Two-particle multiplets splitting as a guideline in nucleon pairing estimations

The ground state multiplet structure for nuclei over the wide range of mass number A was calculated in δ-approximation and different mass relations for pairing energy were analysed in this work. Correlation between the calculated multiplet structure and experimental data offers a guideline in deciding between mass relations for nucleon pairing.     

Synchronization in the BCS pairing dynamics as a critical phenomenon

Fermi gas with time-dependent pairing interaction hosts several different dynamical states. Coupling between the collective BCS pairing mode and individual Cooper pair states can make the latter either synchronize or dephase. We describe transition from phase-locked undamped oscillations to Landau-damped dephased oscillations in the collisionless, dissipationless regime as a function of coupling strength. In the dephased regime, we find a second transition at which the long-time asymptotic pairing amplitude vanishes. Using a combination of numerical and analytical methods we establish a continuous (type II) character of both transitions.     

Neutron-proton pairing

The two topics discussed here are the treatment of neutron-proton pairing and the problem of phase transitions in systems of neutrons and protons. The conclusions are based on exact calculations, possible in simplified situations, and the exact results are compared with the BCS treatment. QRPA, and many of its modifications, which are the most popular approaches to double beta decay, involve the quasiparticle transformation as a decisive first step. It is therefore imperative to understand its strengths and limitations. Presented at Workshop on calculation of double-beta-decay matrix elements (MEDEX’97), Prague, May 27–31, 1997. The work reported here is based on Refs. 3, 4, and 5. The credit for it belongs to my collaborators, in particular to Osvaldo Civitarese, Jonathan Engel, and Stuart Pittel. This work was supported by the U.S. Department of Energy under Grant. No. DE-FG03-88ER-40397.     

Coulomb repulsion-induced hyperbolic pairing as a mechanism of high-T c superconductivity

The hyperbolic metric of the dispersion law (the effective mass tensor components of carriers are opposite in sign) in the vicinity of the Fermi contour in high-T _c superconducting cuprates in the case of repulsive interaction gives rise to a superconducting state characterized by the condensate of pairs with a large total momentum (hyperbolic pairing). The gain in the energy of the superconducting state over the normal state is due to the fact that a change in the kinetic energy of pairs (because of the negative light component of the effective mass) dominates over the change in the potential energy (corresponding to energy loss). The shift of the chemical potential upon the transition to the superconducting phase is substantial in this case. With increasing repulsive interaction, the superconducting gap δ_K increases and the resulting gain in energy changes to an energy loss at a certain critical value of the repulsive potential. The low temperature T _c of the superconducting transition and the large value of δ _K in this region of potential values are the reasons for the high value of the 2δ_K/T _c ratio and for the developed quantum fluctuations that are observed in underdoped cuprate superconductors.     

Electron pairing as a source of cyclic instabilities in enzyme catalysis

Enzymatic reactions can be interpreted in terms of a thermodynamically consistent potential surface with different pathways for complex formation and decomposition. The construction suggests that unstable pairing of parallel spin electrons provides the basis for pathway switching.     

Kinetic step pairing

We report on the theoretical and experimental discovery of pairing of identical crystal steps. We first show that step bunching always occurs at long wavelength in the vicinity of an instability threshold when step dynamics is local. But an instability towards a stable train of pairs can be obtained when steps dynamics is nonlocal. This instability is shown to occur for transparent steps under electromigration. Observations on Si(111) under electromigration around 1230 degrees C show stable trains of pairs. By controlling both supersaturation and electromigration, we establish an experimental morphology diagram, from which we conclude that the transparency kinetic coefficient is negative.     

The pairing model

The consequences of the existence of pairing correlations in nuclei are discussed. Special attention is paid to the dynamical aspects of the pairing degree of freedom, as revealed by two-nucleon transfer reactions. These reactions constitute specific probes of the pairing collective modes.The mathematical framework in which the discussion is carried out is the BCS theory and the Random Phase Approximation.The borderline aspect of the subject, which lies between solid state and nuclear physics is emphasized, pointing out the similarities and differences between analogous phenomena of solid state and nuclear physics.     

Impurity effect as a probe for the pairing symmetry of graphene-based superconductors

We study theoretically the single impurity effect on graphene-based superconductors. Four different pairing symmetries are discussed. Sharp in-gap resonant peaks are found near the impurity site for the d+id pairing symmetry and the p+ip pairing symmetry when the chemical potential is large. As the chemical potential decreases, the in-gap states are robust for the d + id pairing symmetry while they disappear for the p + ip pairing symmetry. Such in-gap peaks are absent for the fully gapped extended s-wave pairing symmetry and the nodal f-wave pairing symmetry. The existence of the ingap resonant peaks can be explained well based on the sign-reversal of the superconducting gap along different Fermi pockets and by analyzing the denominator of the T-matrix. All of the features may be checked by the experiments, providing a useful probe for the pairing symmetry of graphene-based superconductors.     

