Kinds Of Bosons Research Articles

Inhomogeneous hard-core bosonic mixture with checkerboard supersolid phase: Quantum and thermal phase diagram

We introduce an inhomogeneous bosonic mixture composed of two kinds of hard-core and semi-hard-core bosons with different nilpotency conditions and demonstrate that in contrast with the standard hard-core Bose-Hubbard model, our bosonic mixture with nearest- and next-nearest-neighbor interactions on a square lattice develops the checkerboard supersolid phase characterized by the simultaneous superfluid and checkerboard solid orders. Our bosonic mixture is created from a two-orbital Bose-Hubbard model including two kinds of bosons: a single-orbital boson and a two-orbital boson. By mapping the bosonic mixture to an anisotropic inhomogeneous spin model in the presence of a magnetic field, we study the ground-state phase diagram of the model by means of cluster mean field theory and linear spin-wave theory and show that various phases such as solid, superfluid, supersolid, and Mott insulator appear in the phase diagram of the mixture. Competition between the interactions and magnetic field causes the mixture to undergo different kinds of first- and second-order phase transitions. By studying the behavior of the spin-wave excitations, we find the reasons of all first- and second-order phase transitions. We also obtain the temperature phase diagram of the system using cluster mean field theory. We show that the checkerboard supersolid phase persists at finite temperature comparable with the interaction energies of bosons.

New boson realization of the Lipkin model obeying the su(2)-algebra

New boson representation of the su(2)-algebra proposed by the present authors for describing the damped and amplified oscillator is examined in the Lipkin model as one of simple many-fermion models. This boson representation is expressed in terms of two kinds of bosons with a certain positive parameter. In order to describe the case of any fermion number, third boson is introduced. Through this examination, it is concluded that this representation is well workable for the boson realization of the Lipkin model in any fermion number.

First-Order Phase Transition and Anomalous Hysteresis of Binary Bose Mixtures in an Optical Lattice

We study a first-order phase transition between superfluid and Mott insulator phases in binary Bose mixtures loaded into a hypercubic optical lattice. The system is described by a two-component Bose-Hubbard model. Considering the difference between the two kinds of bosons in the intra-component interaction strength, we discuss the metastability of the system and the hysteresis associated with the first-order superfluid-Mott insulator transition. It is found that the sweeping of hopping amplitude induces a conventional hysteresis-loop behavior. We also find an anomalous hysteresis behavior when the chemical potential is varied. In the anomalous hysteresis, the phase transition occurs in a unidirectional way and a hysteresis loop does not form.

Exact diagonalization solution and coherent state variational method of the coupling system of carrier and ferromagnetic material

The problem of the coupling system of carrier and ferromagnetic material has been transformed into that of the coupling system of carrier and two kinds of Bosons by using Schwinger's oscillator theory of angular momentum. That the existence of bound polaron in ferromagnetic material depends on the existence of impurity potential in this material is solved exactly by diagonalization and the conclusion obtained is in agreement with the general view point of other works. The values of the energy of ground state obtained by the exact solution and coherent state variation method is agree quite well.The qualitative characters of state vector given by both methods are consistent. The results shows that the coherent state variation method is valid and precise enough for this problem. Exact solution method will provide a basis to check the validity of any other approximate methods.

A Note on the Two-Level Pairing Model Obeying the su(2) su(2)-Algebra: -- Re-formation in Terms of the su(1,1) su(1,1)-Algebra --

The two-level pairing model obeying the su(2) ⊗ su(2)-algebra, which was discussed in a previous paper, is re-formed in the framework of the su(1, 1) ⊗ su(1, 1)-algebra in the Schwinger boson representation. With the aid of the MYT mapping method, the Schwinger boson representation is reduced to the Holstein-Primakoff boson representation, which is expressed in terms of two kinds of bosons. Further, with the aid of the squeezed coherent state, the classical counterpart is obtained.

PSEUDOSPIN SYMMETRY AND SUPERSYMMETRY

The role of a nearly decoupled pseudospin is investigated. A model of supersymmetry with three kinds of bosons is discussed and compared to data for 194 Pt and 195 Pt . Supersymmetry applied to identical bands is discussed.

