2020/05/11 by J. A. E. Bonart, Wilhelm H. Appelt, W. H. Appelt +2
Mathematics · Physics and Astronomy · #Advanced Chemical Physics Studies #Cold Atom Physics and Bose-Einstein Condensates #Coulomb #Electron #Excited state #Gaussian #Ground state #Mathematics #Momentum (technical analysis) #Physics #Position and momentum space #Quantum mechanics #Quantum, superfluid, helium dynamics #Scaling #cond-mat.other
paper · pdf · doi:10.1103/physrevb.102.024306
published in Physical review. B./Physical review. B 102(2) (American Physical Society) · 6 pages, 5 figures
arxiv created 2020/05/11 · openalex publication_date 2020/07/13 · arxiv updated 2020/07/21 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
We calculate the single-particle momentum distribution of a quantum many-particle system in the presence of the Coulomb interaction and a confining potential. The region of intermediate momenta, where the confining potential dominates, marks a crossover from a Gaussian distribution valid at low momenta to a power-law behavior valid at high momenta. We show that for all momenta the momentum distribution can be parametrized by a q-Gaussian distribution whose parameters are specified by the confining potential. The real-space pair-correlation function calculated in this way can, in principle, be used to construct improved exchange-correlation functionals to solve electronic structure problems. Furthermore, we find that the functional form of the probability of transitions between the confined ground state and the nth excited state is invariant under scaling of the ratio Q2/\ensuremathνn, where Q is the transferred momentum and \ensuremathνn is the corresponding excitation energy. Using the scaling variable Q2/\ensuremathνn the maxima of the transition probabilities can also be expressed in terms of a q-Gaussian.