2002/06/26 by M. Aunola, Aunola, M.
Physics and Astronomy · #Cold Atom Physics and Bose-Einstein Condensates #FOS: Physical sciences #Quantum chaos and dynamical systems #Quantum, superfluid, helium dynamics #Superconductivity (cond-mat.supr-con) #cond-mat.supr-con
paper · pdf · doi:10.48550/arxiv.cond-mat/0206507
8 pages, 3 figures, added 2 references and a notebook that confirms the earlier ansatz. See also papers JMP 44 (2003) 1913 and PRB 68 (2003) 020502
openalex publication_date 2002/06/26 · arxiv created 2003/12/11 · arxiv updated 2009/11/30 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28
The properties of the tunnelling-charging Hamiltonian of a Cooper pair pump are well understood in the regime of weak and intermediate Josephson coupling, i.e. EJ\lesssim EC. Instead of perturbative treatment of charging effects, the present work applies the charge state representation in the the strong coupling case. From the discrete Hamiltonian we construct effective, truncated PDE Hamiltonians which yield approximate, but analytical, wave functions and energies for the ground state. The validity of the expressions is confirmed by comparing the results against numerically obtained eigenstates and eigenenergies, whenever possible. For uniform arrays, the results converge rapidly and even ϕ-dependence of the wave function is rather well described. In the inhomogeneous case we find the Hamiltonian to be parametrically renormalisable in order to obtain an accurate ground state energy. A method for for finding an inhomogeneous trial wave function is explained. As a passing note, we briefly examine the intertwined connection between the pumped charge and the Berry's phase. As addendum, we have explicitly validated the ground state ansatz for ϕ=0 when N<43.