arXiv subjects

B. R. Trees

Publications and source records attributed to B. R. Trees.

5 recordsLinked to original sources

arXiv2004

Synchronization in disordered Josephson junction arrays: Small-world connections and the Kuramoto model

We study synchronization in disordered arrays of Josephson junctions. In the first half of the paper, we consider the relation between the coupled resistively- and capacitively shunted junction (RCSJ) equations for such arrays and effective phase models of the Winfree type. We describe a multiple-time scale analysis of the RCSJ equations for a ladder array of junctions \textit{with non-negligible capacitance} in which we arrive at a second order phase model that captures well the synchronization physics of the RCSJ equations for that geometry. In the second half of the paper, motivated by recent work on small world networks, we study the effect on synchronization of random, long-range connections between pairs of junctions. We consider the effects of such shortcuts on ladder arrays, finding that the shortcuts make it easier for the array of junctions in the nonzero voltage state to synchronize. In 2D arrays we find that the additional shortcut junctions are only marginally effective at inducing synchronization of the active junctions. The differences in the effects of shortcut junctions in 1D and 2D can be partly understood in terms of an effective phase model.

cond-mat.supr-con↗

arXiv2000

Instabilities in Josephson Ladders with Current Induced Magnetic Fields

We report on a theoretical analysis, consisting of both numerical and analytic work, of the stability of synchronization of a ladder array of Josephson junctions under the influence of current induced magnetic fields. Surprisingly, we find that as the ratio of the mutual to self inductance of the cells of the array is increased a region of unstable behavior occurs followed by reentrant stable synchronization. Analytic work tells us that in order to understand fully the cause of the observed instabilities the behavior of the vertical junctions, sometimes ignored in analytic analyses of ladder arrays, must be taken into account.

cond-mat.supr-con↗

arXiv1994

Multiplet Effects in the Quasiparticle Band Structure of the $f^1-f^2$ Anderson Model

In this paper, we examine the mean field electronic structure of the $f^1-f^2$ Anderson lattice model in a slave boson approximation, which should be useful in understanding the physics of correlated metals with more than one f electron per site such as uranium-based heavy fermion superconductors. We find that the multiplet structure of the $f^2$ ion acts to quench the crystal field splitting in the quasiparticle electronic structure. This is consistent with experimental observations in such metals as $UPt_3$.

cond-mat↗

arXiv1994

A Superconducting Instability in the Infinite-U Anderson Lattice in the Presence of Crystal Electric Fields

We report evidence of a superconducting instability (of $T_{1g}$ symmetry) in the infinite-U Anderson lattice in the presence of crystal fields of cubic symmetry. We assume a lattice of $4f$ sites, each with a total angular momentum of $J=5/2$ that is split by crystal fields into a low-lying doublet of $Γ_7$ symmetry and an excited quartet of $Γ_8$ symmetry. Slave Bosons on the $4f$ sites create and destroy $4f^0$ configurations and Lagrange multipliers at each $4f$ site enforce the occupancy constraint due to the infinite Coulomb repulsion. Quasiparticle interactions are due to exchange of $4f$ density fluctuations, which are represented by fluctuations in the slave Bosons and Lagrange multipliers. We use the so-called analytic tetrahedron method to calculate the dressed (to order 1/N) Boson Green functions. In weak couping, the exchange of the dressed Bosons gives rise to a superconducting instability of $T_{1g}$, $xy(x^2-y^2)$, symmetry. The $A_{1g}$, ``s-wave'', channel has strongly repulsive interactions and hence no pairing instability. The $T_{2g}$ channel exhibits weakly repulsive interactions. Average quasiparticle interactions in the $E_g$, $x^2-y^2$, $3z^2-r^2$, channel fluctuate strongly as a function of the number of tetrahedra used to calculate the Bosonic Green functions,

cond-mat↗

arXiv1993

Superconductivity in the Anderson Lattice

Using an anisotropic hybridization matrix element, V($\vec k$), reflecting cubic symmetry at the ``rare-earth'' sites of the infinite U Anderson lattice, we calculate the bare quasiparticle scattering amplitude to order 1/N using slave Bosons and find significant differences with previous results under spherical symmetry. Due to exchange of density fluctuations, we find an instability. toward E$_g$ and T$_{1g}$ (even-parity) pairing.

cond-mat↗