Toshiaki Iitaka

Calculating the linear response functions of noninteracting electrons with a time-dependent Schrödinger equation

An O(N) algorithm is proposed for calculating linear response functions of non-interacting electrons in arbitray potential. This algorithm is based on numerical solution of the time-dependent Schroedinger equation discretized in space, and suitable to parallel- and vector- computation. Since it avoids O(N^3) computational effort of matrix diagonalization, it requires only O(N) computational effort where N is the dimension of the statevector. This O(N) algorithm is very effective for systems consisting of thousands of atoms, since otherwise we have to calculate large number of eigenstates, i.e., the occupied one-electron states up to the Fermi energy and the unoccupied states with higher energy. The advantage of this method compared to the Chebyshev polynomial method recently developed by Wang (L.W. Wang, Phys. Rev. B49, 10154 (1994);L.W. Wang, Phys. Rev. Lett. 73, 1039 (1994)) is that our method can calculate linear response functions without any storage of huge statevectors on external storage. Therefore it can treat much larger systems.

Electronic structure of nanocrystalline/amorphous silicon: a novel quantum size effect

Abstract We report a pseudopotential calculation of a model nanocrystalline Si embedded in amorphous Si up to 13 824 atoms and show a novel quantum size effect in this model system. This large scale pseudopotential calculation has been made possible by a real-time real-space higher-order finite difference method. It is shown that the peaks at around −1 and −2 eV shift to higher energy with decrease in size of nanocrystalline phase.

Calculating response functions in time domain with nonorthonormal basis sets

We extend the recently proposed order-N algorithms for calculating linear- and nonlinear-response functions in time domain to the systems described by nonorthonormal basis sets.

CORRELATION FUNCTIONS FOR A TIME-DEPENDENT CALCULATION OF LINEAR-RESPONSE FUNCTIONS

We emphasize the importance of choosing an appropriate correlation function to reduce numerical errors in calculating the linear-response function as a Fourier transformation of a time-dependent correlation function. As an example we take dielectric functions of silicon crystal calculated with a time-dependent method proposed by Iitaka et al. [Phys. Rev. E 56, 1222 (1997)].

Focusing of tunneling electron in a magnetic field

It is well known how an electron is bent by a magnetic field, but it is not known how a tunneling electron is bent by such a field. We conducted an analysis of how the electron is bent by the field using a Euclidean path integral method. As a result of this analysis, we make it clear that the electron is bent by Lorentz forces, as is an electron that does not tunnel. We then applied this result to scanning tunneling microscopy in order to focus electrons, although we only obtained an unsatisfactory result.

Non-degenerate two photon absorption spectra of Si nanocrystallites

We propose an efficient linear-scaling time-dependent method for calculating nonlinear response function, and study the size effects in non-degenerate two photon absorption spectra of Si nanocrystallites by using semi-empirical pseudopotentials.

Linear scaling calculation of an n-type GaAs quantum dot

A linear scale method for calculating electronic properties of large and complex systems is introduced within a local density approximation. The method is based on the Chebyshev polynomial expansion and the time-dependent method, which is tested on the calculation of the electronic structure of a model n-type GaAs quantum dot.

Calculating the density of states and the linear response functions with time-dependent Schroedinger equations

Abstract An O ( N ) algorithm is proposed for calculating the density of states and the linear response functions of noninteracting electrons. This algorithm is simple and suitable to parallel- and vector-computation. Since it avoids O ( N 3 ) computational effort of matrix diagonalization, it requires only O ( N ) computational efforts where N is the dimension of the statevector. The use of this O ( N ) algorithm is very effective since otherwise we have to calculate a large number of eigenstates, i.e. the occupied one-electron states up to the Fermi energy and the unoccupied states with higher energy. The advantage of this method compared to the Chebyshev polynomial method recently developed by Wang [27, 28] is that our method can calculate linear response functions without any storage of huge statevectors on external storage.

Phase Breaking in a Quantum Billiard

We introduce a theory on phase breaking time, which predicts the temperature dependence of phase breaking time as 1/τϕ∝ kBT and geometrical effects characteristic of ballistic quantum dots. We also compare the result with the experimental data.