Bulletin of the American Physical Society
2005 APS March Meeting
Monday–Friday, March 21–25, 2005; Los Angeles, CA
Session A25: Focus Session: Computational Nanoscience I |
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Sponsoring Units: DMP DCOMP DAMOP Chair: J.R. Manson, Clemson University Room: LACC 501A |
Monday, March 21, 2005 8:00AM - 8:36AM |
A25.00001: Future directions in the simulation of nanomaterials Invited Speaker: Nanotechnology forces us to rethink conventional solid state physics. Quantum phenomena are commonplace. A system with 101 atoms may be very different from one with just 100. Key biomolecules may resemble spaghetti more than silicon; viscosity often dominates over inertia. Statistical physics is often not carrier statistics; equilibrium may be irrelevant, though the kinetics of non-equilibrium processes can be crucial. Even when nanoscale issues concern structure (rather than functionality), a new viewpoint is needed. Important features, like elasticity and electrostatic energies, have clear macroscopic analogies, but different issues arise, reflecting the reproducibility of quantum dots or the accuracy of self-organisation. Concepts like epitaxy and templating are usually micro- or meso-structural, but emerge again in modelling for the nanoscale. Unexpected analogies between biomolecule and semiconductor systems appear. My examples will include quantum dots and possible silicon-based, room temperature, quantum information processing, and will emphasise new opportunities in nanoscale science. [Preview Abstract] |
Monday, March 21, 2005 8:36AM - 8:48AM |
A25.00002: QMC with a Stochastic Poisson Solver: An application to realistic models of quantum dots Dyutiman Das, Jeongnim Kim, Richard Martin Quantum Monte Carlo can be used to study interacting electrons in semiconductor quantum structures. We introduce a new approach in which the potential acting on each electron is found by sampling using a classical Monte Carlo ``Walk On Spheres''(WOS) algorithm within the QMC calculation. This allows cheap and coarse estimates of the potential to be used, since the QMC averages the noise in the potential. The averaging is accomplished simply in VMC, and in DMC we use the penalty method [1] to modify the non-linear branching factor according to the noise in our potential estimate. The WOS algorithm is general enough to be applied to devices with arbitrary geometries, dielectric constants and gate biases. We employ this QMC-WOS hybrid approach to a real heterostructure as described in Ref.[2]. Specifically we calculate the singlet triplet splitting for a two electron double dot and compare with DFT calculations. \newline [1.] Ceperley D. M. and Dewing M. J. Chem. Phys. 110,9812 1999 \newline [2.] Elzerman et. al. PRB 67, 161308(R) 2003 [Preview Abstract] |
Monday, March 21, 2005 8:48AM - 9:00AM |
A25.00003: Quantum Monte Carlo Simulations of Exciton-Exciton Scattering in Quantum Wells John Shumway Exciton-exciton interactions are characterized by the scattering length, which is a property of excited states of a four-particle wavefunction at the zero energy limit. As is well-known in atomic physics, the scattering length can be notoriously hard to predict theoretically, since correlation and van der Waals forces can play a large role. We have developed a quantum Monte Carlo (QMC) approach that can accurately calculate the bulk exciton-exciton scattering length within the effective mass approximation (Shumway and Ceperley, PRB {\bf 63}, 165209, 2001). As an added benefit of this technique, all bound biexciton states are also calculated, providing an additional test for the simulations. Now we have adapted this excited-state QMC technique to exciton-exciton interactions in quantum wells, where there is current interest in exciton or polariton condensates. We discuss predictions of our simulations, especially ways to modify exciton-exciton interaction strength with different well geometries and external fields. [Preview Abstract] |
Monday, March 21, 2005 9:00AM - 9:12AM |
A25.00004: Quantum Perturbation Theory in O(N): Ab initio response theory for nanomaterials Anders Niklasson One of the main obstacles in predicting the electronic properties of complex nanomaterials directly from fundamental theory is the enormous computational complexity involved in solving the equations governing the quantum mechanical response to an external perturbation. We have recently introduced an orbital-free quantum perturbation theory based on perturbed spectral projections of the Hamiltonian. It gives the density matrix and its response upon variation of the Hamiltonian by quadratically convergent recursions. The approach is surprisingly simple and efficient. It allows treatment of both embedded quantum subsystems and response functions. The computational cost scales linearly with the systems size N and for local perturbations it scales linearly with the size of the perturbed region O(N\_pert), i.e. as O(1) with the total system size. Traditional textbook perturbation theory based of wave function or Green's function formalism can be replaced by a quadratically convergent explicit recursion that gives the expansion terms of expectation values to any order. Connecting and disconnecting individual weakly interacting quantum subsystems can be performed by treating off-diagonal elements of the Hamiltonian as a perturbation. This should be highly useful in nanoscience for connecting quantum dots, surfaces, clusters and nanowires, where the different parts can be calculated separately. [Preview Abstract] |
