Multiparticle distributions and intercepts of
r-particle correlation functions in the symmetric Tamm-Dancoff type
q-Bose gas model
Symmetric Tamm-Dancoff (STD) type
q-deformed quantum oscillators are used as the base for constructing the respective STD type
q-Bose gas model. In this letter, within the STD
q-deformed Bose gas model we derive explicit analytic expressions for the
r-particle momentum distribution functions, and for the (momentum) correlation function intercepts of 2nd, 3rd, and any
rth order. Besides, we obtain large-momentum asymptotic formulas for the
rth order intercepts which show dependence on the
q-parameter only. The obtained formulas provide new example, in addition to already known two cases, of exact results for
r-particle distributions and the correlation function intercepts in deformed analogs of Bose gas model.
The paper is devoted to the theory of an ideal Bose-gas with a finite number N of particles. The exact expressions for the partition functions and occupation numbers of the model in the grand canonical, canonical, and microcanonical ensembles are found. From the calculations, it is followed that, oppositely to the accepted opinion that the chemical potential μ of an ideal Bose-gas is only negative, it can take values in the range −∞ < μ < ∞. The asymptotic expressions (in the case N ≫ 1) for the partition functions and occupation numbers for all above-mentioned thermodynamic ensembles are also evaluated.
In quantum many-body systems interactions between particles create correlations and particles can not be described independently. As a consequence the wave function of the system is a complicated object holding a large amount of information and in most cases it is not possible to obtain it exactly or analytically. Studying correlations in the context of strongly interacting onedimensional (1D) systems is interesting because in this regime we can exactly determine many particle wave function through Fermi-Bose (FB) mapping. FB mapping is in the essence of a Tonks Girardeau (TG) gas proposed in 1960, a theoretical model of 1D Bose gas with strongly repulsive contact interactions between particles. TG gas is experimentally realized in 2004 with rubidium atoms conned in tight atomic wave-guides and it is still a topic of experimental studies. Our goal is the study of correlations in TG gas through the formalism of the single particle density matrix. Single particle density matrix, among other important observable's, contains information about the momentum distribution which can be measured in experiments. We explored correlations in dark soliton-like excitations of the TG gas and found that these correlations give rise to a specific form of the momentum distribution which can be used to experimentally detect these states. In addition to the TG gas, FB mapping was used to construct exact wave functions of 1D Bose-Fermi mixtures (fermions are spin polarized). We derived the formula for the single particle density matrix of the mixture and used it to study correlations and momentum distribution of the mixture in the ground state of double well potential. Due to integrability, these systems are convenient to study stability to perturbations of many-body quantum states in different interaction regimes. We explored stability of non-equilibrium dynamics of 1D interacting Bose gases with respect to small spatial noise potential using the concept of Loschmidt echo (quantum fidelity). We used this concept to explore the pinning quantum phase transition. We found that the ground state fidelity and the Loschmidt echo can be used for diagnostics of the pinning quantum phase transition in experimentally relevant conditions.