Related papers: Symplectic Symmetry and the Ab Initio No-Core Shel…
A symplectic semitoric manifold is a symplectic $4$-manifold endowed with a Hamiltonian $(S^1 \times \mathbb{R})$-action satisfying certain conditions. The goal of this paper is to construct a new symplectic invariant of symplectic…
We show that the pre-order defined on the category of contact manifolds by arbitrary symplectic cobordisms is considerably less rigid than its counterparts for exact or Stein cobordisms: in particular, we exhibit large new classes of…
We present an example of a partial dynamical symmetry (PDS) in an interacting fermion system and demonstrate the close relationship of the associated Hamiltonians with a realistic quadrupole-quadrupole interaction, thus shedding new light…
We present a systematic study of the $^{10-14}\text{C}$ isotopes within the \textit{ab initio} no-core shell model theory. We apply four different realistic nucleon-nucleon (NN) interactions: (i) the charge-dependent Bonn 2000 (CDB2K)…
Non-Gaussianity is a key resource for achieving quantum advantages in bosonic platforms. Here, we investigate the symplectic rank: a novel non-Gaussianity monotone that satisfies remarkable operational and resource-theoretic properties.…
Given an SO(3)-bundle with connection, the associated two-sphere bundle carries a natural closed 2-form. Asking that this be symplectic gives a curvature inequality first considered by Reznikov. We study this inequality in the case when the…
Fully-microscopic No-core Shell Model (NCSM) calculations of all stable $s$ and $p$ shell nuclei are used to determine realistic $NN$ interaction JISP16 describing not only the two-nucleon data but the binding energies and spectra of nuclei…
Symplectic integrators are the preferred method of solving conservative $N$-body problems in cosmological, stellar cluster, and planetary system simulations because of their superior error properties and ability to compute orbital…
We extend the results of spin ladder models associated with the Lie algebras $su(2^n)$ to the case of the orthogonal and symplectic algebras $o(2^n),\ sp(2^n)$ where n is the number of legs for the system. Two classes of models are found…
Elliott's SU(3) model is at the basis of the shell-model description of rotational motion in atomic nuclei. We demonstrate that SU(3) symmetry can be realized in a truncated shell-model space if constructed in terms of a sufficient number…
In this paper, we explore scaling symmetries within the framework of symplectic geometry. We focus on the action $\Phi$ of the multiplicative group $G = \mathbb{R}^+$ on exact symplectic manifolds $(M, \omega,\theta)$, with $\omega =…
Ab initio nuclear theory provides not only a microscopic framework for quantitative description of the nuclear many-body system, but also a foundation for deeper understanding of emergent collective correlations. A symplectic…
Motivated by and extending the technical results in our earlier work on symplectic Calabi-Yau $4$-manifolds, a general and systematic approach for studying certain unions of symplectic embedded surfaces in a rational $4$-manifold $X=CP^2\#…
An odd-symplectic form is a closed and maximally non-degenerate $2$-form on a compact odd-dimensional manifold. It describes the dynamics of an autonomous Hamiltonian system on a regular energy level. It is called Zoll if the induced…
We present systematic shell-model studies of even-even $^{98-130}$Cd isotopes using a realistic effective shell-model interaction derived from the G-matrix approach with an inert core $^{88}$Sr. Our calculated low-lying excited energy…
We introduce the no-core full configuration (NCFC) approach and present results for $^4$He, $^{12}$C and $^{14}$F with the realistic NN interaction, JISP16. We obtain ground state energies and their uncertainties through exponential…
We explore, within the framework of an algebraic sp(4) shell model, discrete approximations to various derivatives of the energies of the lowest isovector-paired 0^+ states of atomic nuclei in the 40 <A < 100 mass range. The results show…
A fermion realization of the compact symplectic sp(4) algebra provides a natural framework for studying isovector pairing correlations in nuclei. While these correlations manifest themselves most clearly in the binding energies of 0^+…
We study symplectic structures on K\"ahler surfaces with p_g = 0. We give an example of a projective surface which admits a symplectic structure which is not compatible with any K\"ahler metric.
We report $J^\pi = 0^+$ ground-state energies and point-proton radii of $^4$He, $^8$Be, $^{12}$C, $^{16}$O and $^{20}$Ne nuclei calculated by the $ab$ $initio$ no-core Monte Carlo shell model with the JISP16 and Daejeon16 nonlocal $NN$…