Monday, March 21, 2005 9:12AM - 9:24AM |
A25.00005: Efficient Computational Methods to Treat Multiple Scattering in Electron Diffraction by Nanostructures G.M. Gavaza, Z.X. Yu, L. Tsang, C.H. Chan, S.Y. Tong, M.A. Van Hove Our purpose is to extend the capabilities of surface structure determination methods, such as Low Energy Electron Diffraction, so they can be used for nanostructures. To treat non-periodic systems, a cluster approach is used. The main computational challenge consists in solving a Ax=b matrix-vector equation of large dimension. Since matrix inversion is both memory and compute-time demanding, we have developed and tested two fast iterative methods to solve the above equation: the Sparse-Matrix Canonical Grid (SMCG) method shifts the atoms to a regular space grid and makes use of FFT transformations while the Multi-Level Singular-Value Decomposition (MLSVD) performs fast rank determination and SV decomposition of A. For both these methods, the compute time scales as N x log$_{2}$N per iteration, where N is the number of atoms. These two methods complement each other in terms of the types of nanostructures that they handle best. [Preview Abstract] |
Monday, March 21, 2005 9:24AM - 9:36AM |
A25.00006: New Theoretical Method for Molecular Systems and Nano-molecules Junho Jeong In general, it has been known that electrons of a molecular system are indistinguishable. However, the total electronic energy computed by the conventional theoretical method, the Hartree Fock Theory or the Density Functional Theory, consists of kinetic and attractive energies on distinguishable electrons and repulsive potential energy on indistinguishable electrons on a molecular system. The other question of the conventional methods is singularity on two-electron integrals because electrons in a molecular system cannot exist at the centre of their nucleus which brings about singularity in free space. The new theoretical method that modified above problems has been applied to hydrogen molecule H$_{2}$, and its results have been compared with those of the conventional theoretical methods installed in Gaussian 98 program. The total energies of the conventional methods are much bigger than -1.0 (a.u.) the total energy of hydrogen molecule in the infinite H-H bond distance, and the electron-electron repulsive energies are about 2.911 to 7.728 not 0.0 eV on 1,000 {\AA} H-H bond distance although the energies of the new method agree with the values of the physical concept on H$_{2}$. [Preview Abstract] |
Monday, March 21, 2005 9:36AM - 9:48AM |
A25.00007: Adaptive Quantum Design for Nanoscience Stephan Haas, Jason Thalken, Anthony Levi Recent advances in nano-technology have enabled us to construct ultra-small opto-electronic devices, such as filters, modulators, and resonators. Material response functions can be made to order on the atomic level by explicitely breaking symmetries, such as relative widths in quasi-one-dimensional multi-layer dielectric filter arrays. This requires new software tools that optimize desired material response characteristics by finding the global minimum in large parameter landscapes of possible solutions. In this talk, we show examples of this adaptive quantum design, including optical filters in one and two dimensions and a quantum mechanical tight-binding model. Numerical optimization techniques, such as simulated annealing and the genetic algorithm, will be discussed briefly. This approach is useful in the design of a new generation of nano-devices. [Preview Abstract] |
Monday, March 21, 2005 9:48AM - 10:00AM |
A25.00008: A numerically tractable method for a non-uniform electron gas system with an atomic center Koichi Kusakabe, Masanori Takahashi, Naoshi Suzuki To perform the first-principles calculation of a non-uniform electron system with both localized and delocalized electrons, we have developed a tractable algorithm using the transcorrelated method and Pahl-Handy's mixed basis. Both two-body and three body potentials are expanded in terms of spherical harmonics or in the Fourier series. Radial integrals are analytically evaluated, which makes the numerical simulation as simple as series of matrix multiplication and the fast Fourier transformation. Possible application for a Kondo system is addressed. Our numerical simulation could provide a first-principles evaluation of the U-term and residual exchange-correlation energy functional for an effective many-body system of the density functional theory. [Preview Abstract] |
Monday, March 21, 2005 10:00AM - 10:12AM |
A25.00009: Time-dependent quantum process for electrons assisted by oscillating electric field Masakazu Muraguchi, Kyozaburo Takeda, Yusuke Asari, Naoki Watanabe Significant advances in nanometer-scale techniques have enabled us to control the transport phenomena of electrons artificially. In order to control the electronic states of the quantum dots by using oscillated electric field (OEF), the time development features of the electron wave function should be fully understood, because the state of electron changes sharply for a short time. Here, we study time-dependent quantum process for electrons assisted by OEF based on solving the TD Schr\"odinger equation numerically both in the real-space and -time. Introducing the effective lifetime of an electron in the quantum dot, we discuss how OEF modulates the transmitting probability. We especially focus on the relationship among the lifetime, the strength and frequency of the injected electric field while varying the potential profile. We will further report the effect of the electromagnetic radiation caused by electron's self-motion as well as the inter-electron interaction. [Preview Abstract] |
