302 research outputs found
Measuring the phonon-assisted spectral function by using a non-quilibrium three-terminal single-molecular device
The electron transport through a three-terminal single-molecular transistor
(SMT) is theoretically studied. We find that the differential conductance of
the third and weakly coupled terminal versus its voltage matches well with the
spectral function versus the energy when certain conditions are met.
Particularly, this excellent matching is maintained even for complicated
structure of the phonon-assisted side peaks. Thus, this device offers an
experimental approach to explore the shape of the phonon-assisted spectral
function in detail. In addition we discuss the conditions of a perfect
matching. The results show that at low temperatures the matching survives
regardless of the bias and the energy levels of the SMT. However, at high
temperatures, the matching is destroyed.Comment: 9 pages, 5 figure
Existence and multiplicity of positive solutions for a Schrodinger-Poisson system with a perturbation
In this paper we study the nonlinear Schrodinger-Poisson system with a perturbation: \begin{equation*} \begin{cases} -\Delta u+u+K( x) \phi u=\vert u\vert ^{p-2}u+\lambda f(x)\vert u\vert ^{q-2}u \text{in }\mathbb{R}^{3}, -\Delta \phi =K( x) u^{2} \text{in }\mathbb{R}^{3}, \end{cases} \end{equation*}% where and are nonnegative functions, and , and the parameter . Under some suitable assumptions on and , the criteria of existence and multiplicity of positive solutions are established by means of the Lusternik-Schnirelmann category and minimax method
One-dimensional quantum channel in a graphene line defect
Using a tight-binding model, we study a line defect in graphene where a bulk
energy gap is opened by sublattice symmetry breaking. It is found that
sublattice symmetry breaking may induce many configurations that correspond to
different band spectra. In particular, a gapless state is observed for a
configuration which hold a mirror symmetry with respect to the line defect. We
find that this gapless state originates from the line defect and is independent
of the width of the graphene ribbon, the location of the line defect, and the
potentials in the edges of the ribbon. In particular, the gapless state can be
controlled by the gate voltage embedded below the line defect. Finally, this
result is supported with conductance calculations. This study shows how a
quantum channel could be constructed using a line defect, and how the quantum
channel can be controlled by tuning the gate voltage embedded below the line
defect.Comment: 8 pages, 10 figure
Normalized solutions for the Schr\"{o}dinger equation with combined Hartree type and power nonlinearities
We investigate normalized solutions for the Schr\"{o}dinger equation with
combined Hartree type and power nonlinearities, namely \begin{equation*}
\left\{ \begin{array}{ll} -\Delta u+\lambda u=\gamma (I_{\alpha }\ast
\left\vert u\right\vert ^{p})|u|^{p-2}u+\mu |u|^{q-2}u & \quad \text{in}\quad
\mathbb{R}^{N}, \\ \int_{\mathbb{R}^{N}}|u|^{2}dx=c, & \end{array}% \right.
\end{equation*} where and is a given real number. Under
different assumptions on and , we prove several
nonexistence, existence and multiplicity results. In particular, we are more
interested in the cases when the competing effect of Hartree type and power
nonlinearities happens, i.e. including the cases and Due to the different "strength" of two
types of nonlinearities, we find some differences in results and in the
geometry of the corresponding functionals between these two cases
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