Notation

	...	Scalar
$x^\ast$	...	Complex conjugate of
${\mathbf{x}}$	...	Vector
$\mathbf{e}_x$	...	Unity vector in direction x
$\mathbf{x} \cdot \mathbf{y}$	...	Scalar inner product
$\partial_t(\cdot)$	...	Partial derivative with respect to
$\ensuremath{{\mathbf{\nabla}}}$	...	Nabla operator
$\ensuremath{{\mathbf{\nabla}}}\mathbf{x}$	...	Gradient of ${\mathbf{x}}$
$\ensuremath{{\mathbf{\nabla}}}\cdot \mathbf{x}$	...	Divergence of ${\mathbf{x}}$
$\ensuremath{{\mathbf{\nabla}}}\cdot \ensuremath{{\mathbf{\nabla}}}= \ensuremath{{\mathbf{\nabla}}}^2$	...	LAPLACE operator
$\ensuremath{{\underline{A}}}$	...	Matrix
$A_{ij}$	...	Elements of the matrix ${\underline{A}}$
$\ensuremath{{\underline{A}}}^\dagger$	...	Conjugate transposed matrix: $A_{ij} = A_{ji}^\ast$
	...	Unity matrix
$\ensuremath{\mathrm{det}}(\cdot)$	...	Determinant of a matrix
	...	GREEN's function
	...	HAMILTONian in the first quantization
$\hat{H}$	...	HAMILTONian in the second quantization
$\hat{\psi}$	...	Field operator
	...	Annihilation operator for bosons
	...	Annihilation operator for fermions
$b^{\dagger}$	...	Creation operator for bosons
$c^{\dagger}$	...	Creation operator for fermions
$\langle\cdot\rangle$	...	Statistical average
$\otimes$	...	Convolution

M. Pourfath: Numerical Study of Quantum Transport in Carbon Nanotube-Based Transistors


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