Related papers: A unified formal approach to weak and strong coupl…
Diagrammatic techniques to compute perturbatively the spectral properties of Euclidean Random Matrices in the high-density regime are introduced and discussed in detail. Such techniques are developed in two alternative and very different…
We propose a new method for obtaining complete asymptotic expansions in a systematic manner, which is suitable for counting sequences of various graph families in dense regime. The core idea is to encode the two-dimensional array of…
The algebraic properties of formal power series, whose coefficients show factorial growth and admit a certain well-behaved asymptotic expansion, are discussed. It is shown that these series form a subring of $\mathbb{R}[[x]]$. This subring…
We develop a strong coupling approach for a general lattice problem. We argue that this strong coupling perspective represents the natural framework for a generalization of the dynamical mean field theory (DMFT). The main result of this…
It is well known that quantum-mechanical perturbation theory often give rise to divergent series that require proper resummation. Here I discuss simple ways in which these divergences can be avoided in the first place. Using the elementary…
The principal goal of the physics of the fundamental interactions is to provide a consistent description of the nature of the subnuclear forces, which manifest in our universe, together with the gravitational force, in a unified framework.…
The difficulties of perturbation theory associated with unstable fundamental fields (such as the lack of exact gauge invariance in each order) are cured if one constructs perturbative expansion directly for probabilities interpreted as…
In this paper, we consider the resummation of the divergent Rayleigh-Shrodinger perturbation expansion for the ground state energy of the quartic anharmonic oscillator in one dimension. We apply the Borel-Pade resummation method combined…
This thesis is devoted to the study of some aspects of perturbative QCD, and in particular to the development of high-precision techniques for the extraction of physical parameters such as structure functions, parton distributions, and the…
A strong-coupling expansion for models of correlated electrons in any dimension is presented. The method is applied to the Hubbard model in $d$ dimensions and compared with numerical results in $d=1$. Third order expansion of the Green…
Density functional theory can be extended to excited states by means of a unified variational approach for passive state ensembles. This extension overcomes the restriction of the typical density functional approach to ground states, and…
We construct generally applicable small-loss rate expansions for the density operator of an open system. Successive terms of those expansions yield characteristic loss rates for dissipation processes. Three applications are presented in…
In quantum field theory, the splitting of the Hamiltonian into a strong and an electromagnetic part cannot be performed in a unique manner. We propose a convention for disentangling these two effects: one matches the parameters of two…
A simple model coupling a one-dimensional beam particle to a one-dimensional harmonic oscillator is used to explore complementarity and entanglement. This model, well-known in the inelastic scattering literature, is presented under three…
Projected Hartree-Fock theory provides an accurate description of many kinds of strong correlations but does not properly describe weakly-correlated systems. On the other hand, single-reference methods such as configuration interaction or…
Borel summable semiclassical expansions in 1D quantum mechanics are considered. These are the Borel summable expansions of fundamental solutions and of quantities constructed with their help. An expansion, called topological,is constructed…
Strong coupling expansion is computed for the Einstein equations in vacuum in the Arnowitt-Deser-Misner (ADM) formalism. The series is given by the duality principle in perturbation theory as presented in [M.Frasca, Phys. Rev. A 58, 3439…
For a singularly perturbed system of reaction--diffusion equations, assuming that the 0th order solutions in regular and singular regions are all stable, we construct matched asymptotic expansions for formal solutions to any desired order…
Accurately describing many-body effects in multi-orbital systems remains a major challenge in theoretical condensed matter physics. At present, there is a significant methodological gap between the numerical tools used in ab initio…
A novel mathematical model for fiber-reinforced materials is proposed. It is based on a 1-dimensional beam model for the thin fiber structures, a flexible and general 3-dimensional elasticity model for the matrix and an overlapping domain…