相关论文: Delta Interactions and Electrodynamics of Point Pa…

We discuss the discrete spectrum of the Hamiltonian describing a two-dimensional quantum particle interacting with an infinite family of point interactions. We suppose that the latter are arranged into a star-shaped graph with N arms and a…

We study a class of delta-like perturbations of the Laplacian on the half-line, characterized by Robin boundary conditions at the origin. Using the formalism of nonstandard analysis, we derive a simple connection with a suitable family of…

We consider the dynamics of point particles which are confined to a bounded, possibly nonconvex domain $\Omega$. Collisions with the boundary are described as purely elastic collisions. This turns the description of the particle dynamics…

We consider the motion of a point particle with spin in a stationary spacetime. We define, following Witzany (2019) and later Ramond (2022), a twelve dimensional Hamiltonian dynamical system whose orbits coincide with the solutions of the…

The action of parity inversion, time inversion and charge conjugation operations on several differential equations for a classical point charged particle are described. Moreover, we consider the notion of {\it symmetrized acceleration}…

It is commonly accepted that in hadronic or nuclear collisions at extremely high energies the shortest scales are explored. At the classical level, this property of the interaction is closely related to the Lorentz contraction of the fields…

In this work, we investigate the dynamics of interacting particle systems subjected to repulsive forces, such as lattices of magnetized particles. To this end, we first develop a general model capable of capturing the complete dynamical…

In studies of interaction of matter with laser fields of extreme intensity there are two limiting cases of a multi-beam setup maximizing either the electric field or the magnetic field. In this work attention is paid to the optimal…

We consider a system of N nonrelativistic particles of spin 1/2 interacting with the quantized Maxwell field (mass zero and spin one) in the limit when the particles have a small velocity, imposing to the interaction an ultraviolet cutoff,…

We discuss spectral properties of the Laplacian with multiple ($N$) point interactions in two-dimensional bounded regions. A mathematically sound formulation for the problem is given within the framework of the self-adjoint extension of a…

The interaction between singular and regular fields is considered for Lorentz-invariant scalar and vector wave equations. The singular field is generated by a Dirac source term. Its dynamics are deduced from the total field Lagrangian. At…

In this work we consider the two-dimensional Dirac operator with general local singular interactions supported on a closed curve. A systematic study of the interaction is performed by decomposing it into a linear combination of four…

Given the abstract wave equation $\ddot\phi-\Delta_\alpha\phi=0$, where $\Delta_\alpha$ is the Laplace operator with a point interaction of strength $\alpha$, we define and study $\bar W_\alpha$, the associated wave generator in the phase…

We analyze the stability of super- and subradiant states in a system of identical two-level atoms in the near-Dicke limit, i.e., when the atoms are very close to each other compared to the wavelength of resonant light. The dynamics of the…

Metriplectic dynamical systems consist of a special combination of a Hamiltonian and a (generalized) entropy-gradient flow, such that the Hamiltonian is conserved and entropy is dissipated/produced (depending on a sign convention). It is…

Particles and fields are standard components in numerical simulations like transport simulations in nuclear physics and have very well understood dynamics. Still, a common problem is the interaction between particles and fields due to their…

Using the multisymplectic Hamiltonian formalism, we propose a Poisson bracket for the electromagnetic field that, in addition to satisfying the restricted principle of relativity, reproduces well-established results from the standard…

We discuss the physical nature of elementary singularities arising in the complexified Maxwell field extended into complex spacetime, i.e., in Lanczos-Newman electrodynamics, which may provide a possible link between elementary particle…

The classical electromagnetic interaction of a point charge and a magnet is discussed by first calculating the interaction of point charge with a simple model magnetic moment and then suggesting a multiparticle limit. The Darwin Lagrangian…

The cosmological evolution of an interacting scalar field model in which the scalar field interacts with dark matter, radiation, and baryon via Lorentz violation is investigated. We propose a model of interaction through the effective…