Related papers: Exact downfolding and its perturbative approximati…
This work is devoted to the development of an efficient and robust technique for accurate capturing of the electric field in multi-material problems. The formulation is based on the finite element method enriched by the introduction of…
In this paper, we present decomposition techniques for solving large-scale instances of the security-constrained optimal power flow (SCOPF) problem with primary response. Specifically, under each contingency state, we require that the nodal…
The recently introduced coupled cluster (CC) downfolding techniques for reducing the dimensionality of quantum many-body problems recast the CC formalism in the form of the renormalization procedure allowing, for the construction of…
This work comprises a detailed theoretical and computational study of the boundary value problem for transversely isotropic linear elastic bodies. General conditions for well-posedness are derived in terms of the material parameters. The…
Starting from the full many-body Hamiltonian of interacting electrons the effective self-energy acting on electrons residing in a subspace of the full Hilbert space is derived. This subspace may correspond to, for example, partially filled…
Modern effective-theory techniques are applied to the nuclear many-body problem. A novel approach is proposed for the renormalization of operators in a manner consistent with the construction of the effective potential. To test this…
Ab initio methods aim to solve the nuclear many-body problem with controlled approximations. Virtually exact numerical solutions for realistic interactions can only be obtained for certain special cases such as few-nucleon systems. Here we…
This thesis includes analysis of disordered spin ensembles corresponding to Exact Cover, a multi-access channel problem, and composite models combining sparse and dense interactions. The satisfiability problem in Exact Cover is addressed…
We describe a method for deriving effective low-energy theories of electronic interactions at graphene edges. Our method is applicable to general edges of honeycomb lattices (zigzag, chiral, and even disordered) as long as localized…
We introduce a numerical method for the approximation of functions which are analytic on compact intervals, except at the endpoints. This method is based on variable transforms using particular parametrized exponential and…
Accurate many-body treatments of condensed-phase systems are challenging because correlated solvers such as full configuration interaction (FCI) and the density matrix renormalization group (DMRG) scale exponentially with system size.…
We apply the method of unitary transformations to a model two-nucleon potential and construct from it an effective potential in a subspace of momenta below a given cut-off $\Lambda$. The S-matrices in the full space and in the subspace are…
We investigate the use of inexact solves for interpolatory model reduction and consider associated perturbation effects on the underlying model reduction problem. We give bounds on system perturbations induced by inexact solves and relate…
We present a generalized framework, renormalized density matrix downfolding (RDMD), to derive systematically improvable, highly accurate, and nonperturbative effective models from ab initio calculations. This framework moves beyond the…
In the framework of pionless nucleon-nucleon effective field theory we study different approximation schemes for the nuclear many body problem. We consider, in particular, ladder diagrams constructed from particle-particle, hole-hole, and…
The electronic and magnetic properties of many strongly-correlated systems are controlled by a limited number of states, located near the Fermi level and well isolated from the rest of the spectrum. This opens a formal way for combining the…
The virtues of an effective field theory (EFT) approach to many-body problems are illustrated by deriving the expansion for the energy of an homogeneous, interacting Fermi gas at low density and zero temperature. A renormalization scheme…
In this work, we develop and analyze a higher-order finite element method for the multidimensional fragmentation equation. To the best of our knowledge, this is the first study to establish a rigorous, conforming finite element framework…
We use some exact results in the scalar field theory to revise the analysis by Coleman and Callan about the false vacuum decay and propose a simple non-perturbative formalism. We introduce exact Green's function which incorporates…
The exact renormalisation group equation is studied for a two-dimensional theory with exponential interaction and a background charge at infinity. The motivation for studying this interaction is the flow between unitary minimal models…