Related papers: A Geometrical Method of Decoupling
The Courant-Snyder theory for two-dimensional coupled linear optics is presented, based on the systematic use of the real representation of the Dirac matrices. Since any real $4\times 4$-matrix can be expressed as a linear combination of…
We present a systematic hierarchy of approximations for {\it local} exact-decoupling of four-component quantum chemical Hamiltonians based on the Dirac equation. Our ansatz reaches beyond the trivial local approximation that is based on a…
Based on the technique of the discrete one-turn transfer maps, the problem of linear coupling between horizontal and vertical betatron oscillations in an accelerator has been treated exactly and entirely in explicit form. The stability…
A framework to systematically decouple high order elliptic equations into combination of Poisson-type and Stokes-type equations is developed. The key is to systematically construct the underling commutative diagrams involving the complexes…
In this paper we present a complete linear synchrobetatron coupling formalism by studying the transfer matrix which describes linear horizontal and longitudinal motions. With the technique established in the linear horizontal-vertical…
We consider a Hamiltonian decomposition problem of partitioning a regular graph into edge-disjoint Hamiltonian cycles. It is known that verifying vertex non-adjacency in the 1-skeleton of the symmetric and asymmetric traveling salesperson…
This paper presents a generalization to image matching of the Hamiltonian approach for planar curve matching developed in the context of group of diffeomorphisms. We propose an efficient framework to deal with discontinuous images in any…
Analyses of betatron coupling can be broadly divided into two categories: the matrix approach that decouples the single-turn matrix to reveal the normal modes and the hamiltonian approach that evaluates the coupling in terms of the action…
One of the most used approaches in simulating materials is the tight-binding approximation. When using this method in a material simulation, it is necessary to compute the eigenvalues and eigenvectors of the Hamiltonian describing the…
We present an efficient algorithm for one- and two-component relativistic exact-decoupling calculations. Spin-orbit coupling is thus taken into account for the evaluation of relativistically transformed (one-electron) Hamiltonian. As the…
We develop a theory of continuous decoupling with bounded controls from a geometric perspective. Continuous decoupling with bounded controls can accomplish the same decoupling effect as the bang-bang control while using realistic control…
The classic method for computing the spectral decomposition of a real symmetric matrix, the Jacobi algorithm, can be accelerated by using mixed precision arithmetic. The Jacobi algorithm is aiming to reduce the off-diagonal entries…
Because of the significant increase in size and complexity of the networks, the distributed computation of eigenvalues and eigenvectors of graph matrices has become very challenging and yet it remains as important as before. In this paper…
Hidden symmetries in a covariant Hamiltonian formulation are investigated involving gauge covariant equations of motion. The special role of the Stackel-Killing tensors is pointed out. A reduction procedure is used to reduce the original…
The decomposition method which makes the parallel solution of the block-tridiagonal matrix systems possible is presented. The performance of the method is analytically estimated based on the number of elementary multiplicative operations…
The Separation of Variables theory for the Hamilton-Jacobi equation is 'by definition' related to the use of special kinds of coordinates, for example Jacobi coordinates on the ellipsoid or St\"ackel systems in the Euclidean space. However,…
The paper describes the multiple rotating frame technique for designing modulated rf-fields, that perform broadband heteronuclear decoupling in solution NMR spectroscopy. The decoupling is understood by performing a sequence of coordinate…
We present a protocol to selectively decouple, recouple, and engineer effective couplings in mesoscopic dipolar spin networks. In particular, we develop a versatile protocol that relies upon magic angle spinning to perform Hamiltonian…
Explicit and semi-explicit geometric integration schemes for dissipative perturbations of Hamiltonian systems are analyzed. The dissipation is characterized by a small parameter $\epsilon$, and the schemes under study preserve the…
In this paper we introduce the algorithm and the fixed point hardware to calculate the normalized singular value decomposition of a non-symmetric matrices using Givens fast (approximate) rotations. This algorithm only uses the basic…