0000000000162435
AUTHOR
M. Aunola
Tunnelling-charging Hamiltonian of a Cooper pair pump at large E_J\lesssim E_C: Modified Hamiltonians and renormalisability
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. E_J\lesssim E_C. 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 eve…
Theoretical description of the fourth-forbidden non-unique β decays ofCd113andIn115
The half-lives and $\mathrm{log}\mathit{ft}$ values for the fourth-forbidden non-unique beta decays of the ground states of $^{113}\mathrm{Cd}$ and $^{115}\mathrm{In}$ were calculated using a transparent formulation for the ${\ensuremath{\beta}}^{\ensuremath{-}}$ transition amplitude. The microscopic quasiparticle-phonon model (MQPM) was used to calculate the initial and final states of the transitions. The corresponding wave functions were described as linear combinations of one- and three-quasiparticle configurations built in a realistic single-particle model space by using a realistic microscopic two-body interaction. The computed results for the $\mathrm{log}\mathit{ft}$ values and half…
A study of the tunnelling-charging Hamiltonian of a Cooper pair pump
General properties of the tunnelling-charging Hamiltonian of a Cooper pair pump are examined with emphasis on the symmetries of the model. An efficient block-diagonalisation scheme and a compatible Fourier expansion of the eigenstates is constructed and applied in order to gather information on important observables. Systematics of the adiabatic pumping with respect to all of the model parameters are obtained and the link to the geometrical Berry's phase is identified.
Shell-model study of the highly forbidden beta decay 48 Ca → 48 Sc
Ordinary β− decay of the 0+ ground state of 48Ca is studied. Partial half-lives for the highly-forbidden transitions to the three lowest-lying states (6+,5+,4+) of 48Sc are calculated by using both the harmonic oscillator and the Woods-Saxon mean-field wave functions. We find the decay to be dominated, as expected, by the unique fourth-forbidden transition to the excited 5+ state of 48Sc. The theoretical beta-decay half-life of 48Ca is found to be 1.1−0.6+0.8·1021 years which is approximately 25 times longer than the measured double-beta-decay half-life of T1/22ν = (4.3−1.1+2.4[stat] ± 1.4[syst])·1019 years.
Tunneling-charging Hamiltonian of a Cooper-pair pump
General properties of the tunneling-charging Hamiltonian of a Cooper pair pump are examined with emphasis on the symmetries of the model. An efficient block-diagonalization scheme and a compatible Fourier expansion of the eigenstates is constructed and applied in order to gather information on important observables. Systematics of the adiabatic pumping with respect to all of the model parameters are obtained and the link to the geometrical Berry's phase is identified.
Superconducting single-electron transistor and the phi-modulation of supercurrent
An analytical expression for the supercurrent of a superconducting single-electron transistor (SSET) is derived. The derivation is based on analogy between the model Hamiltonian for E_J>E_C and a discrete, one-dimensional harmonic oscillator (1DDHO). The resulting supercurrent is nearly identical to the supercurrent obtained from a continuous harmonic oscillator Hamiltonian.
Competition Between Beta and Double Beta Decay in 48Ca and 96Zr
Highly forbidden beta decays of 48Ca and 96Zr are studied and their relative importance as compared to the double beta decay of these nuclei is evaluated. 48Ca and 96Zr are the only naturally occurring nuclei in which these processes can occur simultaneously. Although usually ordinary beta decay overwhelms double beta decay unless the former is energetically forbidden, in these cases the high degree of forbiddenness and small release of kinetic energy makes the half-lives of these modes comparable to each other.
Connecting Berry's phase and the pumped charge in a Cooper pair pump
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. when $E_{\mathrm{J}}\lesssim E_{\mathrm{C}}$. It is also known that Berry's phase is related to the pumped charge induced by the adiabatical variation of the eigenstates. We show explicitly that pumped charge in Cooper pair pump can be understood as a partial derivative of Berry's phase with respect to the phase difference $\phi$ across the array. The phase fluctuations always present in real experiments can also be taken into account, although only approximately. Thus the measurement of the pumped current gives reliable, yet indirec…
Arrays of Josephson junctions in an environment with vanishing impedance
The Hamiltonian operator for an unbiased array of Josephson junctions with gate voltages is constructed when only Cooper pair tunnelling and charging effects are taken into account. The supercurrent through the system and the pumped current induced by changing the gate voltages periodically are discussed with an emphasis on the inaccuracies in the Cooper pair pumping. Renormalisation of the Hamiltonian operator is used in order to reliably parametrise the effects due to inhomogeneity in the array and non-ideal gating sequences. The relatively simple model yields an explicit, testable prediction based on three experimentally motivated and determinable parameters.
Adiabatic transport of Cooper pairs in arrays of Josephson junctions
We have developed a quantitative theory of Cooper pair pumping in gated one-dimensional arrays of Josephson junctions. The pumping accuracy is limited by quantum tunneling of Cooper pairs out of the propagating potential well and by direct supercurrent flow through the array. Both corrections decrease exponentially with the number N of junctions in the array, but give a serious limitation of accuracy for any practical array. The supercurrent at resonant gate voltages decreases with N only as sin(v/N)/N, where v is the Josephson phase difference across the array.
Systematic study of neutrinoless double beta decay to excited 0+ states
Abstract A systematic study of neutrinoless double beta (0 νββ ) decay to excited 0 + states, described as monopole-vibrational states or as composed of two collective quadrupole-phonon states, has been performed. Both double β − and double β + /EC decays have been analyzed within the framework of the multiple commutator model (MCM) by using a realistic nuclear many-body Hamiltonian and realistic mean-field single-particle bases. It is found that the associated 0 νββ -decay transitions are suppressed relative to the decay to the final ground state both by the available phase space and especially by the smallness of the involved transition matrix elements. For completeness, also the double β…
The discretized harmonic oscillator: Mathieu functions and a new class of generalized Hermite polynomials
We present a general, asymptotical solution for the discretised harmonic oscillator. The corresponding Schr\"odinger equation is canonically conjugate to the Mathieu differential equation, the Schr\"odinger equation of the quantum pendulum. Thus, in addition to giving an explicit solution for the Hamiltonian of an isolated Josephon junction or a superconducting single-electron transistor (SSET), we obtain an asymptotical representation of Mathieu functions. We solve the discretised harmonic oscillator by transforming the infinite-dimensional matrix-eigenvalue problem into an infinite set of algebraic equations which are later shown to be satisfied by the obtained solution. The proposed ansa…
Exact, explicit and entire solutions to a nontrivial finite-difference equation and their applications
Below, the explicit solution to a certain finite-difference equation is given and the required steps for derivation of these results are outlined. Everything is included as Mathematica formulae, so the notebook itself can be used for checking and improving the present results. Some important references for justifying some steps and crosschecking certain results have been included. Full references and derivations will be made available shortly. It should be noted that several applications for the solutions have been included at the end of the document. These include at least diagonalisation of certain infinite matrices, definition of isospectral operators with simple eigenvalues and alternat…
Mean-field effects on neutrinoless double beta decay
Abstract Mean-field effects on the nuclear matrix elements involved in the neutrinoless double beta (0νββ) decay of several double-electron and double-positron emitters have been studied within the framework of the relativistic quark-confinement model and the quasiparticle random-phase approximation. The single-particle energies of the model space have been generated both by using the standard Woods-Saxon parametrization of the mean field and adjusting the quasiparticle spectra with the data from neutron- and proton-odd nuclei. The 0νββ rates are found to be much less affected by the energies of the mean-field orbitals than the rates of the two-neutrino double beta decay. The present study …