The dynamical properties of an impurity in the hard-sphere Bose gas are investigated by extending the pseudopotential method and Hamiltonian of the author's previous work. The interaction potential between two impurities is calculated up to one quasiparticle exchange and is shown to have a Yukawa form of attraction with a range of (16πρa)−1/2 in addition to the hard-core interaction at the origin. (ρ and a are the density of the boson gas and hard-core diameter of the boson, respectively.) Necessary conditions for impurities to have a bound state are also obtained. It is found that the mass of the impurity must be greater than approximately nine times the boson mass, and the density of the boson gas must lie in some range with a maximum and minimum. Then the differential cross section for Compton-type scattering and one quasiparticle production on an impurity are calculated. The Čerenkov radiation of sound quanta is studied when the impurity is traveling very fast in the hard-sphere Bose gas. It is found that there is no radiation unless the velocity v of the impurity is faster than [k2 + (16πρa)]1/2 and the radiation has a maximum for the angle θ0 such that cosθ0 = (k2 + 16πρa)½/v. The cross section for Čerenkov radiation is also calculated. (k is the momentum of the quasiparticle emitted in the Čerenkov radiation.)
The dynamical properties of an impurity in the hard-sphere Bose gas are investigated by extending the pseudopotential method and Hamiltonian of the author's previous work. The interaction potential between two impurities is calculated up to one quasiparticle exchange and is shown to have a Yukawa form of attraction with a range of (16πρa)−1/2 in addition to the hard-core interaction at the origin. (ρ and a are the density of the boson gas and hard-core diameter of the boson, respectively.) Necessary conditions for impurities to have a bound state are also obtained. It is found that the mass of the impurity must be greater than approximately nine times the boson mass, and the density of the boson gas must lie in some range with a maximum and minimum. Then the differential cross section for Compton-type scattering and one quasiparticle production on an impurity are calculated. The Čerenkov radiation of sound quanta is studied when the impurity is traveling very fast in the hard-sphere Bose gas. It is found that there is no radiation unless the velocity v of the impurity is faster than [k2 + (16πρa)]1/2 and the radiation has a maximum for the angle θ0 such that cosθ0 = (k2 + 16πρa)½/v. The cross section for Čerenkov radiation is also calculated. (k is the momentum of the quasiparticle emitted in the Čerenkov radiation.)
The impurity excitation spectrum is calculated for the hard-sphere Bose gas with dilute impurity concentration, using the pseudopotential method of Lee, Huang, and Yang. The spectrum for the ideal case, in which the mass and interaction of impurity are the same with those of the bosons in the gas, is k2 in the unit of 2ma = h/ = 1 (ma being the mass of boson, and k the momentum of impurity), with an effective mass correction of −6445[(ρa3)12/π12]k2+O[(ρa3)k2,k4], where ρ is the density of the boson gas, and a is the hard-sphere diameter of the boson. The general impurity case is also calculated and found to have an impurity spectrum rk2, with a similar effective mass correction, where r is the mass ratio of the boson to the impurity.
We investigate the properties of an impurity immersed in a dilute Bose gas at zero temperature using quantum Monte Carlo methods. The interactions between bosons are modeled by a hard-sphere potential with scattering length a, whereas the interactions between the impurity and the bosons are modeled by a short-range, square-well potential where both the sign and the strength of the scattering length b can be varied by adjusting the well depth. We characterize the attractive and the repulsive polaron branch by calculating the binding energy and the effective mass of the impurity. Furthermore, we investigate the structural properties of the bath, such as the impurity-boson contact parameter and the change of the density profile around the impurity. At the unitary limit of the impurity-boson interaction, we find that the effective mass of the impurity remains smaller than twice its bare mass, while the binding energy scales with ${\ensuremath{\hbar}}^{2}{n}^{2/3}/m$, where n is the density of the bath and m is the common mass of the impurity and the bosons in the bath. The implications for the phase diagram of binary Bose-Bose mixtures at low concentrations are also discussed.
In this thesis we investigate the properties of impurities immersed in a dilute Bose gas at zero temperature using quantum Monte-Carlo methods. The interactions between bosons are modeled by a hard sphere potential with scattering length a, whereas the interactions between the impurity and the bosons are modeled by a short-range, square-well potential where both the sign and the strength of the scattering length b can be varied by adjusting the well depth. We calculate the binding energy, the effective mass and the pair correlation functions of a impurity along the attractive and the repulsive polaron branch. In particular, at the unitary limit of the impurity-bosons interaction, we find that the binding energy is much larger than the chemical potential of the bath signaling that many bosons dress the impurity thereby lowering its energy and increasing its effective mass. We characterize this state by calculating the bosons-boson pair correlation function and by investigating the dependence of the binding energy on the gas parameter of the bosonic bath. We also investigate the ground-state properties of M impurities in a Bose gas at T=0. In particular, the energy and the phase diagram by using both quantum Monte-Carlo and mean field methods.
The low-lying energy eigenstates of a one-dimensional (1D) system of many impenetrable point bosons and one moving impurity particle with repulsive zero-range impurity-boson interaction are found for all values of the impurity-boson mass ratio and coupling constant. The moving entity is a polaronlike composite object consisting of the impurity clothed by a comoving gray soliton. The special case with impurity-boson interaction of point hard-core form and impurity-boson mass ratio mi/m unity is first solved exactly as a special case of a previous Fermi-Bose (FB) mapping treatment of soluble 1D Bose-Fermi mixture problems. Then a more general treatment is given using second quantization for the bosons and the second-quantized form of the FB mapping, eliminating the impurity degrees of freedom by a Lee-Low-Pines canonical transformation. This yields the exact ground state (total linear momentum q=0) and exact boson-impurity distribution function in the thermodynamic limit for arbitrary mi/m and arbitrary impurity-boson interaction strength. These results are then extended to states with q>0.
The problem of the low-lying spectrum of a system of many bosons and one impurity particle interacting by repulsive, central, two-body forces is treated by first eliminating the dynamical variables of the impurity in terms of an added effective boson-boson interaction, and then treating the boson system by an extension of Bogolubov's method. In this way various physical properties of the clothed impurity particle, including its dispersion relation and effective mass, are obtained; singularities associated with the onset of acoustical wave drag as the impurity speed reaches the speed of sound in the boson medium are predicted. The parameters measuring the smallness of the corrections to the above results are shown to be the dimensionless boson-boson interaction, the dimensionless boson-impurity interaction, and the boson-impurity mass ratio. The treatment is then adapted to the case of hard spheres at low density by employing the Huang-Yang-Lee pseudopotential method; the results are valid if the dimensionless boson density and the boson-impurity mass ratio are small. A few remarks are made concerning the connection of the models treated with experimentally accessible results.
The properties of Bose-Einstein-condensed systems of hard spheres at high density are studied by taking into account higher-order corrections beyond the Hartree-Fock-Bogoliubov approximation. Based on a diagrammatic technique of the perturbation expansion starting from the Bogoliubov approximation, we show that the effective interactions separate into two distinct parts: the screened and condensate-mediated interactions. The latter is described by the exchange of virtual quasiparticles between noncondensate bosons via the Bose-Einstein condensate and is attractive for small energy transfer. We calculate the condensation temperature, excitation spectrum, and condensate density in the whole region of the gas parameter. It is shown that the condensate temperature decreases compared to that of an ideal Bose gas due to hard-sphere interactions. We find that the condensate-mediated attraction between noncondensate bosons leads to an enhancement of the anomalous self-energy and, as a consequence, to the emergence of a roton minimum in the excitation spectrum and to the strong suppression of the condensate fraction in the region of high density.