Bosonization Method Research Articles

Pairing and surface bosons and the group Sp(4)

The Dyson-Maleev boson method for representing the group SU(2) is extended to the group Sp(4) resulting in a considerable simplification over the corresponding extension of the Holstein-Primakoff expansion. The underlying physical system contains simultaneous excitations of particle, hole and particle-hole pairs for which both collective and non-collective bosons are introduced.

Anisotropy of flux-line lattice in cubic superconductors

The magnetic field due to a single vortex in anisotropic type-II superconductors with cubic crystal symmetry is calculated at $T=0$\ifmmode^\circ\else\textdegree\fi{}K by means of the boson method. The results for the magnetic field are used in our analysis of stable orientation of the flux-line lattice with respect to the crystal lattice. The theoretical results agree well with the stable orientation of the flux-line lattice observed in weak-field region in Nb and Pb-Tl at low temperature. The boson characteristic function for cubic superconductors is also presented.

Surface electromagnetic waves in superconductors

Abstract Varying electromagnetic fields at the surface of a superconductor are studied by means of the boson method. It is found that the frequency of the surface electromagnetic waves satisfies a dispersion relation which is entirely controlled by the system itself.

Temperature and impurity effects on type-II superconductors

An analysis of the magnetic properties of type-II superconductors is made by means of the boson method. Temperature and impurity effects are considered and the results are compared with some experimental data.

Analysis of the mixed state of superconductors at various temperatures

Making use of the boson method we obtain the magnetization curves of type-II superconductors for various values of t= T/ T c and ϰ B = λ L/ξ 0. These results are compared with some experimental data.

Boson method in superconductivity: Study of systems containing scalar impurities

The boson formulation of superconductivity is extended to the study of superconducting systems containing randomly distributed non-magnetic impurities.

The Boson Method for Anisotropic Superconductors

AbstractIn this paper a rigorous derivation of the boson method for anisotropic superconductors is presented. A most general form of macroscopic equations for the current and magnetic field is obtained from the assumption that the Lagrangian is gauge invariant. We then proceed to explain what kind of approximations can be introduced in order to simplify these macroscopic equations. We formulate the results in a form convenient for analysing the magnetic properties of anisotropic superconductors. An improved version of analysis for the vortex normal‐core energy is also presented.

Large-amplitude collective motion in the Lipkin model

It is shown how a simple reinterpretation of the ''transition-operator boson method'' eliminates the difficulty noted by Okubo. The revised method is applied to the problem of anharmonic motion in the Lipkin model. The occurrence of a non-positive-definite mass parameter, as obtained by Holzwarth and by Giraud and Grammaticos, is then exposed as the easily avoidable consequence of an inauspicious choice of collective coordinate. (AIP)

On the validity of the boson method for transitional nuclei

Two different approximation schemes for calculating low-lying collective states in transitional nuclei are investigated. Approximate matrix elements of the Hamiltonian in multiphonon space are compared with a fourth-order Marumori boson expansion. The two-phonon norm is decisive for the quality of the approximations and it is found that in realistic cases the truncation of the boson expansion leads to inaccuracies comparable to those caused by the restriction of the fermion space to the multiphonon states only. For the investigated cases of quadrupole phonons the inaccuracies lie around 10–15 %.

A Rigorous Formulation of the Boson Method in Superconductivity

AbstractA rigorous formulation of the boson method in superconductivity is presented. Assuming the local gauge invariance and presence of a phase‐dependent order parameter and utilizing the path‐integral formalism, we derive a set of macroscopic equations which control all the superconducting states. These equations are model‐independent. They contain certain functions and parameters which should be calculated for a given model. Using this rigorous formulation, we study what kind of approximations are involved in the usual formulation of the boson method and how these approximations can be improved.

Quark confinement and quantum vortex strings in Nambu-Heisenberg model

By way of the Boson method in superconductivity, interacting vortex string are derived from a Nambu-Heisenberg quark-gluon field theory with an inhomogeneous vacuum. Quarks and gluons can be completely confined within Nambu strings seen as the dominant low energy manifestation of subhadronic interactions.

Generalised Hartree-Fock method for bosons with attractive interactions

Abstract The generalised Hartree-Fock method is used to discuss the zero-temperature properties of a system of bosons interacting through a short-ranged repulsive potential and weak, long-ranged attractive potential. It is shown that, provided the negative scattering amplitude associated with the two-body potential is suitably restricted, a stable N -body bound state of the system exists. The excitation spectrum at small momenta is well defined and of the phonon type. These results substantiate earlier calculations based on perturbation theory.

Computation of the magnetization curve for vanadium at T = 0°C

Abstract The magnetization of pure vanadium for H close to Hcl at T = 0°K is calculated by the boson method. The results are in very good agreement with experiment.

Time-dependent phenomena in weakly-coupled superconductors

Two superconducting systems joined by a weak link present a great variety of phenomena which are not totally explained by the Josephson formulation. In this paper we give a general theory of the phenomena observed in these systems when time-dependent effects are taken into account. The formulation, presented as an application of the boson method in superconductivity, is derived from first principles in the framework of a microscopic theory. Our results show the appearance of harmonic and subharmonic steps in theI-V characteristic of the system; the presence or not of subharmonic steps is essentially determined by the geometry of the system. The existence of subharmonic terms in a.c. effects is shown to be strongly related to the diffraction pattern presented by theI c -H curves in d.c. experiments performed on the same sample. A comparison of the usual theory and the present formulation is discussed.

The boson method in superconductivity: Application to the study of the Josephson effect

The boson method in superconductivity is applied to the study of the Josephson effect. This approach permits us to calculate all the important observable quantities, like the magnetic field and the current, at any point of the system, without making’ use of any phenomenological assumption, such asJ =j1 sinϕ. The results of our calculation show a qualitative agreement with those computed by other authors on the basis of the Josephson equation, though we do not have and we do not use this equation. The boson method is also able to yield results for a neutral superconductor, so that the calculations can be applied to the analogous effects that can be found in superfluid liquids. Finally, we would like to point out that our results do not necessarily satisfy the phenomenological equationJ =j1 sinϕ.

Nuclear structure in ideal space

The boson method, previously developed for quasiparticles, is used to transcribe the shell model Hamiltonian directly from the particle space to the boson space preserving both the particle number and the Pauli principle. The method is tested with a calculation of the spectrum of 59Ni.

Boson Method not Violating the Pauli Principle Applied to the Three-Quasiparticle System

The boson method is studied for a system with one and three quasiparticles. A basis is constructed in the ideal space in such a way that the Pauli principle is fully satisfied. The spurious states due to the particle nonconservation are properly eliminated. Numerical calculations are presented and a comparison is made with Kuo's method. The boson method can be easily extended to the study of systems having two phonons.

Quantum effects in weakly coupled superconductors

The boson method in superconductivity is applied to the study of two superconductors weakly joined. A general theory of the a.c. effects is obtained; in particular the presence of harmonic and subharmonic steps in the 1–5 characteristic of the system is derived.

Quantum effects in weakly coupled superfluid liquids

The boson method is applied to the study of two superfluid liquids joined together by a weak link. A microscopic derivation of experimental results is presented.

The boson method and the antisymmetrization problem

Abstract The transcription of the quasiparticle in the ideal space is studied for systems containing up to five quasiparticles. A way is found to introduce properly the Pauli exclusion principle and the states are completely antisymmetrized. The quasiparticle operators and their products appearing in the Hamiltonian are also transcribed in that space. The matrix elements of the products of quasiparticle operators evaluated in the ideal space are exactly the same as those evaluated in the quasiparticle space. This enables one to determine many anharmonic corrections.