Monday, March 21, 2005 10:12AM - 10:24AM |
A25.00010: Using quantum mechanics to synthesize electronic devices Petra Schmidt, Stephan Haas, Anthony Levi Adaptive quantum design [1] has been used to explore the possibility of creating new classes of electronic semiconductor devices. We show how non-equilibrium electron transmission through a synthesized conduction band potential profile can be used to obtain a desired current - voltage characteristic. We illustrate our methodology by designing a two-terminal linear resistive element in which current is limited by quantum mechanical transmission through a potential profile and power is dissipated non-locally in the electrodes. As electronic devices scale to dimensions in which the physics of operation is dominated by quantum mechanical effects, classical designs fail to deliver the desired functionality. Our device synthesis approach is a way to realize device functionality that may not otherwise be achieved. [1] Y.Chen, R.Yu, W.Li, O.Nohadani, S.Haas, A.F.J. Levi, Journal of Applied Physics, Vol.94, No.9, p6065, 2003 [Preview Abstract] |
Monday, March 21, 2005 10:24AM - 10:36AM |
A25.00011: Coupling Classical Molecular Dynamics Simulations to Continuum Current and Heat Flow Equations: Application to Frictional and Resistive Heating of Nanoscale Metal Contacts Clifford Padgett, David Schall, Donald Brenner To reproduce experimental heat flow rates and to model resistive heating, atomic kinetic energies in a molecular dynamics (MD) simulation are coupled via an ad hoc feedback loop to continuum current and heat transfer equations that are solved numerically on a finite difference grid (FDG). For resistive heating, the resistance in each region of the FDG is calculated from the experimental resistivity and atomic density, and a network of resistors is established from which the potential at every FD point is calculated given an applied voltage. The potential difference between connected FDG regions and the resistance are then used to calculate the current between the two points, the heat resulting from that current, and the magnetic and electrical force between grid regions. This information is then added back into the atomic simulation. To illustrate this method, simulations of the frictional and resistive heating of a nanoscale metal contract will be presented. This work was funded by MURI Project No. N00014-04-1- 0601. [Preview Abstract] |
Monday, March 21, 2005 10:36AM - 10:48AM |
A25.00012: The Solution of the Interior Eigenvalue Problem for Large Scale Nanosystems Andrew Canning, Lin-Wang Wang, Osni Marques, Julien Langou First-principles materials science calculations typically involve a self-consistent solution of the Kohn-Sham equations. These types of methods typically scale with the cube of the system size and can only be used to study systems of up to a thousand atoms. To study larger systems we use semi-empirical potentials or approximated ab initio potentials such as those constructed using the charge patching method. Using these types of potentials does not require a selfconsistent solution of our effective single particle equations and we can solve directly for the few states of interest around the gap. The solution of our single particle equations now becomes an interior eigenvalue problem for a few states around a given energy rather than the self-consistent solution for the lowest n states where n is the number of bands. In this talk I will compare different methods (conjugate gradient, Jacobi-Davidson, Lanczos) for this problem with particular emphasis on solving large nanosystems on parallel computers. Work supported by the DOE under the Modeling and Simulation in Nanoscience Initiative. [Preview Abstract] |
Monday, March 21, 2005 10:48AM - 11:00AM |
A25.00013: Choosing a Classical Potential in Multi-Scale Modeling Aditi Mallik, Krishna Muralidharan, DeCarlos Talyor, Keith Runge, James Dufty For problems relating to fracture in multi-scale modeling, a consistent embedding of a quantum (QM) domain in its classical (CM) environment requires that the classical potential chosen for the CM region should yield the same geometry and elastic properties as the QM domain. It is proposed that such a classical potential can be constructed using \textit{ab initio} data on the equilibrium structure and weakly strained configurations calculated from the quantum description, rather than the more usual approach of fitting to a wide range of empirical data. This scheme is illustrated in detail for a model system, a silica nanorod that has the same stiochiometric ratio of Si:O as observed in real silica. The potential is chosen to have the same functional form as TTAM but the parameters are fitted using a genetic algorithm with force data obtained from a quantum calculation. The Young's modulus (Y) obtained from this classical potential matches closely with that obtained from the QM method for strains up to 10{\%}, unlike the standard TTAM which differs by 18{\%}. Furthermore, the bond lengths and bond angles in the rod are an order of magnitude more accurate for the new potential in comparison to that from the current TTAM or BKS potential parameters. This potential provides a ``seamless'' coupling between the QM and CM regions in applications of QM/CM multi-scale modeling for this silica nanorod. The wider application of this potential can be found in glasses. [Preview Abstract] |
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