Variables and Fundamental Constants

a	radius of sphere [m]; multiplier of congruential random number generator
A	complex amplitude
bx	orthonormal vector in a Krylov subspace
B	complex amplitude
Bm	orthonormal basis in m-dimensional Krylov subspace
c	offset of a linear congruential random number generator
c(t)	complex time dependent scattering amplitude
C	capacitance [F]
C	capacitance matrix
Cx	sub-matrices of the capacitance matrix
Cij	capacitance between conductor i and j [F]
$C_{\Sigma }$	sum of capacitances [F]
$C_{\text{eff}}$	effective capacitance of a Thévenin equivalent circuit
d	diameter or width [m]
Dpq(X)	denominator polynomial for Padé approximation of degree p+q
$\delta()$	delta-function
$\delta_{mn}$	Kronecker-delta; is 1 for m=n otherwise 0.
$\Delta$	difference between two values ( $\Delta E, \Delta t, \ldots$)
e	elementary charge $1.602\cdot 10^{-19}$ As; charge of one electron (-e)
e1	unit vector
E	energy [J] or [eV]
E	error matrix
Ec	conduction band edge [eV]
EC	Coulomb energy [eV]
EF	Fermi energy [eV]
EF,i	Fermi energy of intrinsic semiconductor [eV]
Ef	energy of a final state (for instance after tunneling) [eV]
Ei	energy of an initial state (for instance before tunneling) [eV]
$E_{\Sigma}$	total energy stored in a system [eV]
$\epsilon$	dielectric permittivity $\epsilon = \epsilon_0 \epsilon_r$
$\epsilon_0$	dielectric permittivity of vacuum $8.854\cdot 10^{-12}$ As/Vm
$\epsilon_r$	relative dielectric permittivity [1]
f	frequency [1/s]
f()	Fermi function
F	Helmholtz's free energy [eV]
$\Gamma$	tunnel rate [1/s]
$\Gamma^{(x)}$	xth-order co-tunneling rate [1/s]
$\Gamma_{ij}$	tunnel rate from state j to state i [1/s]
$\Gamma(\boldsymbol{S}\vert\boldsymbol{S'})$	tunnel rate from state S' to state S [1/s]
h	Planck constant $6.626\cdot 10^{-34}$ Js
$\hbar$	$h/2\pi = 1.055\cdot 10^{-34}$ Js
H	Hamilton operator
Hm	upper Hessenberg matrix
I	electric current [A]
I	unit matrix
Jx	tunnel junction x
Ji	Jordan block

k	wave number [1/m]
kB	Boltzmann constant $1.381\cdot 10^{-23}$ J/K
Km	m-dimensional Krylov subspace
$\lambda_F$	Fermi wavelength [m]
$\lambda_i$	matrix eigenvalue
m	module of a linear congruential random number generator
me	electron mass $9.1\cdot 10^{-31}$ kg
me*	effective electron mass [kg]
n	electron concentration; charge carrier concentration [ $1/\text{m}^{3}$]
$n_{\text{net}}$	net carrier concentration $n_{\text{net}}=n-p$ [ $1/\text{m}^{3}$]
N	number of electrons; number of nodes
$\langle N\rangle$	time averaged number of electrons
Nc	number of charge-nodes
Nf	number of floating-nodes
Nfm	number of nodes in a macro-node
Nm	number of macro-nodes
Np	number of potential-nodes
Npq(X)	numerator polynomial for Padé approximation of degree p+q
$\omega_n, \omega_m$	eigenvalues [1/s]
$\omega_{mn}$	difference of two eigenvalues $\omega_m-\omega_n$ [1/s]
$\omega_x$	electron hole excitation energy
p	hole concentration [ $1/\text{m}^{3}$]
Pi(t)	probability of state i
$\tilde{P}_i(s)$	Laplace transform of Pi(t)
$P_{\text{error}}$	error probability
p	state probability vector
p(S,t)	probability density function in state space
$\varphi$	electrostatic potential [V]
$\boldsymbol{\varphi_{p,f}}$	potential vector for potential-nodes and floating-nodes
$\boldsymbol{\varphi_c}$	potential vector for charge-nodes
$\varphi_{p,f_{\text{initial}}}$	potential of a potential-node or floating-node from which an electron tunnels
$\varphi_{p,f_{\text{final}}}$	potential of a potential-node or floating-node to which an electron tunnels
$\psi$	wave function
$\psi^*$	complex conjugate wave function
$\psi_n, \psi_m$	orthonormal eigenfunctions
q	charge [As]
$q_{\Sigma}$	sum of charges [As]
$q_{f\Sigma}$	charge of macro-node
q	charge vector
qp,f	charge vector for potential-nodes and floating-nodes
qc	charge vector for charge-nodes
$q_{\text{crit}}$	critical charge for the Coulomb blockade [As]
Q0	background charge
r	magnitude of space vector [m]; random number
r	space vector
rn	on the interval [0,1] uniformly distributed random number
$\tilde{r}_n$	integer random number
RQ	quantum resistance $h/e^2 = \text{25813}\ \mathsf{\Omega}$
RT	tunnel resistance [ $\mathsf{\Omega}$]
Rpq(X)	rational Padé approximation of order p+q
$\rho$	spectral radius
t	time [s]
T	absolute temperature [K]
|T|2	tunnel transmission probability [1]
$\tau$	duration to the next tunnel event [s]
$\bar{\tau}$	average duration to the next tunnel event [s]
$\theta$	angle [rad]
V	voltage [V]
Vb	bias voltage [V]
$V_{\text{in}}$	input voltage [V]
$V_{\text{out}}$	output voltage [V]
$V_{\text {th}}$	threshold voltage [V]
$V_{\text{crit}}$	critical voltage for the Coulomb blockade [V]
V(x)	one-dimensional potential function
W	work done by voltage sources [J]
x	x-coordinate [m]