Related papers: Accuracy control in ultra-large-scale electronic s…
Fundamental theories and practical methods for large-scale electronic structure calculations are given, in which the computational cost is proportional to the system size. Accuracy controlling methods for microscopic freedoms are focused on…
Several methodologies are developed for large-scale atomistic simulations with fully quantum mechanical description of electron systems. The important methodological concepts are (i) generalized Wannier state, (ii) Krylov subspace and (iii)…
We review our recently developed methods for large-scale electronic structure calculations, both in one-electron theory and many-electron theory. The method are based on the density matrix representation, together with the Wannier state…
Several methods are constructed for large-scale electronic structure calculations. Test calculations are carried out with up to 10^7 atoms. As an application, cleavage process of silicon is investigated by molecular dynamics simulation with…
We show that open-loop dynamical control techniques may be used to synthesize unitary transformations in open quantum systems in such a way that decoherence is perturbatively compensated for to a desired (in principle arbitrarily high)…
Model Predictive Control (MPC) can efficiently control constrained systems in real-time applications. MPC feedback law for a linear system with linear inequality constraints can be explicitly computed off-line, which results in an off-line…
In this article, a novel adaptive controller is designed for Euler-Lagrangian systems under predefined time-varying state constraints. The proposed controller could achieve this objective without a priori knowledge of system parameters and,…
We present here a constructive method of Lagrangian approximate control- lability for the Euler equation. We emphasize on different options that could be used for numerical recipes: either, in the case of a bi-dimensionnal fluid, the use of…
An efficient and robust linear scaling method is presented for large scale {\it ab initio} electronic structure calculations of a wide variety of materials including metals. The detailed short range and the effective long range…
Along with the scaling of dimensions in quantum systems, transitions between the system's energy levels would become close in frequency, which are conventionally resolved by weak and lengthy pulses. Here, we extend and experimentally…
The challenge of mastering computational tasks of enormous size tends to frequently override questioning the quality of the numerical outcome in terms of accuracy. By this we do not mean the accuracy within the discrete setting, which…
There is a fundamental limit to what is knowable about atomic and molecular scale systems. This fuzziness is not always due to the act of measurement. Other contributing factors include system parameter uncertainty, functional uncertainty…
An early-stage version of simulation package is developed for electronic structure calculation and dynamics of atom process in large-scale systems, particularly, nm-scale or 10nm-scale systems. We adopted the Extensible Markup Language…
We study quantum control of the full hyperfine manifold in the ground-electronic state of alkali atoms based on applied radio frequency and microwave fields. Such interactions should allow essentially decoherence-free dynamics and the…
In this paper we consider the problem of computing control invariant sets for linear controlled high-dimensional systems with constraints on the input and on the states. Set inclusions conditions for control invariance are presented that…
In mathematics and engineering, control theory is concerned with the analysis of dynamical systems through the application of suitable control inputs. One of the prominent problems in control theory is controllability which concerns the…
The fractional calculus of variations and fractional optimal control are generalizations of the corresponding classical theories, that allow problem modeling and formulations with arbitrary order derivatives and integrals. Because of the…
The theory of controlled mechanical systems of [6, 3, 4] is extended to the case of ideal incompressible fluids consisting of charged particles in the presence of an external magnetic field. The resulting control is of feedback type and…
This work presents a framework for control theory based on constructive analysis to account for discrepancy between mathematical results and their implementation in a computer, also referred to as computational uncertainty. In control…
A pivotal task in quantum metrology, and quantum parameter estimation in general, is to de- sign schemes that achieve the highest precision with given resources. Standard models of quantum metrology usually assume the dynamics is fixed, the…