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Spectral properties of random Schr\"odinger operators are encoded in the average of products of Greens functions. For probability distributions with enough finite moments, the supersymmetric approach offers a useful dual representation.…
Various sum rules accounting for the coupling between density and particle excitations and emphasizing in an explicit way the role of the Bose-Einstein condensation are discussed. Important consequences on the fluctuations of the particle…
Within the Quartet Condensation Model (QCM), the isovector pairing correlations for $N = Z$ nuclei are described with a very high accuracy by a condensate of $\alpha$-like quartets. The usual approach involves cumbersome recurrence…
Suspensions of swimming particles exhibit complex collective behaviors driven by hydrodynamic interactions, showing persistent large-scale flows and long-range correlations. While heavily studied, it remains unclear how such structures…
An alternative approach to symmetry restoration within Energy Density Functional, the Symmetry-Conserving EDF is discussed. In this approach, the energy is directly written in terms of the degrees of freedom encoded in the one-, two-...…
In this paper, we study the generalized gapped k-mer filters and derive a closed form solution for their coefficients. We consider nonnegative integers $\ell$ and $k$, with $k\leq \ell$, and an $\ell$-tuple $B=(b_1,\ldots,b_{\ell})$ of…
We briefly summarize properties of quantum Hall states with a pairing or clustering property. Their study employs a fundamental connection with parafermionic Conformal Field Theories. We report on closed form expressions for the many-body…
In this work, standard methods of the mixed thin-shell foramlism are refined using the framework of Colombeau's theory of generalized functions. To this end, systematic use is made of smooth generalized functions, in particular…
The diagrammatic analysis of interacting particle assemblies harbors a fundamental mismatch between two of its main implementations: Phi-derivable (conserving) approximations and parquet (crossing symmetric) models. No termwise expansion,…
This paper concerns the construction and analysis of a numerical scheme for a mixed discrete-continuous fragmentation equation. A finite volume scheme is developed, based on a conservative formulation of a truncated version of the…
For coupled-channel resonance scattering we derive a model with a closed form solution for the $T$-matrix that satisfies unitarity and analyticity. The two-channel case is handled explicitly for an arbitrary number of resonances. The method…
By exploiting the properties of q-deformed Coxeter elements, the scattering matrices of affine Toda field theories with real coupling constant related to any dual pair of simple Lie algebras may be expressed in a completely generic way. We…
We apply the Hulth\`en-Kohn method suggested by V. D. Efros [Phys. Rev. C 99, 034620 (2019)] for calculating various observables in the continuum and discrete spectrum using two-body interactions in single- and coupled-channel systems. This…
A variational formulation for the calculation of interacting fermion systems based on the density-matrix functional theory is presented. Our formalism provides for a natural integration of explicit many-particle effects into standard…
State-of-the-art multi-reference energy density functional calculations require the computation of norm overlaps between different Bogoliubov quasiparticle many-body states. It is only recently that the efficient and unambiguous calculation…
We derive a mode-coupling theory for the slow dynamics of fluids confined in disordered porous media represented by spherical particles randomly placed in space. Its equations display the usual nonlinear structure met in this theoretical…
We apply reduced density-matrix functional theory to the parabolically confined quantum Hall droplet in the spin-frozen strong magnetic field regime. One-body reduced density matrix functional method performs remarkably well in obtaining…
Within the framework of thermofield dynamics, we construct a thermalized coherent thermal state, which is a general type of the coherent state with the thermal effects and can be presumably produced experimentally. The wavefunction and the…
The multichannel generalization of the theory of spectral, scattering and decay control is presented. New universal algorithms of construction of complex quantum systems with given properties are suggested. Particularly, transformations of…
We develop the diagrammatic formulation of the many-body theory for the coupled collective modes in interacting electron systems of different dimensions. The formalism is then applied in detail to a two-dimensional system coupled to a…