相关论文: Small Numerators Canceling Small Denominators: Is …
We introduce two numerical conjugacy invariants for dynamical systems -- the complexity and weak complexity indices -- which are well-suited for the study of "completely integrable" Hamiltonian systems. These invariants can be seen as "slow…
Two new families of completely integrable perturbations of the N-dimensional isotropic harmonic oscillator Hamiltonian are presented. Such perturbations depend on arbitrary functions and N free parameters and their integrals of motion are…
We consider a system of interacting fermions on a chain in a periodic potential incommensurate with the chain spacing. We derive a convergent perturbative expansion, afflicted by a small denominator problem and based on renormalization…
A wide class of matrix pencils connected with dissipative Hamiltonian descriptor systems is investigated. In particular, the following properties are shown: all eigenvalues are in the closed left half plane, the nonzero finite eigenvalues…
The paper considers a boundary value problem for the high-order Lavrent'ev-Bitsadze equation. Necessary and sufficient conditions for the uniqueness of the solution are found. When substantiating the existence, the problem of "small…
Starting from the formal solution to the Heisenberg equation, we revisit an universal model for a quantum open system with a harmonic oscillator linearly coupled to a boson bath. The analysis of the decay process for a Fock state and a…
We treat infinite horizon optimal control problems by solving the associated stationary Hamilton-Jacobi-Bellman (HJB) equation numerically to compute the value function and an optimal feedback law. The dynamical systems under consideration…
We investigate the problem of determining the Hamiltonian of a locally interacting open-quantum system. To do so, we construct model estimators based on inverting a set of stationary, or dynamical, Heisenberg-Langevin equations of motion…
Several explicit examples of quasi exactly solvable `discrete' quantum mechanical Hamiltonians are derived by deforming the well-known exactly solvable Hamiltonians of one degree of freedom. These are difference analogues of the well-known…
We investigate the asymptotic behavior of solutions of Hamilton-Jacobi equations with large drift term in an open subset of two-dimensional Euclidean space. When the drift is given by $\varepsilon^{-1} (H_{x_2}, -H_{x_1})$ of a Hamiltonian…
We study a high-dimensional regression setting under the assumption of known covariate distribution. We aim at estimating the amount of explained variation in the response by the best linear function of the covariates (the signal level). In…
The three integrable two-dimensional Henon-Heiles systems and their integrable perturbations are revisited. A family of new integrable perturbations is found, and N-dimensional completely integrable generalizations of all these systems are…
We consider perturbations of Hamiltonians whose Fourier symbol attains its minimum along a hypersurface. Such operators arise in several domains, like spintronics, theory of supercondictivity, or theory of superfluidity. Variational…
The controls enacting logical operations on quantum systems are described by time-dependent Hamiltonians that often include rapid oscillations. In order to accurately capture the resulting time dynamics in numerical simulations, a very…
Evidently, some relaxation dynamics, e.g. exponential decays, are much more common in nature than others. Recently there have been attempts to explain this observation on the basis of ``typicality of perturbations'' with respect to their…
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…
We consider quantum systems consisting of a linear chain of n harmonic oscillators coupled by a nearest neighbour interaction of the form $-q_r q_{r+1}$ ($q_r$ refers to the position of the $r$th oscillator). In principle, such systems are…
The open inflation model recently proposed by Hawking and Turok is investigated in scalar-tensor gravity context. If the dilaton-like field has no potential, the instanton of our model is singular but has a finite action. The…
We propose a scalable method to find a subspace $\widehat{\mathcal{H}}$ of low-rank tensors that simultaneously approximates a set of integral operators. The method can be seen as a generalization of the Tucker-2 decomposition model, which…
A close inspection on the 3D hydrogen atom Hamiltonian revealed formal eigenvectors often discarded in the literature. Although not in its domain, such eigenvectors belong to the Hilbert space, and so their time evolution is well defined.…