4,052 research outputs found
Automatic Generation of Matrix Element Derivatives for Tight Binding Models
Tight binding (TB) models are one approach to the quantum mechanical many
particle problem. An important role in TB models is played by hopping and
overlap matrix elements between the orbitals on two atoms, which of course
depend on the relative positions of the atoms involved. This dependence can be
expressed with the help of Slater-Koster parameters, which are usually taken
from tables. Recently, a way to generate these tables automatically was
published. If TB approaches are applied to simulations of the dynamics of a
system, also derivatives of matrix elements can appear. In this work we give
general expressions for first and second derivatives of such matrix elements.
Implemented in a computer program they obviate the need to type all the
required derivatives of all occuring matrix elements by hand.Comment: 11 pages, 2 figure
Power dissipation in nanoscale conductors: classical, semi-classical and quantum dynamics
Modelling Joule heating is a difficult problem because of the need to introduce correct correlations between the motions of the ions and the electrons. In this paper we analyse three different models of current induced heating (a purely classical model, a fully quantum model and a hybrid model in which the electrons are treated quantum mechanically and the atoms are treated classically). We find that all three models allow for both heating and cooling processes in the presence of a current, and furthermore the purely classical and purely quantum models show remarkable agreement in the limit of high biases. However, the hybrid model in the Ehrenfest approximation tends to suppress heating. Analysis of the equations of motion reveals that this is a consequence of two things: the electrons are being treated as a continuous fluid and the atoms cannot undergo quantum fluctuations. A means for correcting this is suggested
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