Related papers: Dimensionality reduction through tensor factorizat…
We present an introduction to ab initio nuclear theory with a focus on nuclear reactions. After a high-level overview of ab initio approaches in nuclear physics, we give a more detailed description of the no-core shell model technique…
The nuclear many-body problem for medium-mass systems is commonly addressed using wave-function expansion methods that build upon a second-quantized representation of many-body operators with respect to a chosen computational basis. While…
Determining the proper level of details to develop and solve physical models is usually difficult when one encounters new engineering problems. Such difficulty comes from how to balance the time (simulation cost) and accuracy for the…
The development and implementation of increasingly accurate methods for electronic structure calculations mean that, for many atomistic simulation problems, treating light nuclei as classical particles is now one of the most serious…
In this work, we derive a closed solution of the Shr$ \ddot{o} $dinger equation for Bohr Hamiltonien within the minimal length formalism. This formalism is inspired by Heisenberg algebra and a generlized uncertainty principle (GUP), applied…
Variational algorithms are a promising paradigm for utilizing near-term quantum devices for modeling electronic states of molecular systems. However, previous bounds on the measurement time required have suggested that the application of…
In this thesis, the ground state properties of nuclear matter, namely the energy per particle and the response to weak probes, are computed, studying the effects of three nucleon interactions. Both the variational approach, based on the…
This paper presents a quantum algorithm for solving the fractional Poisson equation \((-\Delta)^s u = f\) with \(s \in (0,1)\) on bounded domains. The proposed approach combines rational approximation techniques with quantum linear system…
We study low-rank tensor methods for the numerical solution of Schr\"odinger's equation with time-independent and explicitly time-dependent Hamiltonians, motivated by large-scale simulations of many-body quantum systems and quantum…
In the book the mathematical methods of nuclear cross sections and phases of elastic scattering, energy and characteristics of bound states in two- and three-particle nuclear systems, when the potentials of interaction contain not only…
Three-nucleon forces are an essential ingredient for an accurate description of nuclear few- and many-body systems. However, implementing them directly in many-body calculations is technically very challenging. Thus, there is a need for an…
Preparing quantum many-body states on classical or quantum devices is a very challenging task that requires accounting for exponentially large Hilbert spaces. Although this complexity can be managed with exponential ans\"atze (such as in…
Sufficient dimension reduction methods often require stringent conditions on the joint distribution of the predictor, or, when such conditions are not satisfied, rely on marginal transformation or reweighting to fulfill them approximately.…
In pursuing the essential elements of nuclear binding, we compute ground-state properties of atomic nuclei with up to $A=20$ nucleons, using as input a leading order pionless effective field theory Hamiltonian. A variational Monte Carlo…
Numerical annealing and renormalization group have conceived various successful approaches to study the thermodynamics of strongly-correlated systems where perturbation or expansion theories fail to work. As the process of lowering the…
Neural networks have been applied to tackle many-body electron correlations for small molecules and physical models in recent years. Here we propose a new architecture that extends molecular neural networks with the inclusion of periodic…
Nuclear structure models built from phenomenological mean fields, the effective nucleon-nucleon interactions (or Lagrangians), and the realistic bare nucleon-nucleon interactions are reviewed. The success of covariant density functional…
Microscopic nuclear theory is based on the tenet that atomic nuclei can be accurately described as collections of point-like nucleons interacting via two- and many-body forces obeying nonrelativistic quantum mechanics -- and the concept of…
There has been significant recent progress in solving the long-standing problems of how nuclear shell structure and collective motion emerge from underlying microscopic inter-nucleon interactions. We review a selection of recent significant…
In this work we present recent results on application of low-rank tensor decompositions to modelling of aggregation kinetics taking into account multi-particle collisions (for three and more particles). Such kinetics can be described by…