PHONON SPECTRA OF QUANTUM WIRES
This paper is based
on our previous works which dealt with ultrathin crystalline films.
The quantum wires are quasi $1D$ crystalline systems bounded in two
perpendicular directions ($y$ and $z$) while infinite in $x$ direction.
The phonon
excitation energies are defined by the poles of Green's functions, which
can be found from the condition that the $3D$ determinant of the set of
equations of motion vanishes.
Using the Chebyshev's polynomial representation of this block matrix, we
obtain the solutions as roots of the characteristic matrix equation.
By numerical analysis (for simplest cases: $N_{y/z} \in [2,5]$) we
conjectured that the solution of this equation is of the same form as for
thin films, but with the discretization along $y$ direction too.
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