Related papers: Correlated Gaussian Hyperspherical Method for Few-…
When seeking a numerical representation of a quantum-mechanical multiparticle problem it is tempting to replace a singular short-range interaction by a smooth finite-range pseudopotential. Finite basis set expansions, e.g.~in Fock space,…
We apply the atom counting theory to strongly correlated Fermi systems and spin models, which can be realized with ultracold atoms. The counting distributions are typically sub-Poissonian and remain smooth at quantum phase transitions, but…
We develop a Bayesian graphical modeling framework for functional data for correlated multivariate random variables observed over a continuous domain. Our method leads to graphical Markov models for functional data which allows the graphs…
Formalism based on complex-scaling method is developed for solving the few particle scattering problem by employing only trivial boundary conditions. Several applications are presented proving efficiency of the method in describing elastic…
We introduce a density functional formalism to study the ground-state properties of strongly-correlated dipolar and ionic ultracold bosonic and fermionic gases, based on the self-consistent combination of the weak and the strong coupling…
A self-consistent many-body approach is proposed to build a first-principles crystal field theory, where crystal field parameters are calculated ab initio. Many-body theory is used to write the energy of the interacting system as a function…
Transcorrelated coupled cluster and distinguishable cluster methods are presented. The Hamiltonian is similarity transformed with a Jastrow factor in the first quantisation, which results in up to three-body integrals. The coupled cluster…
This work reviews recent advances in the analytical treatment of the continuum spectrum of correlated few-body non-relativistic Coulomb systems. The exactly solvable two-body problem serves as an introduction to the non-separable…
Graphical models are commonly used to represent conditional dependence relationships between variables. There are multiple methods available for exploring them from high-dimensional data, but almost all of them rely on the assumption that…
Ultra-cold atomic systems provide a versatile platform for exploring quantum phenomena, offering tunable interactions and diverse trapping geometries. In this study, we investigate a one-dimensional system of trapped fermionic atoms using…
A challenge in modeling time-dependent strong-field processes such as high-harmonic generation for many-body systems, is how to effectively represent the electronic continuum. We apply Rothe's method to the time-dependent Hartree-Fock…
The variational determination of the two-fermion reduced density matrix is described for harmonically trapped, ultracold few-fermion systems in one dimension with equal spin populations. This is accomplished by formulating the problem as a…
Variational approximation methods have proven to be useful for scaling Bayesian computations to large data sets and highly parametrized models. Applying variational methods involves solving an optimization problem, and recent research in…
This paper presents a general neural network framework for solving quantum few-body systems, extending prior methods to handle diverse particle masses, interaction types, and system configurations. Our architecture, which combines an…
A simple two-level model is developed and used to test the properties of effective interactions for performing nuclear structure calculations in truncated model spaces. It is shown that the effective many-body interactions sensitively…
Reduced basis methods provide an efficient way of mapping out phase diagrams of strongly correlated many-body quantum systems. The method relies on using the exact solutions at select parameter values to construct a low-dimensional basis,…
Two-body matrix elements of arbitrary local interactions are written as the sum of separable terms in a way that is well suited for the exchange and pairing channels present in mean-field calculations. The expansion relies on the…
A convergent approximation is proposed for a mean field density-density correlation function in a system with a two-phase interface. It is based on a fourth-order expansion of the Hamiltonian in terms of fluctuations around the equilibrium…
Theoretical descriptions of non equilibrium dynamics of quantum many-body systems essentially employ either (i) explicit treatments, relying on truncation of the expansion of the many-body wave function, (ii) compressed representations of…
An analysis of the characteristic function of Gaussian quadratic forms is presented in [1] to study the performance of multichannel communication systems. This technical report reviews this analysis, obtaining alternative expressions to…