94,654 research outputs found
Quantum master equation scheme of time-dependent density functional theory to time-dependent transport in nano-electronic devices
In this work a practical scheme is developed for the first-principles study
of time-dependent quantum transport. The basic idea is to combine the transport
master-equation with the well-known time-dependent density functional theory.
The key ingredients of this paper include: (i) the partitioning-free initial
condition and the consideration of the time-dependent bias voltages which base
our treatment on the Runge-Gross existence theorem; (ii) the non-Markovian
master equation for the reduced (many-body) central system (i.e. the device);
and (iii) the construction of Kohn-Sham master equation for the reduced
single-particle density matrix, where a number of auxiliary functions are
introduced and their equations of motion (EOM) are established based on the
technique of spectral decomposition. As a result, starting with a well-defined
initial state, the time-dependent transport current can be calculated
simultaneously along the propagation of the Kohn-Sham master equation and the
EOM of the auxiliary functions.Comment: 9 pages, no figure
A principled approach to programming with nested types in Haskell
Initial algebra semantics is one of the cornerstones of the theory of modern functional programming languages. For each inductive data type, it provides a Church encoding for that type, a build combinator which constructs data of that type, a fold combinator which encapsulates structured recursion over data of that type, and a fold/build rule which optimises modular programs by eliminating from them data constructed using the buildcombinator, and immediately consumed using the foldcombinator, for that type. It has long been thought that initial algebra semantics is not expressive enough to provide a similar foundation for programming with nested types in Haskell. Specifically, the standard folds derived from initial algebra semantics have been considered too weak to capture commonly occurring patterns of recursion over data of nested types in Haskell, and no build combinators or fold/build rules have until now been defined for nested types. This paper shows that standard folds are, in fact, sufficiently expressive for programming with nested types in Haskell. It also defines buildcombinators and fold/build fusion rules for nested types. It thus shows how initial algebra semantics provides a principled, expressive, and elegant foundation for programming with nested types in Haskell
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