Related papers: Partial Dynamical Symmetries in the g9/2 Shell-Pro…
A simple approximation to shell model is proposed in which the low energy excitation spectra corresponds to the identical nucleons occupying the same single particle states where they preferred to form pairs for the ground states. We call…
We present a symmetry-based approach for shape coexistence in nuclei, founded on the concept of partial dynamical symmetry (PDS). The latter corresponds to a situation when only selected states (or bands of states) of the coexisting…
Analytical expressions of the total number of $J$ levels for three and four fermions in a nuclear $j^n$ shell are provided. The formulas were derived using a combination of sum rules for coefficients of fractional parentage, and "unusual"…
A system of N two-dimensional weakly interacting bosons in a harmonic trap is considered. When the two-particle potential is a delta function Smith and Wilkin have analytically proved that the elementary symmetric polynomials of particle…
Excited states in low-energy spectra in $^{70-76}$Ni are considered. To this end, pairing forces in form of surface delta interaction are employed to account for formation of the ground state multiplet with seniority $\nu = 2$ states. The…
The coherent states for a particle on a sphere are introduced. These states are labelled by points of the classical phase space, that is the position on the sphere and the angular momentum of a particle. As with the coherent states for a…
This letter presents quantum mechanical inequalities which distinguish, for systems of $N$ spin-$\half$ particles ($N>2$), between fully entangled states and states in which at most $N-1$ particles are entangled. These inequalities are…
We study nuclear high-spin states undergoing the transition to the fully stretched configuration with maximum angular momentum I_max within the space of valence nucleons. To this end, we perform a systematic theoretical analysis of…
We present the visible entangled states of 4-qubit system which can be observed easily in physical laboratories. This was motivated from the fact that the entangled state of 2-qubit system comes from singlet and triplet states which are…
The $^{66}$Ge and $^{68}$Ge nuclei are studied by means of the shell model with the extended $P+QQ$ Hamiltonian, which succeeds in reproducing experimentally observed energy levels, moments of inertia and other properties. The investigation…
We apply a large-scale shell model to the study of proton-rich odd-mass nuclei with $N \approx Z$. Calculations predict unexpected structure in the $^{69}$As nucleus for which a detailed experiment was recently performed. In this odd-proton…
Systems of four nonbinary particles, each having three or more internal states, exhibit maximally entangled states that are inaccessible to four qubits. This breaks the pattern of two- and three-particle systems, in which the existing graph…
We propose a simple approach to predict the angular momentum I ground state (I g.s.) probabilities of many-body systems that does not require the diagonalization of hamiltonians with random interactions. This method is found to be…
In this paper we study the enumeration of number (denoted as ${D_I}$) of spin $I$ states for fermions in a single-$j$ shell and bosons with spin $l$. We show that $D_I$ can be enumerated by the reduction from SU$(n+1)$ to SO(3). New…
The $6^{+}_{1}$ and $6^{+}_{2}$ in $^{48}$Ti form a nearly degenerate doublet. In a single j shell calculation with the matrix elements from experiment the $6^{+}_{1}$ changes sign under the interchange of protons and neutron holes (odd…
The geometric phase of a bi-particle model is discussed. For different initial states, especially when the initial state is pure or mixed, the geometric phase will show different properties. The relationship between the geometric phase and…
Recent high-precision mass measurements and shell model calculations~[Phys. Rev. Lett. {\bf 108}, 212501 (2012)] have challenged a longstanding explanation for the requirement of a cubic isobaric multiplet mass equation for the lowest $A =…
The structure of the $N \approx Z$ nuclei $^{66}$Ge and $^{68}$Ge is studied by the shell model on a spherical basis. The calculations with an extended $P+QQ$ Hamiltonian in the configuration space ($2p_{3/2}$, $1f_{5/2}$, $2p_{1/2}$,…
In this work we obtain all the allowed values of the angular momentum and parity for two massless non-Abelian fields. In particular, we show that, unlike the two photons system, two gluons can be in a state with $J^P=1^\pm$, $(2k)^-$, and…
For the case of two spin-1/2 particles in the singlet state, we provide a GHZ-type proof of Bell's theorem by using the idea of postselected measurements. Furthermore, we show that in spite of the low efficiency of the detectors one can…