We use theoretical methods to study properties of excitations in various granular materials.We begin with three topics involving superconducting qubits.
First, a three Josephson-junction persistent-current qubit is considered, with two junctions being identical, and the third junction differing from the
other two by a factor of
α in Josephson energy and capacitance. We show that when α > 1 and the bias voltages are such that the total charge stored on the two gate
capacitors is an odd multiple of electronic charge, the two levels of the qubit become degenerate. Secondly, energy loss of a Cooper-pair box (CPB)
capacitively coupled to a nanomechanical oscillator (NMO) is studied within the rotating wave approximation (RWA).
We show that the energy decay rate of the CPB can be decreased by coupling it to a high quality factor (Q) NMO. Finally, we extend the last study
beyond the RWA.
Four topics in the theory of superlattices are considered next.
First, an electronic graphene superlattice is studied.
We show that if graphene is subjected to the potential from an external superlattice, a band gap develops at the Dirac point provided the
superlattice potential has broken inversion symmetry. Secondly, a magnetic superlattice of
periodically arranged ferromagnetic cylinders embedded in a different ferromagnetic host is considered.
We show that when the two ferromagnets have different Gilbert damping factors, this superlattice acts as a waveguide for spin waves.
Thirdly, a photonic superlattice of silicon (Si) dielectric cylinders in air is considered. A simple method for calculating the effective
dielectric constant of the superlattice is presented. Finally, we show the presence of a Dirac point in the photonic band structure of a
triangular superlattice of Si cylinders in air.
The final topics presented involve inhomogeneous carbon based materials. We use an effective medium approximation (EMA) to calculate
the magnetoresistance of a graphene sheet broken into
n-type and p-type puddles. Finally, we use EMA to show that the effective sound speed of a suspension of carbon nanotubes in dimethyl formaldehyde (DMF) is
lower than the sound speed in pure DMF.