Rotational states and interacting bosons

Rotational states are investigated in terms of the interacting boson model. A ground-state rotational band is built from a shell-model many-nucleon system. It is shown that the S and D collective nucleon pairs play dominant roles in low-spin states of the band and that this S-D dominance is broken in high-spin states. The intrinsic hamiltonian is constructed from the effective nucleon-nucleon interaction used in the shell model calculation and the intrinsic state of the rotational band is shown to be comprised primarily of S and D pairs. We introduce a λ boson which is a linear combination of s, d and higher angular momentum bosons, and the boson intrinsic state is given by the λ boson condensate state. The s and d bosons constitute approximately 90 % of the λ boson, and the boson intrinsic state reproduces very well the energy and the intrinsic quadrupole moment of the nucleon intrinsic state. The s-d boson hamiltonian is constructed from the S and D pairs, while effects of non S-D pairs are also included by renormalization of the boson hamiltonian. The renormalization is made by using the λ boson. The s-d boson quadrupole operator is derived similarly. The boson hamiltonian and quadrupole operator thus derived reproduce well the exactly calculated values for low-spin states of the rotational band, although the accuracy decreases in high-spin states. It is shown that the IBM possesses the same physical picture of the rotational states as the Nilsson scheme with pairing correlations. It is therefore concluded that the IBM is capable of describing low-lying rotational states.     

Polarization of interacting bosons with spin

We prove that in the absence of explicit spin-dependent forces one of the ground states of interacting bosons with spin is always fully polarized. Generally, this state is degenerate with other states, but one can specify the exact degeneracy. For T>0, the magnetization and zero-field susceptibility exceed that of a pure paramagnet. The results are relevant to experimental work on triplet superconductivity and condensation of atoms with spin. They eliminate the possibility, raised in some theoretical speculations, that the ground state or positive temperature state might be antiferromagnetic.     

Shell model description of interacting bosons

The interacting boson model, describing collective states of even-even nuclei, is introduced as a drastic truncation of large scale shell model calculations. The shell model hamiltonian can be diagonalized by using a correspondence, or mapping, of the nucleon states in the truncated space into states obtained by coupling proton and neutron s- and d-bosons. The equivalent boson hamiltonian in a simple case is obtained and diagonalized. Eigenstates with definite proton-neutron symmetry (good F-spin) emerge for certain values of proton and neutron numbers. In general the situation is more complex but the results obtained follow closely the experimental data.     

An intrinsic spin for interacting bosons

The addition, to the usual set of T=1 bosons, of s and d bosons with T=0 and an intrinsic spin of S=1 leads to a version of the IBM which incorporates the Wigner supermultiplet symmetry.     

Theory of interacting bosons without anomalous propagators

A self-consistent theory of an interacting many-boson system is presented in the framework of the formalism of thermodynamic Green's functions without introducing anomalous propagators referring to the concept of a restricted average or any other symmetry-breaking assumption. Depending on the interaction, the theory comprises both phenomena of Bose-Einstein condensation and of boson pairing without a macroscopic occupation of the zero-momentum single-particle state. The results are discussed with reference to the problem of Bose-Einstein condensation of ⁴He II and to the phenomenon of exciton condensation and exciton pairing in highly excited semiconductors.     

A reference model for anomalously interacting bosons

A simple reference model for anomalously interacting bosons is proposed and implemented in the CompHEP package. This allows preparing for an experimental search of these bosons at powerful colliders, such as Tevatron and LHC. New signatures and some experimental consequences are shortly considered.     

Mixtures of strongly interacting bosons in optical lattices

We investigate the properties of strongly interacting heteronuclear boson-boson mixtures loaded in realistic optical lattices, with particular emphasis on the physics of interfaces. In particular, we numerically reproduce the recent experimental observation that the addition of a small fraction of 41K induces a significant loss of coherence in 87Rb, providing a simple explanation. We then investigate the robustness against the inhomogeneity typical of realistic experimental realizations of the glassy quantum emulsions recently predicted to occur in strongly interacting boson-boson mixtures on ideal homogeneous lattices.     

Infrared behavior of interacting bosons at zero temperature

We review the infrared behavior of interacting bosons at zero temperature. After a brief discussion of the Bogoliubov approximation and the breakdown of perturbation theory due to infrared divergences, we present two approaches that are free of infrared divergences—Popov’s hydrodynamic theory and the nonperturbative renormalization group—and allow us to obtain the exact infrared behavior of the correlation functions. We also point out the connection between the infrared behavior in the superfluid phase and the critical behavior at the superfluid-Mott-insulator transition in the Bose-Hubbard model.     

Condensation of interacting bosons in a random potential

We study the effects of random scatterers on the ground state of the one-dimensional Lieb-Liniger model of interacting bosons on the unit interval. We prove that, in the Gross-Pitaevskii limit, Bose Einstein condensation takes place in the whole parameter range considered. The character of the wave function of the condensate, however, depends in an essential way on the interplay between randomness and the strength of the two-body interaction. For low density of scatterers or strong interactions the wave function extends over the whole interval. High density of scatterers and weak interaction, on the other hand, leads to localization of the wave function in a fragmented subset of the unit interval.     

Calculation of sound velocity and structure factor for interacting bosons

We have calculated the velocities of the first and second sound and the structure factor for a system of interacting bosons. The two-body interatomic potential used is assumed to be composed of a hard core followed by a sum of both repulsive and attractive gaussians.     

Universal vortex formation in rotating traps with bosons and fermions

We show that the rotation of trapped quantum mechanical particles with a repulsive interaction can lead to vortex formation, irrespective of whether the particles are bosons or (unpaired) fermions. The exact many-particle wave function constitutes similar structures in both cases, implying that this vortex formation is indeed universal.     

Radial distribution function and second virial coefficient for interacting bosons

We have studied the radial distribution function and the second virial coefficient of interacting bosons. The second virial coefficient has been deduced theoretically and is in good agreement with experimental values. The third virial coefficient has been calculated from the experimental values of the pressure.     

Superfluid-insulator transition in a moving system of interacting bosons

We analyze the stability of superfluid currents in a system of strongly interacting ultracold atoms in an optical lattice. We show that such a system undergoes a dynamic, irreversible phase transition at a critical phase gradient that depends on the interaction strength between atoms. At commensurate filling, the phase boundary continuously interpolates between the classical modulation instability of a weakly interacting condensate and the equilibrium quantum phase transition into a Mott insulator state at which the critical current vanishes. We argue that quantum fluctuations smear the transition boundary in low dimensional systems. Finally we discuss the implications to realistic experiments.     

Competitive localization

Many problems may be cast into the form of entities utilizing resources and competing for those resources. Several models inspired by such competition have previously been shown to exhibit clumping and in some cases localization in their stable equilibrium states. We show that such localization, which we wish to call ‘competitive localization’, is generic, and we provide techniques to accurately find the equilibrium states when competitive localization occurs. We also expose some difficulties in relying on numerical simulations when exploring models of this type.