formation of…
We investigate the convergence of McKean-Vlasov diffusions in a nonconvex landscape. These processes are linked to nonlinear partial differential equations. According to our previous results, there are at least three stationary measures…
We elucidate consistency of the so-called corner equations which are elementary building blocks of Euler-Lagrange equations for two-dimensional pluri-Lagrangian problems. We show that their consistency can be derived from the existence of…
This paper concerns the inverse source problems for the time-harmonic elastic and electromagnetic wave equations. The goal is to determine the external force and the electric current density from boundary measurements of the radiated wave…
A convergence result for a discontinuous Galerkin multiscale method for a second order elliptic problem is presented. We consider a heterogeneous and highly varying diffusion coefficient in $L^\infty(\Omega,\mathbb{R}^{d\times d}_{sym})$…
We investigate the relevance of the conformal method by investigating stability issues for the Einstein-Lichnerowicz conformal constraint system in a nonlinear scalar-field setting. We prove the stability of the system with respect to…
While the breakdown of the perturbation expansion for the many-electron problem has several formal consequences, here we unveil its physical effect: Flipping the sign of the effective electronic interaction in specific scattering channels.…
We show that the equations underlying the $GW$ approximation have a large number of solutions. This raises the question: which is the physical solution? We provide two theorems which explain why the methods currently in use do, in fact,…
This paper is devoted to the investigation of the backward problem for a multi-term time-fractional diffusion equation. Backward problems for fractional diffusion equations are typically studied using regularization methods due to their…
The aim of this article is to investigate the well-posedness, stability and convergence of solutions to the time-dependent Maxwell's equations for electric field in conductive media in continuous and discrete settings. The situation we…