相关论文: Quaternionic Hamilton equations

Spatio-temporally chaotic dynamics of a classical field can be described by means of an infinite hierarchy of its unstable spatio-temporally periodic solutions. The periodic orbit theory yields the global averages characterizing the chaotic…

We investigate a special class of quadratic Hamiltonians on so(4) and so(3,1) and describe Hamiltonians that have additional polynomial integrals. One of the main results is a new integrable case with an integral of sixth degree.

The objective of this paper is to find some inequalities satisfied by periodical solutions of multi-time Hamilton systems, when the Hamiltonian is convex. To our knowledge, this subject of first-order field theory is still open. Section 1…

A harmonic oscillator Hamiltonian augmented by a non-Hermitian \pt-symmetric part and its su(1,1) generalizations, for which a family of positive-definite metric operators was recently constructed, are re-examined in a supersymmetric…

The classical and quantum dynamics of the noncanonically coupled oscillators is considered. It is shown that though the classical dynamics is well--defined for both harmonic and anharmonic oscillators, the quantum one is well--defined in…

We notice new Hermitian counterpart of Swanson's Hamiltonian.

An indeterministic interpretation of classical physics has been proposed recently, in which the argument relies on attacking an alleged unwarranted metaphysical hidden assumption of the standard deterministic interpretation. This short…

Gravitomagnetic equations result from applying quaternionic differential operators to the energy-momentum tensor. These equations are similar to the Maxwell's EM equations. Both sets of the equations are isomorphic after changing…

The algebraic and geometric properties of a novel generalization of Clifford's classical C4 point-circle configuration are analysed. A connection with the integrable quaternionic discrete Schwarzian Kadomtsev-Petviashvili equation is…

In a first part we propose an introduction to multisymplectic formalisms, which are generalisations of Hamilton's formulation of Mechanics to the calculus of variations with several variables: we give some physical motivations, related to…

Dirac's equation of the electron will be discussed by using quaternions as the basis of a new formalism which seems to be very well adapted to the problem. The transformation properties of the equations as well as the invariant and…

The Dirac equation with Lorentz violation involves additional coefficients and yields a fourth-order polynomial that must be solved to yield the dispersion relation. The conventional method of taking the determinant of $4\times 4$ matrices…

We solve direct and inverse problems for two-dimensional (quasi) canonical systems related to exponential polynomials of a specific but sufficiently general type. The approach to the inverse problem in this paper provides an interpretation…

In this paper we present a perturbation theory for constant quaternionic potentials. The effects of quaternionic perturbations are explicitly treated for bound states of hydrogen atom, infinite potential well and harmonic oscillator.…

Several completely integrable, indeed solvable, Hamiltonian many-body problems are exhibited, characterized by Newtonian equations of motion ("acceleration equal force"), with linear and cubic forces, in N-dimensional space (N being an…

For higher derivative theories, using the approach of Caratheodory's equivalent Lagrangian, we show that there exist novel formulations of Hamilton-Jacobi equations, which are different from the formulations derived from Hamilton's…

In recent years we've seen the birth of a new field known as hamiltonian complexity lying at the crossroads between computer science and theoretical physics. Hamiltonian complexity is directly concerned with the question: how hard is it to…

We characterize the subclass of quasianti-Hermitian quaternionic Hamiltonian dynamics such that their complex projections are one-parameter semigroup dynamics in the space of complex quasi-Hermitian density matrices. As an example, the…

An intriguingly natural generalization, using complex octonions, of general relativity is pointed out. The starting point is the vierbein-based double dual formulation of the Einstein-Hilbert action. In terms of two natural structures on…

We extend some classical results dealing with boundary Harnack inequatilities to a class of quasilinear elliptic equations and derive some new estimates for solutions of such equations with an isolated singularity on the boundary of a…