BCS–BEC crossover in a trapped gas of Fermi atoms with a Feshbach resonance

We present a theoretical study of the BCS–BEC (Bose–Einstein condensation) crossover in a trapped gas of Fermi atoms including the effect of a Feshbach resonance. Going past the simple mean field approximation, we include the effect of fluctuations in the strong coupling limit involving two kinds of Bose molecules, i.e., Feshbach molecules associated with the resonance and preformed Cooper-pairs in which the pairing interaction is mediated by Feshbach quasi-molecules. The superfluid phase transition is shown to change continuously from the BCS-type to a BEC of these two kinds of Bosons, as the threshold energy of the Feshbach resonance is lowered.

The Triaxial Superdeformed Bands in163Lu

Triaxial superdeformed bands in 163 Lu are analysed by applying the Holstein-Primakoff transformation both to the total and single-particle angular momenta. Quite good agreements with the experimental values are reproduced in the energy difference between two superdeformed bands as a function of angular momentum, and also in the ratio of E2 transitions among these bands. The results coming from the exact diagonalization of the particle plus rotor Hamiltonian are compared with the approximate calculation. Recently, triaxial superdeformed bands in 163 Lu nucleus 1) have been observed, which are interpreted as the wobbling motion. 2) We have already proposed the theory for the triaxially deformed bands nearly thirty years ago. 3) The difference between our treatment and Bohr-Mottelson’s text book is in the quantization axis and in the order of approximation. We chose z-axis as the quantization axis, while BohrMottelson chose x-axis. We included the whole effect coming from 1/I where I is the total angular momentum. These two differences help us to get the exact energy eigenvalue at the axially symmetric limit. Moreover, our paper is the first work that applied the Holstein-Primakoff transformation to the nuclear physics. In this paper we extend our old theory to the odd nuclei by introducing two kinds of bosons for the total angular momentum I and the single-particle angular momentum j. Here, we pay attention to the symmetry of the nucleus. Both the rotor and the intrinsic Hamiltonian have D2-symmetry, and are also the function of deformations β and γ. There appears another symmetry in 5-dimensional space (three Eulerian angles, β and γ), which is called Bohr’s symmetry. 4) Thus, it is different from the classical precession around rigid body given in the text book by Landav-Lifshits. 5) We adopt an approximate wave function as, [D I φΩ +( −) I−j+κ D I −K φ−Ω], where κ = Ω − K is restricted to the even value because of the Bohr’s symmetry. Then the energy eigenvalue becomes the average of κ and −κ, and the energy difference between κ+2 and κ becomes constant independent from I. We adopt the irrotational flow formula for the moments of inertia as Ji = Cβ 2 sin 2 (γ− 2π 3 i), and the quadrupole moments are proportional to these moments of inertia. In the numerical analysis for 163 Lu, we adopt the state for the triaxially deformed superdeformed band 1 (TSD1) as K = 1 Ω = 1 (κ = 0), and for the triaxially deformed superdeformed band 2 (TSD2) as K = − 3 Ω = 1 (κ = 2). We adopt γ =1 9 ◦ , and unique-parity level i13/2 for the last nucleon. The band head energies of TSD1 and TSD2 are adjusted to the experimental energies. Three moments of inertia become J irr

Axial baryon number nonconserving antisymmetric tensor four-quark effective interaction

We discuss the phenomenological consequences of the ${U}_{A}(1)$ symmetry-breaking two-flavor four-fermion antisymmetric (AS) Lorentz tensor interaction Lagrangians. We use the recently developed methods that respect the ``duality'' symmetry of this interaction. Starting from the Fierz transform of the two-flavor 't Hooft interaction (a four-fermion Lagrangian with AS tensor interaction terms augmented by a Nambu--Jona-Lasinio- type Lorentz scalar interaction responsible for dynamical symmetry breaking and quark mass generation), we find the following. (1) Four antisymmetric tensor and four antisymmetric pseudotensor bosons exist which satisfy a mass relation previously derived for scalar and pseudoscalar mesons from the 't Hooft interaction. (2) Antisymmetric tensor bosons mix with vector bosons via one-fermion-loop effective couplings so that both kinds of bosons have their masses shifted and the fermions (quarks) acquire anomalous magnetic moment form factors that explicitly violate chiral symmetry. (3) The mixing of massive antisymmetric tensor fields with vector fields leads to two sets of spin-one states. The second set of spin-one mesons is heavy and has not been observed. Moreover at least one member of this second set is tachyonic, under standard assumptions about the source and strength of the antisymmetric tensor interaction. The tachyonic state also shows up as a pole in the spacelike region of the EM form factors. (4) The axial-vector fields' mixing with antisymmetric tensor bosons is proportional to the (small) isospin-breaking up-down quark mass difference, so the mixing-induced mass shift of axial vector mesons is negligible. (5) The antisymmetric tensor version of the Veneziano-Witten ${U}_{A}(1)$ symmetry-breaking interaction does not lead to tachyons, or any antisymmetric tensor field propagation to leading order in ${N}_{C}.$

