69,500 research outputs found
Binomial coefficients, Catalan numbers and Lucas quotients
Let be an odd prime and let be integers with and . In this paper we determine
mod for ; for example,
where is the Jacobi symbol, and is the Lucas
sequence given by , and for
. As an application, we determine modulo for any integer , where denotes the
Catalan number . We also pose some related conjectures.Comment: 24 pages. Correct few typo
Proximity and anomalous field-effect characteristics in double-wall carbon nanotubes
Proximity effect on field-effect characteristic (FEC) in double-wall carbon
nanotubes (DWCNTs) is investigated. In a semiconductor-metal (S-M) DWCNT, the
penetration of electron wavefunctions in the metallic shell to the
semiconducting shell turns the original semiconducting tube into a metal with a
non-zero local density of states at the Fermi level. By using a two-band
tight-binding model on a ladder of two legs, it is demonstrated that anomalous
FEC observed in so-called S-M type DWCNTs can be fully understood by the
proximity effect of metallic phases.Comment: 4 pages, 4 figure
Magnetization reversal through synchronization with a microwave
Based on the Landau-Lifshitz-Gilbert equation, it can be shown that a
circularly-polarized microwave can reverse the magnetization of a Stoner
particle through synchronization. In comparison with magnetization reversal
induced by a static magnetic field, it can be shown that when a proper
microwave frequency is used the minimal switching field is much smaller than
that of precessional magnetization reversal. A microwave needs only to overcome
the energy dissipation of a Stoner particle in order to reverse magnetization
unlike the conventional method with a static magnetic field where the switching
field must be of the order of magnetic anisotropy.Comment: 4 pages, 5 figure
Zero-field magnetization reversal of two-body Stoner particles with dipolar interaction
Nanomagnetism has recently attracted explosive attention, in particular,
because of the enormous potential applications in information industry, e.g.
new harddisk technology, race-track memory[1], and logic devices[2]. Recent
technological advances[3] allow for the fabrication of single-domain magnetic
nanoparticles (Stoner particles), whose magnetization dynamics have been
extensively studied, both experimentally and theoretically, involving magnetic
fields[4-9] and/or by spin-polarized currents[10-20]. From an industrial point
of view, important issues include lowering the critical switching field ,
and achieving short reversal times. Here we predict a new technological
perspective: can be dramatically lowered (including ) by
appropriately engineering the dipole-dipole interaction (DDI) in a system of
two synchronized Stoner particles. Here, in a modified Stoner-Wohlfarth (SW)
limit, both of the above goals can be achieved. The experimental feasibility of
realizing our proposal is illustrated on the example of cobalt nanoparticles.Comment: 5 pages, 4 figure
Quantum state swapping via qubit network with Hubbard interaction
We study the quantum state transfer (QST) in a class of qubit network with
on-site interaction, which is described by the generalized Hubbard model with
engineered couplings. It is proved that the system of two electrons with
opposite spins in this quantum network of sites can be rigorously reduced
into one dimensional engineered single Bloch electron models with central
potential barrier. With this observation we find that such system can perform a
perfect QST, the quantum swapping between two distant electrons with opposite
spins. Numerical results show such QST and the resonant-tunnelling for the
optimal on-site interaction strengths.Comment: 4 pages, 3 figure
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