One-dimensional Cooper pairing

We study electron pairing in a one-dimensional (1D) fermion gas at zero temperature under zero- and finite-range, attractive, two-body interactions. The binding energy of Cooper pairs (CPs) with zero total or center-of-mass momentum (CMM) increases with attraction strength and decreases with interaction range for fixed strength. The excitation energy of 1D CPs with nonzero CMM display novel, unique properties. It satisfies a dispersion relation with two branches: a phonon-like linear excitation for small CP CMM; this is followed by roton-like quadratic excitation minimum for CMM greater than twice the Fermi wavenumber, but only above a minimum threshold attraction strength. The expected quadratic-in-CMM dispersion in vacuo when the Fermi wavenumber is set to zero is recovered for any coupling. This paper completes a three-part exploration initiated in 2D and continued in 3D.     

Isovector pairing vibrations

The experimental corpus of L = 0 two nucleon transfer reactions induced by light ion projectiles in 1f-2p shell nuclei is reviewed. A unified picture of these processes is attempted in terms of pairing elementary modes of excitation (bosons) generated by fluctuations of the isovector pairing gap around its zero equilibrium value.     

Non-empirical pairing functional

The present contribution reports the first systematic finite-nucleus calculations performed using the Energy Density Functional method and a non-empirical pairing functional derived from low-momentum interactions. As a first step, the effects of Coulomb and the three-body force are omitted while only the bare two-nucleon interaction at lowest order is considered. To cope with the finite-range and non-locality of the bare nuclear interaction, the ¹S₀ channel of V_{low k} is mapped onto a convenient operator form. Neutron-neutron and proton-proton pairing correlations generated in finite nuclei by the direct term of the two-nucleon interaction are characterized in a systematic manner. Eventually, such predictions are compared to those obtained from empirical local functionals derived from density-dependent zero range interactions. The characteristics of the latter are analyzed in view of that comparison and a specific modification of their isovector density dependence is suggested to accommodate Coulomb effects and the isovector trend of neutron gaps at the same time.     

Quantum entanglement and pairing correlation in the reduced BCS pairing model

Using the particle-hole version of the density-matrix renormalization-group technique, the pairing correlation and the quantum entanglement of the reduced BCS pairing model are investigated. Both of them behave smoothly from the weak to the strong coupling regimes. A convergence radius (∼1/ln Ω) of condensation energy is detected by the first order derivative of the block-block entanglement. Furthermore, the block-block entanglement in the strong coupling regime shows distinct size dependence, and a logarithmic volume law is suggested numerically.     

On-site repulsion as the source of pairing in carbon nanotubes and intercalated graphite

We show that different non-conventional superconductors have one fundamental feature in common: pair eigenstates of the Hamiltonian are repulsion-free, the W = 0 pairs. In extended Hubbard models, pairing can occur for reasonable parameter values. For (N, N) nanotubes the binding energy of the pair depends strongly on the filling and decreases towards a reduced but nonzero value for the graphite sheet N → ∞. Received 13 July 2002 Published online 29 November 2002     

Reflectionless spatial beam benders with arbitrary bending angle by introducing optic-null medium into transformation optics

By introducing an optic-null medium into the finite embedded transformation,a reflectionless spatial beam bender is designed,which can steer the output beam by a fixed pre-designed angleβfor an arbitrary incident angle.The bending angleβof the beam bender is determined by the geometrical angle of the device,which can be changed by simply choosing different geometrical angles.For various bending angles,the designed spatial beam bender can be realized by the same materials(i.e.,an optic-null medium),which is a homogenous anisotropic material.Numerical simulations verify the reflectionless bending effect and rotated imaging ability of the proposed beam bender.A reduction model of the optic-null medium is studied,which can also be used for a reflectionless spatial beam bender with a pre-designed bending angle.     

A semiclassical approach to pairing vibrations and pairing correlation effects on giant resonances

We extend the semiclassical approaches to the dynamics of nuclear collective motions, based on the Wigner transform of quantum mean field theories, to the inclusion of pairing correlation effects. We develop simple analytic equations for the contributions to giant resonance frequencies, which are in general quite small. We are able also to study pairing vibrations, related to oscillations of the superfluid part. Hydrodynamics-like solutions are obtained, without distortion of the Fermi surface, corresponding to low energy excitations.