Compositeantisymmetric tensor bosons in a four-fermion interactionmodel

We discuss the phenomenological consequences of the UA(1) symmetry-breaking two-flavour four-fermionantisymmetric (AS) Lorentz tensor interaction Lagrangians. Weuse the recently developed methods that respect the `duality'symmetry of this interaction. Starting from the Fierztransform of the two-flavour 't Hooft interaction (afour-fermion Lagrangian with AS tensor interaction termsaugmented by Nambu and Jona-Lasinio (NJL)-type Lorentz scalarinteraction responsible for dynamical symmetry breaking andquark mass generation), we find the following.(a) Four antisymmetrictensor and four AS pseudotensor bosons exist which satisfy amass relation previously derived for scalar and pseudoscalarmesons from the 't Hooft interaction. (b) Antisymmetrictensor bosons mix with vector bosons via one-fermion-loopeffective couplings so that both kinds of bosons have theirmasses shifted and the fermions (quarks) acquire anomalousmagnetic moment form factors that explicitly violate chiralsymmetry. (c) The mixing of massive AS tensor fields withvector fields leads to two sets of spin-1 states. Thesecond set of spin-1 mesons is heavy and has not beenobserved. Moreover, at least one member of this second setis tachyonic, under standard assumptions about the source andstrength of the AS tensor interaction. The tachyonic statealso shows up as a pole in the space-like region of the electromagneticform factors. (d) The mixingof axial-vector fields withantisymmetric tensor bosons is proportional to the (small)isospin-breaking up-down quark mass difference, so themixing-induced mass shift is negligible. (e) The AS tensor versionof the Veneziano-Witten UA(1) symmetry-breakinginteraction does not lead to tachyons, or any AS tensor fieldpropagation to leading order in NC.

Boson-boson stars and their gravitational redshifts

We study the static spherically symmetric equilibrium configurations made from two kinds of bosons with different masses and their stabilities. The resulting configurations can have larger gravitational redshift than the ordinary boson stars. We find that the limiting value of the redshift is 1.08 for the mass ratio α≫1.

Enhancement of the Debye frequency due to a charged-boson exchange model of high temperature superconductors

A simple model of 1-2-3 superconductors in which electrons (holes) in CuO 2 planes interact via exchange with two kinds of bosons is considered. Namely, via one-phonon exchange (weak coupling-Cooper pairing), and via paired holes on oxygen O 0 from Cu-O chains. The mechanisms of paired holes exchange (“charged bosons”-“O 0” exchange) considered here in strong coupling leads to the enhancement of the Fröhlich constant g f ( g 2 F→ Kg 2 F), and as a consequence to the enhancement of the Debye frequency ω D K = f K ω D , f K ≫ 1. In the proposed model the exact expression for the constant K is derived.

The 3-quadrupole phonon states in second quantization

The properties of phonon states built up of 3 quadrupole bosons are studied in second quantization. A new representation is proposed in the case of 3 identical bosons. Three equivalent representations are found to take place in the case of two kinds of bosons. The previously known results are not altered when all the three bosons are different.

