Related papers: Deformed Boson Scheme including Conventional q-Def…
Schematic su(2)+h3 interaction Hamiltonians, where su(2) plays the role of the pseudo-spin algebra of fermion operators and h3 is the Heisenberg algebra for bosons, are shown to be closely related to certain nonlinear models defined on a…
Two-level boson systems displaying a quantum phase transition from a spherical (symmetric) to a deformed (broken) phase are studied. A formalism to diagonalize Hamiltonians with $O(2L+1)$ symmetry for large number of bosons is worked out.…
The extended interacting boson model with s-, p-, d-, f- and g-bosons being included (spdfg IBM) are investigated. The algebraic structure including the generators, the Casimir operators of the groups at the SU(5) dynamical symmetry and the…
It is shown that there exists an isomorphism between q-oscillator systems covariant under $ SU_q(n) $ and $ SU_{q^{-1}}(n) $. By the isomorphism, the defining relations of $ SU_{q^{-1}}(n) $ covariant q-oscillator system are transmuted into…
The concept of a quantum algebra is made easy through the investigation of the prototype algebras $u_{qp}(2)$, $su_q(2)$ and $u_{qp}(1,1)$. The latter quantum algebras are introduced as deformations of the corresponding Lie algebras~; this…
The polynomial algebra is a deformed SU(2) algebra. Here, we use polynomial algebra as a method to solve a series of deformed oscillators. Meanwhile, we find a series of physics systems corresponding with polynomial algebra with different…
In the recently proposed two-parameter $\tilde{\mu},q$-deformed Bose gas model [Ukr. J. Phys. {\bf 58}, 1171 (2013), arXiv:1312.1573] aimed to take effectively into account both compositeness of particles and their interaction, the…
Following the Schwinger boson representation for the su(M+1)- and the su(N,1)-algebra presented by two of the present authors (J. da P. and M. Y.) and Kuriyama, a possible counterpart of the Lipkin model in the su(M+1)-algebra formulated in…
Patterns of shape-phase transition in the proton-neutron coupled systems are studied within the $SD$-pair shell model. The results show that some transitional patterns in the $SD$-pair shell model are similar to the $U(5)-SU(3)$,…
We build in this paper the algebra of q-deformed pseudo-differential operators shown to be an essential step towards setting a q-deformed integrability program. In fact, using the results of this q-deformed algebra, we derive the…
The 1/$N$ expansion solutions for the interacting boson model are extended to higher orders using computer algebra. The analytic results are compared with those obtained from an exact diagonalization of the Hamiltonian and are shown to be…
The two-parametric quantum superalgebra $U_{p,q}[gl(2/1)]$ is consistently defined. A construction procedure for induced representations of $U_{p,q}[gl(2/1)]$ is described and allows us to construct explicitly all (typical and nontypical)…
An operator formalism for bosonic $\beta-\gamma$ systems on arbitrary algebraic curves is introduced. The classical degrees of freedom are identified and their commutation relations are postulated. The explicit realization of the algebra…
We analyze in detail the quantum phase transitions that arise in models based on the $u(2)$ algebraic description for bosonic systems with two types of scalar bosons. First we discuss the quantum phase transition that occurs in hamiltonians…
Based on the boson realization, the ground state and phase structure are investigated in a many-quark model with algebraic structure developed in our previous paper, in which the two-body pairing and particle-hole type interactions are…
We construct the thermodynamic geometry of an ideal q-deformed boson and fermion gas. We investigate some thermodynamic properties such as the stability and statistical interaction. It will be shown that the statistical interaction of…
Composite bosons, here called {\it quasibosons} (e.g. mesons, excitons, etc.), occur in various physical situations. Quasibosons differ from bosons or fermions as their creation and annihilation operators obey non-standard commutation…
We introduce an elliptic algebra $U_{q,p}(\hat{sl_2})$ with $p=q^{2r} (r\in \R_{>0})$ and present its free boson representation at generic level $k$. We show that this algebra governs a structure of the space of states in the $k-$fusion…
New integral representations for form factors in the two parametric SS model are proposed. Some form factors in the parafermionic sine-Gordon model and in an integrable perturbation of SU(2) coset conformal field theories are…
After recapitulating the eigenvalue problem of the su(1,1)-algebra in the conventional form, the same problem is treated in an unconventional form, in which the eigenvalue is pure imaginary. Further, the coupling scheme of two su(1,1)-spins…