相关论文: A 2 - Component Generalization of the Degasperis -…
Given an n-dimensional natural Hamiltonian L on a Riemannian or pseudo-Riemannian manifold, we call "extension" of L the n+1 dimensional Hamiltonian $H=\frac 12 p_u^2+\alpha(u)L+\beta(u)$ with new canonically conjugated coordinates…
The Holstein-Primakoff representation for the su(2)-algebra is derived in the deformed boson scheme. The following two points are discussed : (i) connection between a simple Hamiltonian and the Hamiltonian obeying the su(2)-algebra such as…
The Dirac Hamiltonian in the (2+1) dimensional curved space-time has been studied with a metric for an expanding de Sitter space-time which is a two sphere. The spectrum and the exact solutions of the time dependent non-Hermitian and angle…
We introduce a two-parameter deformation of the classical Poisson distribution from the viewpoint of noncommutative probability theory, by defining a $(q,t)$-Poisson type operator (random variable) on the $(q,t)$-Fock space \cite{Bl12} (See…
This work explores a structure of the Deprit perturbation series and its connection to a Kato resolvent expansion. It extends the formalism previously developed for the Hamiltonians linearly dependent on perturbation parameter to a…
A time operator $\hat T_\eps$ of the one-dimensional harmonic oscillator $ \hat h_\eps=\half(p^2+\eps q^2)$ is rigorously constructed. It is formally expressed as $ \hat T_\eps=\half\frac{1}{\sqrt \eps } (\arctan (\sqrt \eps \hat…
Given a first order dynamical system possessing a commutative algebra of dynamical symmetries, we show that, under certain conditions, there exists a Poisson structure on an open neighbourhood of its regular (not necessarily compact)…
This paper is concerned with the asymptotic expansions of the amplitude of the solution of the Helmholtz equation. The original expansions were obtained using a pseudo-differential decomposition of the Dirichlet to Neumann operator. This…
We address the generalized measurement of the two-boson operator $Z_\gamma= a_1 + \gamma a_2^\dag$ which, for $|\gamma|^2 \neq 1$, is not normal and cannot be detected by a joint measurement of quadratures on the two bosons. We explicitly…
We develop KAM theory close to an elliptic fixed point for quasi-linear Hamiltonian perturbations of the dispersive Degasperis-Procesi equation on the circle. The overall strategy in KAM theory for quasi-linear PDEs is based on Nash-Moser…
Starting with the average particle distribution function for bosons and fermions for non-extensive thermodynamics , as proposed in \cite{CMP}, we obtain the corresponding density matrix operators and hamiltonians. In particular, for the…
The paper focuses on various properties and applications of the homotopy operator, which occurs in the Poincar\'{e} lemma. In the first part, an abstract operator calculus is constructed, where the exterior derivative is an abstract…
In a recent paper a slightly modified version of the Bateman system, originally proposed to describe a damped harmonic oscillator, was proposed. This system is really different from the Bateman's one, in the sense that this latter cannot be…
The present paper is a continuation of our work [11], where we introduced a fractional operator calculus related to a fractional ${\psi}-$Fueter operator in the one-dimensional Riemann-Liouville derivative sense in each direction of the…
A numerical method is proposed to solve the full-Eulerian time-dependent Vlasov-Poisson system in high dimension. The algorithm relies on the construction of a tensor decomposition of the solution whose rank is adapted at each time step.…
We propose an efficient quantum algorithm for simulating the dynamics of general Hamiltonian systems. Our technique is based on a power series expansion of the time-evolution operator in its off-diagonal terms. The expansion decouples the…
The Hamiltonian approach to isomonodromic deformation systems is extended to include generic rational covariant derivative operators on the Riemann sphere with irregular singularities of arbitrary Poincar\'e rank. The space of rational…
This work is devoted to the establishment of a Poisson structure for a format of equations known as Generalized Lotka-Volterra systems. These equations, which include the classical Lotka-Volterra systems as a particular case, have been…
Motivated by the problem of longitudinal data assimilation, e.g., in the registration of a sequence of images, we develop the higher-order framework for Lagrangian and Hamiltonian reduction by symmetry in geometric mechanics. In particular,…
Hamilton's equations with noise and friction possess a hidden supersymmetry, valid for time-independent as well as periodically time-dependent systems. It is used to derive topological properties of critical points and periodic trajectories…