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We consider the Hamiltonian system of scalar wave field and a single nonrelativistic particle coupled in a translation invariant manner. The particle is also subject to a confining external potential. The stationary solutions of the system…
We study an extended Lipkin-Meshkov-Glick model that permits a transition to a deformed phase with a broken continuous symmetry. Unlike simpler models, one sees a persistent zero-frequency Goldstone mode past the transition point into the…
Coupled cluster theory provides hierarchical many-particle models and is presently considered as the ultimate benchmark in quantum chemistry. Despite is practical significance, a rigorous mathematical analysis of its properties is still in…
A linear response framework is set up for the evaluation of collective excitations in a confined vapour of interacting Bose atoms at finite temperature. Focusing on the currently relevant case of contact interactions between the atoms, the…
A fully nonlinear, time-asymptotic theory of resonant particle trapping in large-amplitude quasi-parallel Alfven waves is presented. The effect of trapped particles on the nonlinear dynamics of quasi-stationary Alfvenic discontinuities and…
A Kubo-Greenwood-like equation for the Gilbert damping parameter $\alpha$ is presented that is based on the linear response formalism. Its implementation using the fully relativistic Korringa-Kohn-Rostoker (KKR) band structure method in…
We assess the performance of a recently proposed renormalized adiabatic local density approximation (rALDA) for \textit{ab initio} calculations of electronic correlation energies in solids and molecules. The method is an extension of the…
We present a technique which allows us to solve the Random Phase Approximation equations with finite-range interactions and treats the continuum part of the excitation spectrum without approximations. The interaction used in the…
Resonant scattering of fast particles off low frequency plasma waves is a major process determining transport characteristics of energetic particles in the heliosphere and contributing to their acceleration. Usually, only Alfv\'en waves are…
The random-phase approximation (RPA) as an approach for computing the electronic correlation energy is reviewed. After a brief account of its basic concept and historical development, the paper is devoted to the theoretical formulations of…
We have carried out theoretical investigations of electron correlation effects on the atomic properties of the Ca atom trapped inside an attractive spherically symmetric potential well of an endohedral fullerene C$_{60}$ cluster.…
Starting from the Random Phase Approximation (RPA), we generalize the schematic model of separable interaction defning subspaces of ph excitations with different coupling constants between them. This ansatz simplifies the RPA eigenvalue…
Using Gaussian integral transform techniques borrowed from functional-integral field theory and the replica trick we derive a version of the coherent-potential approximation (CPA) suited for describing ($i$) the diffusive (hopping) motion…
Relativistic quantum theories are usually thought of as being quantum field theories, but this is not the only possibility. Here we consider relativistic quantum theories with a fixed number of particles that interact neither through…
Although there exists a clear and, in principle, exact theoretical formulation for the equation of motion for the response of a correlated fermionic system, its numerical implementations for atomic nuclei require feasible approximations.…
We report the development of a parallel FORTRAN code, RCCPAC, to solve the relativistic coupled-cluster equations for closed-shell and one-valence atoms and ions. The parallelization is implemented through the use of message passing…
A formally exact Bethe-Salpeter-like equation for the linear-response function is introduced with a kernel which depends only on the one frequency of the applied field. This is in contrast with the standard Bethe-Salpeter equation (BSE)…
The deformed Dirac equation invariant under the $\kappa$-Poincar\'{e}-Hopf quantum algebra in the context of minimal and scalar couplings under spin and pseudospin symmetries limits is considered. The $\kappa$-deformed Pauli-Dirac…
A zero-range approach to atom-molecule coupling is developed in analogy to the Fermi-Huang pseudo-potential treatment of atom-atom interactions. It is shown by explicit comparison to an exactly-solvable finite-range model that replacing the…
The longitudinal and transverse nuclear responses to inclusive electron scattering reactions are analyzed within the Random Phase Approximation (RPA) framework. Several residual interactions are considered and it is shown that the exchange…