Related papers: Computing with Hamiltonian operators
We study the algebra of differential operators on non-compact simply connected harmonic manifolds and provide sufficient conditions for them to have a radial fundamental solution and be surjective on the space of smooth function.…
This text is devoted to hyperbolic equations admitting differential operators that map any function of one independent variable into a symmetry of the corresponding equation. We use the term `symmetry driver' for such operators and prove…
Supersymmetry transformations of first and second order are used to generate Hamiltonians with known spectra departing from the harmonic oscillator with an infinite potential barrier. It is studied also the way in which the eigenfunctions…
Differential equations on spaces of operators are very little developed in Mathematics, being in general very challenging. Here, we study a novel system of such (non-linear) differential equations. We show it has a unique solution for all…
A method for the nonintrusive and structure-preserving model reduction of canonical and noncanonical Hamiltonian systems is presented. Based on the idea of operator inference, this technique is provably convergent and reduces to a…
We describe all fifth-order Hamiltonian operators in one dependent and one independent variable that possess the momentum, i.e., for which there exists a Hamiltonian associated with translation in the independent variable. Similar results…
We present an algorithm to compute the Hecke operators on the equivariant cohomology of an arithmetic subgroup $\Gamma$ of the general linear group $\mathrm{GL}_n$. This includes $\mathrm{GL}_n$ over a number field or a finite-dimensional…
A framework for statistical-mechanical analysis of quantum Hamiltonians is introduced. The approach is based upon a gradient flow equation in the space of Hamiltonians such that the eigenvectors of the initial Hamiltonian evolve toward…
We give a simple proof of the fact that every diagonalizable operator that has a real spectrum is quasi-Hermitian and show how the metric operators associated with a quasi-Hermitian Hamiltonian are related to the symmetry generators of an…
Hamiltonian systems are differential equations which describe systems in classical mechanics, plasma physics, and sampling problems. They exhibit many structural properties, such as a lack of attractors and the presence of conservation…
An algorithm for the symbolic computation of recursion operators for systems of nonlinear differential-difference equations (DDEs) is presented. Recursion operators allow one to generate an infinite sequence of generalized symmetries. The…
We compute general compatibility conditions between a weakly nonlocal homogeneous Hamiltonian operator and a third-order homogeneous Hamiltonian operator. Such operators determine a bi-Hamiltonian structure for many integrable PDEs…
Numerical lattice gauge theory computations to generate gauge field configurations including the effects of dynamical fermions are usually carried out using algorithms that require the molecular dynamics evolution of gauge fields using…
Quantum computing can efficiently simulate Hamiltonian dynamics of many-body quantum physics, a task that is generally intractable with classical computers. The hardness lies at the ubiquitous anti-commutative relations of quantum…
This paper concerns a first-order algorithmic technique for a class of optimal control problems defined on switched-mode hybrid systems. The salient feature of the algorithm is that it avoids the computation of Fr\'echet or G\^ateaux…
In this article we provide a framework for the study of Hecke operators acting on the Bredon (co)homology of an arithmetic discrete group. Our main interest lies in the study of Hecke operators for Bianchi groups. Using the Baum-Connes…
An infinite family of quasi-maximally superintegrable Hamiltonians with a common set of (2N-3) integrals of the motion is introduced. The integrability properties of all these Hamiltonians are shown to be a consequence of a hidden…
We investigate $\rho$-orthogonality and its local symmetry in the space of bounded linear operators. A characterization of Hilbert space operators with symmetric numerical range is established in terms of $\rho$-orthogonality. Further, we…
Our main theorem is in the generality of the axioms of Hilbert space, and the theory of unbounded operators. Consider two Hilbert spaces such that their intersection contains a fixed vector space D. It is of interest to make a precise…
In this article, we conduct a study of integral operators defined in terms of non-convolution type kernels with singularities of various degrees. The operators that fall within our scope of research include fractional integrals, fractional…