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Background: The $R$ matrix formalism of Lane and Thomas has proven to be a convenient reaction theory for solving many-coupled channel systems. The theory provides solutions to bound states, scattering states, and resonances for microscopic…
Simple models for spherical particles with a soft shell have been shown to self-assemble into numerous crystal phases and even quasicrystals. However, most of these models rely on a simple pairwise interaction, which is usually a valid…
We present a general theory for semiconductor polarons in the framework of the Froehlich interaction between electrons and phonons. The latter is investigated using non-commuting phonon creation/annihilation operators associated with a…
Kohn-Sham (KS) formalism of Density Functional Theory is modified to include the systems with strong non-dynamic electron correlation. Unlike in extended KS and broken symmetry unrestricted KS formalisms, cases of both singlet-triplet and…
Rotational bands are commonplace in the spectra of atomic nuclei. Inspired by early descriptions of these bands by quadrupole deformations of a liquid drop, Elliott constructed a discrete nucleon representations of $\mathrm{SU}(3)$ from…
We present the first ab initio calculations for p-shell single-Lambda hypernuclei. For the solution of the many-baryon problem, we develop two variants of the no-core shell model with explicit $\Lambda$ and $\Sigma^+$, $\Sigma^0$,…
Steady, dihedrally symmetric patterns with sharp peaks may be observed on a spinning skirt, lagging behind the material flow of the fabric. These qualitative features are captured with a minimal model of traveling waves on an inextensible,…
We investigate the Fr\"ohlich polaron model on a three-dimensional torus, and give a proof of the second-order quantum corrections to its ground-state energy in the strong-coupling limit. Compared to previous work in the confined case, the…
Using Chandrasekhar's S-type coupling between rotational and intrinsic vortical modes one may simply reproduce the HFB dynamical properties of rotating nuclei within Routhian HF calculations free of pairing correlations yet constrained on…
We report on our analysis of the Coulomb singularity problem in the frame of the coupled channel scattering theory including spin-orbit interaction. We assume that the coupling between the partial wave components involves orbital angular…
The description of weakly bound nuclei using deformed few-body models has proven to be crucial in the study of reactions involving certain exotic nuclei. However, these core+valence models face the challenge of applying the Pauli exclusion…
In a previous paper a semi-microscopic core-particle coupling method that includes the conventional strong coupling core-particle model as a limiting case, was applied to spectra and electromagnetic properties of several well-deformed odd…
We consider classical N-particle system with arbitrary central pair potential. Mechanical equilibrium condition in spherically-symmetric case leads to a nonlinear integro-differential equation for concentration n(r). For special state…
When an electron is confined to a triangular atomic thick layer of graphene [1-5] with zig-zag edges, its energy spectrum collapses to a shell of degenerate states at the Fermi level (Dirac point) [6-9]. The degeneracy is proportional to…
The Peierls-Yoccoz (PY) rotational energy of nuclei has been analyzed by the angular-momentum projection (AMP) on the axial Hartree-Fock solutions, by using the semi-realistic effective Hamiltonian M3Y-P6. The rotational energy is…
We present an approach to derive effective shell-model interactions from microscopic nuclear forces. The similarity-transformed coupled-cluster Hamiltonian decouples the single-reference state of a closed-shell nucleus and provides us with…
We address the outstanding problem of electron pairing in the presence of strong Coulomb repulsion at small to moderate values of the Coulomb parameter, $r_s \lesssim 2$, and demonstrate that the pseudopotential framework is fundamentally…
In this paper, we present a 2D numerical model developed to simulate the dynamics of soft, deformable particles. To accommodate significant particle deformations, the particle surface is represented as a narrow shell composed of mass points…
Quantum annealing is a promising technique which leverages quantum mechanics to solve hard optimization problems. Considerable progress has been made in the development of a physical quantum annealer, motivating the study of methods to…
The focus of the thesis is to obtain a universal formalism to evaluate the perturbations during inflation at all orders that can be applied to any theory of gravity and matter source in the early universe. We first look at the equivalence…