Thermalization in one- plus two-body ensembles for dense interacting boson systems

Employing one- plus two-body random matrix ensembles for bosons, temperature and entropy are calculated, using different definitions, as a function of the two-body interaction strength λ   for a system with 10 bosons (m=10$m=10$) in five single-particle levels (N=5$N=5$). It is found that in a region λ∼_λt$\lambda \sim {\lambda }_t$, different definitions give essentially the same values for temperature and entropy, thus defining a thermalization region. Also, (m,N)$(m,N)$ dependence of _λt${\lambda }_t$ has been derived. It is seen that _λt${\lambda }_t$ is much larger than the λ values where level fluctuations change from Poisson to GOE and strength functions change from Breit–Wigner to Gaussian.     

Quasidynamical symmetry in an interacting boson model phase transition

The apparent persistence of symmetry in the face of strong symmetry-breaking interactions is examined in a many-boson model. The model exhibits a transition between two phases associated with U(5) and O(6) symmetries, respectively, as the value of a control parameter progresses from 0 to 1. The remarkable fact is that, in spite of strong mixing of the symmetries for intermediate values of the control parameter, the model continues to exhibit the characteristics of its closest symmetry limit for all but a relatively narrow transition region that becomes progressively narrower as the boson number increases. This phenomenon is explained in terms of quasidynamical symmetry.     

Eigenstates of boson creation operator

We examine the existence of right-hand eigenstates (or eigenkets) of the boson creation operator a and determine their coordinate and their Bargmann representation. The eigenkets of the creation operator are ultrasingular and cannot be considered as a limiting case of normalizable states. Applications of these eigenstates as auxiliary states for purposes of representation of states by path integrals over coherent states are discussed. A completeness relation for coherent states on paths through the complex plane is derived and special examples of its application are considered. Received 9 March 2001 and Received in final form 13 June 2001     

Proton-neutron sdg boson model and spherical-deformed phase transition

The spherical-deformed phase transition in nuclei is described in terms of the proton-neutron sdg interacting boson model. The sdg hamiltonian is introduced to model the pairing+quadrupole interaction. The phase transition is reproduced in this framework as a function of the boson number in the Sm isotopes, while all parameters in the hamiltonian are kept constant at values reasonable from the shell-model point of view. The sd IBM is derived from this model through the renormalization of g-boson effects.     

Coherent incoherent transition in the spin boson model with a super-ohmic bath

The temperature effect on tunnelling splitting in the spin--boson model with a super-ohmic bath is studied by the small polaron theory. The coherent--incoherent transition temperature is calculated and its dependence on dissipation strength and bare tunnelling splitting is analysed. In additional to the traditional transition point described in textbooks, a new kind of transition is found in the low dissipation region, showing different temperature dependence in the transition. The relation to the corresponding transition in the polaron--phonon system is also discussed.     

E1 calculations in thesdf-interacting boson model

A simple IBA-sdf form for theE1 transition operator containing an one-body term and a two-body term is tested in a non-analytical case. TheE 1 transition probabilities in the rare-earth region are reproduced rather well.     

On an interpolation model for the transition operator for Markov and non-Markov processes

A phenomenological interpolation model for the transition operator of a stationary Markov process is shown to be equivalent to the simplest difference approximation in the master equation for the conditional density. Comparison with the formal solution of the Fokker-Planck equation yields a criterion for the choice of the correlation time in the approximate solution. The interpolation model is shown to be form-invariant under an iteration-cum-rescaling scheme. Next, we go beyond Markov processes to find the effective time-development operator (the counterpart of the conditional density) in the following very general situation: the stochastic interruption of the systematic evolution of a variable by an arbitrary stationary sequence of randomizing pulses. Continuous-time random walk theory with a distinct first-waiting-time distribution is used, along with the interpolation model for the transition operator, to obtain the solution. Convenient closed-form expressions for the ‘averaged’ time-development operator and the autocorrelation function are presented in various special cases. These include (i) no systematic evolution, but correlated pulses; (ii) systematic evolution interrupted by an uncorrelated (Poisson) sequence of pulses.     

Effective operator for the transition density

The effective shell-model operator for electric transition densities is evaluated. The influence of the choice of single-particle wavefunctions, residual interaction (G-matrix) and correlations within the valence shell as well as core-polarisation effects, is investigated. The excitation of the lowest 2⁺ in ⁵⁸Ni is considered as an example. The shape of the transition density can be reproduced only after renormalisation of the effective transition density operator to account for core polarisation. The possible importance of screening terms and many-body terms in the expansion for the effective operator are discussed.     

The operator algebra of theE 8 typesu(2) WZW theory

The operator product coefficients for primary fields of theE ₈ typesu(2) Wess-Zumino-Witten theory are calculated. The results confirm the equivalence of this theory to the level oneG ₂ WZW theory. They can also be used to clarify the relation to the level three (A type)su(2) WZW theory.     

M1 transitions in the (sdg) boson model

Using the $\text{1}\text{N}$ expansion technique we derive expressions for β→g, γ→g and γ→γ M1 transitions in a general boson model. The M1 matrix elements in the sdg-boson model are similar in form to those in the neutron-proton IBM. Comparisons are made to some selected M1 data exhibiting collective character.     

Normal and antinormal ordering of boson operator functions

It is shown that the divergences associated with antinormally ordered forms of boson operators, as discovered computationally by Baltin, is due to an unjustifiable interchange of order of summation.     

Dynamical invariants and the collision operator in the limit of long time for a perturbed two-body problem

The collision operator for a hamiltonian system of two bodies interacting through a perturbed Kepler potential is obtained and analyzed in the limit corresponding to long time. In this limit, the collision operator differs from zero for resonance. The implications on dynamical invariants are discussed.     

A microscopic boson model for collective transition nuclei: Schwinger representation of the SO(8) shell model algebra

An equivalent representation of the SO(8) fermion pair algebra is given in terms of s- and d-bosons. The s-boson is a quasispin vector-boson in our formalism. Boson quasispin is the clue to treating the pairing degrees of freedom on the same footing as the particle-hole degrees of freedom. As a consequence, we obtain the pairing rotation as a collective mode, in addition to the spatial rotations described by the IBM. We compare results of the exact numerical solution of the secular equation with those calculated in the HFB mean field approximation which attains the form of boson coherent states in our method. Goldstone bosons can be introduced which represent collective soft modes. Two components of the quasispin vector-boson can be associated with the removal and addition modes of the pairing vibration. The third component is the IBM s-boson.     

Prospects for the search for a standard model Higgs boson in ATLAS using vector boson fusion

The European Physical Journal C - The potential for the discovery of a Standard Model Higgs boson in the mass range m H < 2 m Z in the vector boson fusion mode has been studied for the ATLAS...