Related papers: Static and Dynamic Bethe-Salpeter Equations in the…
The $GW$ approximation is a well-established method for calculating ionization potentials and electron affinities in solids and molecules. For numerous years, obtaining self-consistent $GW$ total energies in solids has been a challenging…
Shaping the reachable set of a dynamical system is a fundamental challenge in control design, with direct implications for both performance and safety. This paper considers the problem of selecting the optimal input matrix for a linear…
Semi-analytic expressions for the static limit of the T-matrix for electromagnetic scattering are derived for a circular torus, expressed in bases of both toroidal and spherical harmonics. The scattering problem for an arbitrary static…
Strongly correlated electron systems are generally described by tight binding lattice Hamiltonians with strong local (on site) interactions, the most popular being the Hubbard model. Although the half filled Hubbard model can be simulated…
In this paper, we propose a low rank approximation method for efficiently solving stochastic partial differential equations. Specifically, our method utilizes a novel low rank approximation of the stiffness matrices, which can significantly…
We introduce a method "DMT" for approximating density operators of 1D systems that, when combined with a standard framework for time evolution (TEBD), makes possible simulation of the dynamics of strongly thermalizing systems to arbitrary…
The Bethe free energy approximation provides an effective way for relaxing NP-hard problems of probabilistic inference. However, its accuracy depends on the model parameters and particularly degrades if a phase transition in the model…
We present an extension of the quasiparticle self-consistent $GW$ approximation (QS$GW$) [Phys. Rev. B, 76 165106 (2007)] to include vertex corrections in the screened Coulomb interaction $W$. This is achieved by solving the Bethe-Salpeter…
A new method of approximation scheme with potential application to a general interacting quantum system is presented. The method is non-perturbative, self- consistent, systematically improvable and uniformly applicable for arbitrary…
Direct simulation of biomolecular dynamics in thermal equilibrium is challenging due to the metastable nature of conformation dynamics and the computational cost of molecular dynamics. Biased or enhanced sampling methods may improve the…
We consider linear systems arising from the use of the finite element method for solving scalar linear elliptic problems. Our main result is that these linear systems, which are symmetric and positive semidefinite, are well approximated by…
New stochastic approaches for the computation of electronic excitations are developed within the many-body perturbation theory. Three approximations to the electronic self-energy are considered: $G_0W_0$, $G_0W_0^tc$, and…
The simulation of complex stochastic network dynamics arising, for instance, from models of coupled biomolecular processes remains computationally challenging. Often, the necessity to scan a models' dynamics over a large parameter space…
A general form of multi-channel Bethe-Salpeter equation is considered. In contradistinction to the hitherto applied approaches, our coupled system of equations leads to the simultaneous solutions for all relativistic four-point Green…
We present a variational solution of the T-matrix integral equation within a local approximation. This solution provides a simple form for the T matrix similar to Hubbard models but with the local interaction depending on momentum and…
We present a diagrammatic approach to construct self-energy approximations within many-body perturbation theory with positive spectral properties. The method cures the problem of negative spectral functions which arises from a…
We investigate the Twisted Bilayer Graphene (TBG) model to obtain an analytic understanding of its energetics and wavefunctions needed for many-body calculations. We provide an approximation scheme which first elucidates why the BM…
In this paper, we consider the problem of stabilizing discrete-time linear systems by computing a nearby stable matrix to an unstable one. To do so, we provide a new characterization for the set of stable matrices. We show that a matrix $A$…
For the coefficients of the amplitude a set of simultaneous equations is derived in momentum space. By the auxiliary conditions they are equivalent to nonrelativistic equations and suitable for the investigation of two-nucleon system.
The Bethe-Salpeter equation is combined with the temperature-cutoff functional renormalization group approach to analyze the order parameter structure for the leading instabilities of the 2D t-t' Hubbard model. We find significant…