Chapter 2. Outline of the Mode-Mode Coupling Theory

The main purpose of this chapter is to recapitulate an essential part of the mode-mode coupling theoryu~a> by putting great emphasis on clarifying the basic idea, because it has been published in separate papers in a splitted form. The theory of the dressed n-quasiparticle (nQP) mode was developed for the purpose of taking account of the anharmonicity effects automatically, since it had become dear by means of the boson-expansion method4>. 5> that the anharmonicity effects neglected in the random-phase approximation (RPA) play a decisive role in such a finite quantal system as nuclei. Furthermore it has been developed into a microscopic theory capable to treat the dynamical mutual interplay between the pairing and the quadrupole correlation which are generally considered to be the basic correlations in transitional nuclei. On the other hand, there is a phenomenological approach called the inter­ acting boson model (IBM) by Arima and Iachello.6> In this model two kinds of bosons are used; they may be regarded to be introduced in order to embrace the main dyrramical correlations in nuclei. It can successfully classify many experimental data by using a group theoretical language. There have also been some efforts to give a microscopic foundation of the phenomenologi­ cal IBM by using the single-j-shell model.n.s> As extensively discussed in Chapter 1, the dynamical interplay between the pairing and the quadrupole degrees of freedom might play a decisive role for the mechanism of the phase transition from spherical to deformed nuclei and the microscopic structure of the collective excited states could be changed from nucleus to nucleus. Such a dynamical interplay can never be described by the simple group theory (e.g. the IBM), where the microscopic structure of the collective boson is supposed to be unchangeable. In order to make clear the structural change of the collective excited states, therefore, we have to construct a theory which can treat the dynamical interplay between the

Theory of Pairing Vibration Mode

A simple and exactly solvable model is proposed which exhibits all the characteristic features of the pairing vibration model of A. Bohr; the near-harmonic level sequences and the strong enhancements of the (L=O) two-nucleon transfer reaction. This model consists of degenerate many-j single particle levels and degenerate hole levels with an energy-gap between them. The pairing interactions are taken into account, except for those between the particle and hole states. Using the empirical values of the single particle and hole energies together with the strength of the pairing interaction, the model is compared with the experi­ mental data in Ni, Sn and Ph isotopes to get quantitative agreement. This model is further used as the basis states to diagonalize the more realistic case of the non-degenerate model with pairing interactions among all levels. It is found that our pair­ ing vibration mode remains predominantly in the ground state of the non-degenerate model. 1l has been proved to be a convenient way of the classification of o+ states of spherical even nuclei. The essential idea is to view the quanta associating with the particle pair correlation as a boson with energy hw, while the quanta arising from pair correlation of holes is regarded as an another kind of boson with the same energy. Taking these two kinds of boson as building stones, a o+ state can be considered as consisting of w bosons of' the particle pair and w bosons of the hole pair, its energy being given by E= (w+w)hw measured from the (w=w=O) o+ state. This pairing vibrational state will be denoted as ( w, w). Bohr1l and Nathan2l made a systematic survey of this scheme in the regions around Ni66, Sn114 and Pb 208• Since the bosons in this model are related to the pairing correlation, the pairing vibration states will be characterized by the strong enhancement of (L= 0) two-nucleon transfer reaction. After this proposal, many high resolution experiments of the two-nucleon transfer reaction have been performed to test the pairing vibration scheme. Microscopic treatment of the pairing vibration model has been made first by Bes and Broglia8l and later by several authors.4l All these works are based on the formal analogy of the pairing correlation to the conventional random-phase­ approximation treatment of nuclear surface vibration, so that the microscopic foundation of the pairing vibration model seems to be not necessarily clear. In view of the above situation, we shall propose an exactly solvable, but nevertheless, realistic model which exhibits all the characteristic features of the pairing vibration model--near-harmonic level sequences and the strong enhance

Two Kinds of Bosons and Bose Condensates

This paper deals with ordinary material systems whose elementary constitutents are fermions. It is pointed out that in such systems there can occur two kinds of bosons with quite different physical and mathematical characteristics. Type I bosons are bound complexes of an even number of fermions (such as $^{4}\mathrm{He}$); and type II bosons are elementary excitations which are bound complexes of fermions and their holes (such as excitons). When the first type condenses, a superfluid state results with so-called off-diagonal, long-range order; while when the second type condenses, there is no superfluidity, but a change in spatial order. Thus both kinds of long-range order are related to Bose condensation.