Related papers: Deciding finiteness of bosonic dynamics with tunab…

Accurate control of quantum evolution is an essential requirement for quantum state engineering, laser chemistry, quantum information and quantum computing. Conditions of controllability for systems with a finite number of energy levels…

We classify up to isomorphism all finite-dimensional Lie algebras that can be realised as Lie subalgebras of the complex Weyl algebra $A_1$. The list we obtain turns out to be discrete and for example, the only non-solvable Lie algebras…

Exact unitary transformations play a central role in the analysis and simulation of many-body quantum systems, yet the conditions under which they can be carried out exactly and efficiently remain incompletely understood. We show that exact…

By resorting to the Fock--Bargmann representation, we incorporate the quantum Weyl--Heisenberg algebra, $q$-WH, into the theory of entire analytic functions. The $q$--WH algebra operators are realized in terms of finite difference operators…

Unlike their fermionic counterparts, the dynamics of Hermitian quadratic bosonic Hamiltonians are governed by a generally non-Hermitian Bogoliubov-de Gennes effective Hamiltonian. This underlying non-Hermiticity gives rise to a dynamically…

In this paper we discuss some physical applications of topological *-algebras of unbounded operators. Our first example is a simple system of free bosons. Then we analyze different models which are related to this one. We also discuss the…

We present a product formula to approximate the exponential of a skew-Hermitian operator that is a sum of generators of a Lie algebra. The number of terms in the product depends on the structure factors. When the generators have large norm…

The integrability condition called shape invariance is shown to have an underlying algebraic structure and the associated Lie algebras are identified. These shape-invariance algebras transform the parameters of the potentials such as…

Quantum Groups can be constructed by applying the quantization by deformation procedure to Lie groups endowed with a suitable Poisson bracket. Here we try to develop an understanding of these structures by investigating dynamical systems…

In this paper, we show how to use the analysis of the Lie algebra associated with a quantum mechanical system to study its dynamics and facilitate the design of controls. We give algorithms to decompose the dynamics and describe their…

Motivated by Weyl algebra analogues of the Jacobian conjecture and the Tame Generators problem, we prove quantum versions of these problems for a family of analogues to the Weyl algebras. In particular, our results cover the Weyl-Hayashi…

Let $F$ be a field of characteristic not $2$ . An associative $F$-algebra $R$ gives rise to the commutator Lie algebra $R^{(-)}=(R,[a,b]=ab-ba).$ If the algebra $R$ is equipped with an involution $*:R\rightarrow R$ then the space of the…

There is developed a current algebra representation scheme for reconstructing algebraically factorized quantum Hamiltonian and symmetry operators in the Fock type space and its application to quantum Hamiltonian and symmetry operators in…

Irreducible sigma models, i.e. those for which the partition function does not factorise, are defined on Riemannian spaces with irreducible holonomy groups. These special geometries are characterised by the existence of covariantly constant…

In this paper, we introduce the commutativity degree of a finite-dimensional Lie algebra over a finite field and determine upper and lower bounds for it. Moreover, we study some relations between the notion of commutativity degree and known…

We give an overview of some properties of Lie algebras generated by at most 5 extremal elements. In particular, for any finite graph {\Gamma} and any field K of characteristic not 2, we consider an algebraic variety X over K whose K-points…

Let W_n(K) be the Lie algebra of derivations of the polynomial algebra K[X]:=K[x_1,...,x_n] over an algebraically closed field K of characteristic zero. A subalgebra L of W_n(K) is called polynomial if it is a submodule of the K[X]-module…

The space of realizations of a finite-dimensional Lie algebra by first order differential operators is naturally isomorphic to H^1 with coefficients in the module of functions. The condition that a realization admits a finite-dimensional…

We study from an algebraic and geometric viewpoint Hamiltonian operators which are sum of a non-degenerate first-order homogeneous operator and a Poisson tensor. In flat coordinates, also known as Darboux coordinates, these operators are…

We describe a new exact lattice bosonization of matrix quantum mechanics (equivalently of non-relativistic fermions) that is valid for arbitrary rank N of the matrix, based on an exact operator bosonization introduced earlier in [1]. The…