Extended Dirac oscillator in (2 + 1)-dimensional space-time

We consider a soluble covariant extension of the two-dimensional Dirac oscillator (2D DO), which breaks the infinite degeneracy of the energy spectrum. The energy eigenvalues and the corresponding eigenstates of the system are obtained algebraically using chiral creation and annihilation operators. The effect of the coupling to an external constant transverse magnetic field is investigated. The connection with Jaynes-Cummings (JC) and Anti-Jaynes-Cummings (AJC) models of quantum optics, and other features of the system are also discussed.     

Spin Dynamics and Dirac Nodes in a Kagome Lattice

Herein, the spin dynamics for various magnetic configurations arranged on a Kagome lattice is investigated. Using a Holstein–Primakoff expansion of the isotropic Heisenberg Hamiltonian with multiple exchange parameters, the development and evolution of magnetic Dirac nodes with both anisotropy and magnetic field are examined. From the classical energies, the phase diagrams for the ferromagnetic (FM), antiferrimagnetic (AfM), and the 120°  phases are shown as functions of J₁, J₂, J₃, and anisotropy. Furthermore, the production of bosonic Dirac and Weyl nodes in the spin-wave spectra is shown. Through frustration of the magnetic geometry, a connection to the asymmetric properties of the Kagome lattice and the various antiferromagnetic configurations is discerned. Most interesting is the 120°  phase, which does not have Dirac nodes when considering only J₁ due to the formation of an analogous antiferromagnetic honeycomb lattice, but gains Dirac symmetry with next-nearest neighbor interactions. Additionally, the presence of flat modes that are characteristic of cluster excitations is shown. Further study of external frustrations from a magnetic field and anisotropy reveals a tunability of the exchange interactions and nodal points.     

Constructing the time independent Hamiltonian from a time dependent one

In this paper we introduce a method for finding a time independent Hamiltonian of a given Hamiltonian dynamical system by canonoid transformation of canonical momenta. We find a condition that the system should satisfy to have an equivalent time independent formulation. We study the example of a damped harmonic oscillator and give the new time independent Hamiltonian for it, which has the property of tending to the standard Hamiltonian of the harmonic oscillator as damping goes to zero.      

Radiation-induced fermion resonance

The Dirac equation is solved for two novel terms which describe the interaction energy between the half-integral spin of a fermion and the classical, circularly polarized, electromagnetic field. A simple experiment is suggested to test the new terms and the existence of radiation-induced fermion resonance.     

Deriving Energy-Gap of Some Nonlinear Hamiltonians by Invariant Eigen-operator Method

By virtue of the invariant eigen-operator method we search for the invariant eigen-operators for some Hamiltonians describing nonlinear processes in particle physics. In this way the energy-gap of the Hamiltonians can be naturally obtained. The characteristic polynomial theory has been fully employed in our derivation.     

Wigner function for the Dirac oscillator in spinor space

The Wigner function for the Dirac oscillator in spinor space is studied in this paper.Firstly,since the Dirac equation is described as a matrix equation in phase space,it is necessary to define the Wigner function as a matrix function in spinor space.Secondly,the matrix form of the Wigner function is proven to support the Dirac equation.Thirdly,by solving the Dirac equation,energy levels and the Wigner function for the Dirac oscillator in spinor space are obtained.     

Detection and analysis of new bands of O3 by CRDS between 6500 and 7300 cm

The absorption spectrum of the ¹⁶O₃ isotopologue of ozone has been recorded in the 7000-7920 cm⁻¹ region by high sensitivity CW-Cavity Ring Down Spectroscopy. This report is devoted to the analyses of the 7065-7300 cm⁻¹ region dominated by the ν₁ + 2ν₂ + 5ν₃ and ν₁ + 5ν₂ + 3ν₃ A-type bands at 7130.8 and 7286.8 cm⁻¹ respectively. 289 transitions were assigned to the ν₁ + 2ν₂ + 5ν₃ band. The corresponding line positions were modeled with an effective Hamiltonian involving Coriolis resonance interactions between the (1 2 5) upper state and the (4 4 0), (0 2 6) and (6 1 0) dark states, and an anharmonic resonance interaction with the (2 0 5) state. The very strong interaction (up to 50% mixing of the wavefunctions) between the (1 2 5) and (6 1 0) states leads to the observation of two extra lines of the 6ν₁ + ν₂ band due to a resonance intensity transfer. 213 transitions of the ν₁ + 5ν₂ + 3ν₃ band were assigned and modeled taking into account a Coriolis resonance interaction with the (3 6 0) state.We take the opportunity of the present work to report the analysis of the very weak 4ν₂ + 4ν₃ B-type band at 6506.1 cm⁻¹ which was assigned from previously recorded CRDS spectra. 286 transitions were modeled using the effective Hamiltonian approach.The dipole transition moment parameters of the three analyzed bands were determined by a least-squares fit to the measured line intensities. For the three studied band systems, the effective Hamiltonian and transition moment operator parameters were used to generate line lists provided as Supplementary Materials.     

New development in Poincaré's problem of irregular integrals

In connection with non-Fuchsian equations Poincaré has made an important conclusion: It is impossible to obtain explicit expressions of irregular integrals .To elucidate the essence of Poincaré's problem, we establish correspondence theorem. Irregular integrals are analytic functions of new kind, possessing tree structure; part of which can be represented by conventional recursive series, while its remaining part is expressed by the so-called tree series, not subjecting to any recursive relation at all.In contrast to the numerical solution calculated by infinite determinant of classical theory (Hill-Poincaré-von Koch), our method yields naturally exact analytic solution in explicit form. The method proposed may be used to construct a unifying theory for general equations with variable coefficients, having various kinds of singularities as singular lines.The significance of Poincaré conjecture is discussed, the tree series obtained belong to higher automorphic functions.     

An example of applications of the elementary catastrophe theory in Hamiltonian systems

The convection in atmosphere discussed in ref. [1] is rigorously treated by considering the variation of environmental temperature with the height. This represents an example of applications of the elementary catastrophe theory in Hamiltonian systems.