Related papers: Physical and unphysical solutions of random-phase …
An application of a self-consistent version of RPA to quantum field theory with broken symmetry is presented. Although our approach can be applied to any bosonic field theory, we specifically study the $\phi^4$ theory in 1+1 dimensions. We…
We study the spectral properties of a class of random matrices where the matrix elements depend exponentially on the distance between uniformly and randomly distributed points. This model arises naturally in various physical contexts, such…
The Random Phase Approximation (RPA) and its variations and extensions are, without any doubt, the most widely used tools to describe Giant Resonances within a microscopic theory. In this chapter, we will start by discussing how RPA comes…
By coupling a doorway state to a see of random background states, we develop the theory of doorway states in the framework of the random-phase approximation (RPA). Because of the symmetry of the RPA equations, that theory is radically…
It has been revealed through numerical calculations that the Second Random Phase Approximation (SRPA) with the Hartree-Fock solution as its reference state results in 1) spurious states at genuinely finite energy, contrary to common…
The ground state of a many body Hamiltonian considered in the quasiparticle representation is redefined by accounting for the quasiparticle quadrupole pairing interaction. The residual interaction of the newly defined quasiparticles is…
We consider large-dimensional dynamical systems involving a linear force and a random force comprising both potential and non-conservative contributions. Such systems are known to exhibit a topological trivialization phase transition as the…
In this article, we give a few classes of solutions for the Yang-Baxter type matrix equation, $AXA=XAX$. We provide all solutions for the cases when $A$ is equivalent to a Jordan block or has precisely two Jordan blocks. We also have given…
This Ph.D. thesis derives the equations of the Faddeev Random Phase Approximation (FRPA) and applies the method to a set of small atoms and molecules. The occurence of RPA instabilities in the dissociation limit is addressed in molecules…
In this paper we provide detailed information about the instability of equilibrium solutions of a nonlinear family of localized reaction-difussion equations in dimensione one. Beyond we provide explicit formulas to the equilibrium…
This paper presents a method for computing eigenvalues and eigenvectors for some types of nonlinear eigenvalue problems. The main idea is to approximate the functions involved in the eigenvalue problem by rational functions and then apply a…
Standard perturbation theory of eigenvalue problems consists of obtaining approximations of eigenmodes in the neighborhood of an operator where the corresponding eigenmode is known. Nevertheless, if the corresponding eigenmodes of several…
Low-lying shell model states may be approximated accurately by a sum over products of proton and neutron states. The optimal factors are determined by a variational principle and result from the solution of rather low-dimensional eigenvalue…
Two novel frameworks for handling mathematical and physical problems are introduced. The first, the emerging Jordan form, generalizes the concept of the Jordan canonical form, a well-established tool of linear algebra. The second, dual…
Exactly solvable potentials of nonrelativistic quantum mechanics are known to be shape invariant. For these potentials, eigenvalues and eigenvectors can be derived using well known methods of supersymmetric quantum mechanics. The majority…
A limitation common to all extensions of random-phase approximation including only particle-hole configurations is that they violate to some extent the energy weighted sum rules. Considering one such extension, the improved RPA (IRPA),…
Nuclear physics is ideal to test and develop techniques to describe the microscopic dynamics of quantum many-body systems. At low energy, nuclear dynamics is described with non-relativistic approaches based on the mean-field approximation…
We present a quantum algorithm for solving algebraic Riccati equations, with applications to quantum-chemical random-phase approximation (RPA) and higher-order RPA theories. Our method block-encodes stabilizing Riccati solutions via Riesz…
We consider the problem of finding optimally stable polynomial approximations to the exponential for application to one-step integration of initial value ordinary and partial differential equations. The objective is to find the largest…
A modern chiral potential incorporating the three-body force is adopted to investigate bulk properties, spectra, and nuclear responses of closed-(sub)shell nuclei throughout the nuclear chart within a particle-hole (p-h) renormalized…