Related papers: How To Treat An N-Level System : A Proposal
We propose a variant formulation of Hamiltonian systems by the use of variables including redundant degrees of freedom. We show that Hamiltonian systems can be described by extended dynamics whose master equation is the Nambu equation or…
James' effective Hamiltonian method has been extensively adopted to investigate largely detuned interacting quantum systems. This method is just corresponding to the second-order perturbation theory, and cannot be exploited to treat the…
Hamiltonian formulation of N=3 systems is considered in general. The most general solution of the Jacobi equation in ${\mathbb R}^3$ is proposed. Compatible Poisson structures and the corresponding bi-Hamiltonian N=3 systems are also…
This paper presents a generalised two-level implementation which can handle linear and non-linear morphological operations. An algorithm for the interpretation of multi-tape two-level rules is described. In addition, a number of issues…
We introduce a systematic approach for treating the large N limit of matrix field theories.
An observer-based Hamiltonian identification algorithm for quantum systems is proposed. For the 2-level case an exponential convergence result based on averaging arguments and some relevant transformations is provided. The convergence for…
The linearity inherent in quantum mechanics limits current quantum hardware from directly solving nonlinear systems governed by nonlinear differential equations. One can opt for linearization frameworks such as Carleman linearization, which…
In this paper we propose an idea of constructing a macro--scale matrix system given a micro--scale matrix linear system. Then the macro--scale system is solved at cheaper computing costs. The method uses the idea of the generalized…
A simple recursive scheme for parameterisation of n-by-n unitary matrices is presented.
A Hamiltonian renormalization group is presented. Such a formulation is relevant for chiralic systems and more appropriate than the Lagrangian formalism. An application to 1D system is presented.
The main purpose of this paper is to give a topological and symplectic classification of completely integrable Hamiltonian systems in terms of characteristic classes and other local and global invariants.
A general method to derive the diagonal representation for a generic matrix valued quantum Hamiltonian is proposed. In this approach new mathematical objects like non-commuting operators evolving with the Planck constant promoted as a…
The factorization technique for superintegrable Hamiltonian systems is revisited and applied in order to obtain additional (higher-order) constants of the motion. In particular, the factorization approach to the classical anisotropic…
The aim of this paper is to present a self contained introduction to the Hubbard model and some of its applications.The paper consists of two parts: the first will introduce the basic notions of the Hubbard model starting from the…
We have studied a three-level {\Lambda}-type atomic system with all the energy levels exhibiting decay. The system is described by a pseudo-Hermitian Hamiltonian and subject to certain conditions, the Hamiltonian shows parity-time (PT)…
In this paper, an approach to facilitate the treatment with variabilities in system families is presented by explicitly modelling variants. The proposed method of managing variability consists of a variant part, which models variants and a…
In this paper, an approach to facilitate the treatment with variabilities in system families is presented by explicitly modelling variants. The proposed method of managing variability consists of a variant part, which models variants and a…
We first point out it is conditional to apply the variational approach to the nonlocal nonlinear Schr\"{o}dinger equation (NNLSE), that is, the response function must be an even function. Different from the variational approach, the…
An overview of Hamiltonian systems with noncanonical Poisson structures is given. Examples of bi-Hamiltonian ode's, pde's and lattice equations are presented. Numerical integrators using generating functions, Hamiltonian splitting,…
Before we proposed an algebraic technics for the Hamiltonian approach to the evolution systems of partial differential equations, including systems with constraints. Here we further develop this approach and present the defining system of…