Related papers: Equivalent Hamiltonians
We describe some semiclassical spectral properties of Harper-like operators, i.e. of one-dimensional quantum Hamiltonians periodic in both momentum and position. The spectral region corresponding to the separatrices of the classical…
We give a condition for an almost constant-type manifold to be a constant-type manifold, and holomorphic and $R$-invariant submanifolds of almost Hermitian manifolds are studied. Generalizations of some results in [5] are given.
The difference and similarity between the velocity- and position-Verlet integrators are discussed from the viewpoint of their Hamiltonian representations for both linear and nonlinear systems. For a harmonic oscillator, the exact…
Some functorial and topological properties of vertical cohomologies and their application to completely integrable Hamiltonian systems are studied.
We examine the problem of integrability of two-dimensional Hamiltonian systems by means of separation of variables. The systematic approach to construction of the special non-pure coordinate separation of variables for certain natural…
Motivated by applications in databases, this paper considers various fragments of the calculus of binary relations. The fragments are obtained by leaving out, or keeping in, some of the standard operators, along with some derived operators…
We construct quantum models of two particles on a compact metric graph with singular two-particle interactions. The Hamiltonians are self-adjoint realisations of Laplacians acting on functions defined on pairs of edges in such a way that…
This paper deals with eigenvalues and eigenvectors of bicomplex linear operators defined on bicomplex space. We investigate the properties of these operators in the context of eigenvalues and eigenvectors, along with some relevant theorems.…
In this paper we study local Hamiltonian operators for multi-component evolutionary differential-difference equations. We address two main problems: the first one is the classification of low order operators for the two-component case. On…
A bi-Hamiltonian formulation is proposed for triangular systems resulted by perturbations around solutions, from which infinitely many symmetries and conserved functionals of triangular systems can be explicitly constructed, provided that…
A condition to have a real spectrum for a non-Hermitian Hamiltonian is given. As special cases, it is shown that the condition is reduced to Hermiticity and PT symmetric conditions.
The theme of this paper is the multiplicity of the consistent sets appearing in the consistent histories approach to quantum mechanics. We propose one criterion for choosing preferred families among them: that the physically realizable…
Operator-type estimates of homogenization are obtained for elliptic operators of arbitrary even order equal or greater than two. Operators under consideration are non-selfadjoint with lower-order terms.
The two weight inequality for the Hilbert transform arises in the settings of analytic function spaces, operator theory, and spectral theory, and what would be most useful is a characterization in the simplest real-variable terms. We show…
We define quantum bi-Hamiltonian systems, by analogy with the classical case, as derivations in operator algebras which are inner derivations with respect to two compatible associative structures. We find such structures by means of the…
A number of new L$\acute{e}$vi-Leblond type equations admitting four component spinor solutions have been proposed. The pair of linearized equations thus obtained in each case lead to Hamiltonians with characteristic features like L-S…
The paper presents several new sufficient conditions, as well as new equivalent criteria for the classical Riemann Hypothesis. Noteworthy are also other statements and remarks about $\zeta$ to be found throughout the paper.
We address the multiplicity of solutions to the time-energy canonical commutation relation for a given Hamiltonian. Specifically, we consider a particle spatially confined in a potential free interval, where it is known that two distinct…
In this paper we give some sufficient conditions of analyticity and univalence for functions defined by an integral operator. Next, we refine the result to a quasiconformal extension criterion with the help of the Becker's method. Further,…
In the article arXiv:0903.5277 [quant-ph], we have presented a mathematically rigorous quantum-mechanical treatment of a one-dimensional motion of a particle in the Calogero potential $V(x)=\alpha x^{-2}$. In such a way, we have described…