Related papers: Coexisting partial dynamical symmetries and multip…
In this work, we conduct a systematic study of Hamiltonian and quasi-Hamiltonian systems within the framework of nondecomposable generalized Poisson geometry. Our focus lies on the interplay between the algebraic structure of…
Detailed description of nuclei necessitates model Hamiltonians which break most dynamical symmetries. Nevertheless, generalized notions of partial and quasi dynamical symmetries may still be applicable to selected subsets of states, amidst…
Background: The Po, Pb, Hg, and Pt region is known for the presence of coexisting structures that correspond to different particle-hole configurations in the Shell Model language or equivalently to nuclear shapes with different deformation.…
We propose the use of partial dynamical symmetry (PDS) as a selection criterion for higher-order terms in situations when a prescribed symmetry is obeyed by some states and is strongly broken in others. The procedure is demonstrated in a…
In the context of the interacting boson model with $s$, $d$ and $g$ bosons, the conditions for obtaining an intrinsic shape with octahedral symmetry are derived for a general Hamiltonian with up to two-body interactions.
Background: The lead region, Po, Pb, Hg, and Pt, shows up the presence of coexisting structures having different deformation and corresponding to different particle-hole configurations in the Shell Model language. Purpose: We intend to…
Spectral features of the odd-mass nucleus $^{195}$Pt are analyzed by means of an interacting boson-fermion Hamiltonian with SO(6) partial dynamical symmetry. For the latter, selected eigenstates are solvable and preserve the symmetry…
We show that distinct emergent symmetries, such as partial dynamical symmetry and quasi dynamical symmetry, can occur simultaneously in the same or different eigenstates of the Hamiltonian. Implications for nuclear spectroscopy in the…
The concept of partial symmetry is introduced for an interacting fermion system. The associated Hamiltonians are shown to be closely related to a realistic nuclear quadrupole-quadrupole interaction. An application to $^{12}$C is presented.
We consider the cubic nonlinear Schr\"odinger equation (NLS) in any spatial dimension, which is a well-known example of an infinite-dimensional Hamiltonian system. Inspired by the knowledge that the NLS is an effective equation for a system…
We construct a hierarchy of integrable systems whose Poisson structure corresponds to the BMS$_{3}$ algebra, and then discuss its description in terms of the Riemannian geometry of locally flat spacetimes in three dimensions. The analysis…
A prepotential approach to constructing the quantum systems with dynamical symmetry is proposed. As applications, we derive generalizations of the hydrogen atom and harmonic oscillator, which can be regarded as the systems with…
Some positive answers to the problem of endowing a dynamical system with a Hamiltonian formulation are presented within the class of Poisson structures in a geometric framework. We address this problem on orientable manifolds and by using…
Given a first order dynamical system possessing a commutative algebra of dynamical symmetries, we show that, under certain conditions, there exists a Poisson structure on an open neighbourhood of its regular (not necessarily compact)…
Explicit forms of IBM Hamiltonians with a generalized partial dynamical O(6) symmetry are presented and compared with empirical data in $^{162}$Dy.
The use of dynamical symmetries or spectrum generating algebras for the solution of the nuclear many-body problem is reviewed. General notions of symmetry and dynamical symmetry in quantum mechanics are introduced and illustrated with…
Number-non-conserving terms in quadratic bosonic Hamiltonians can induce unwanted dynamical instabilities. By exploiting the pseudo-Hermitian structure built in to these Hamiltonians, we show that as long as dynamical stability holds, one…
In the present paper we examine in a systematic way the most relevant orderings of pure kinetic Hamiltonians for five different position-dependent mass (PDM) profiles: soliton-like, reciprocal quadratic and biquadratic, exponential and…
A $\gamma$-deformed version of $\mathfrak{su}(2)$ algebra has been obtained from a bi-orthogonal system of vectors in $\bf{C^2}$. Fusion of Jordan-Schwinger realization of complexified $\mathfrak{su}(2)$ with Dyson-Maleev representation…
The phenomenon of shape coexistence is discussed within the self-consistent Hartree-Fock method and the nuclear shell model. The occurrence of the coexisting configurations with different intrinsic shapes is traced back to the properties of…