Related papers: Effective Caldirola-Kanai Model for Accelerating T…
The one dimensional (1D) driven quantum coupled pseudoforce system governing the dynamics of collective Langmuir electron oscillations is used in order to investigate the effects of variety of space charge distributions on plasmon…
Nonlinear wave formation and propagation on a complex network with excitable node dynamics is of fundamental interest in diverse fields in science and engineering. Here, we propose a new model of the Kuramoto type to study nonlinear wave…
A multispecies, collisionless plasma is modeled by the Vlasov-Poisson system. Assuming that the electric field decays with sufficient rapidity as $t \to\infty$, we show that the velocity characteristics and spatial averages of the particle…
One of the unitary forms of the quantum mechanical time evolution operator is given by Cayley's approximation. A numerical implementation of the same involves the replacement of second derivatives in Hamiltonian with the three-point…
Observational studies of the Earth's radiation belts indicate that Alfv\'enic fluctuations in the frequency range of 2-25 mHz accelerate magnetically trapped electrons to relativistic energies. For decades, statistical models of the Earth's…
We derive from a microscopic Hamiltonian a set of stochastic equations of motion for a system of spinless charged particles in an electromagnetic (EM) field based on a consistent application of a dimensionful 1/c expansion of quantum…
We study the spinless Pauli-Fierz Hamiltonian in a semiclassical mean-field limit of many fermions. For appropriate initial conditions, we prove, in the trace norm topology of reduced density matrices, that the many-body quantum state…
We study the clustering of passive, non-interacting particles moving under the influence of a fluctuating field and random noise, in one dimension. The fluctuating field in our case is provided by a surface governed by the…
We derive an exact solitary wave solution for the $\PTb$-symmetric nonlinear Dirac equation with a scalar-scalar interaction. We consider a power-law nonlinearity of the form $|\bar{\Psi}\,\Psi|^{k}\,\Psi$ for positive values of $k$. The…
The linear equations for transverse spin dynamics in a weakly polarized degenerate Fermi liquid with arbitrary relationship between temperature and polarization are derived from Landau-Silin phenomenological kinetic equation with general…
We introduce a dynamic stabilization scheme universally applicable to unidirectional nonlinear coherent waves. By abruptly changing the waveguiding properties, the breathing of wave packets subject to modulation instability can be…
This article offers a new approach for analysing the dynamic behaviour of distributions of charged particles in an electromagnetic field. After discussing the limitations inherent in the Lorentz-Dirac equation for a single point particle a…
We study here the random diffusion model. This is a continuum model for a conserved scalar density field $\phi$ driven by diffusive dynamics. The interesting feature of the dynamics is that the {\it bare} diffusion coefficient $D$ is…
In this paper we study the linearized Vlasov-Poisson equation for localized disturbances of an infinite, homogeneous Maxwellian background distribution in $\mathbb R^3_x \times \mathbb R^3_v$. In contrast with the confined case $\mathbb T^d…
The nonlinear theory of Landau damping of electrostatic wave envelopes (WEs) is revisited in a quantum electron-positron (EP) pair plasma. Starting from a Wigner-Moyal equation coupled to the Poisson equation and applying the multiple scale…
The self-conjugate Dirac Hamiltonian is obtained in the Kerr-Newman field. A transition is implemented to a Schr\"odinger-type relativistic equation. For the case where the angular and radial variables are not separated, the method of…
The 1D bump-on-tail problem is studied in order to determine the influence of drag on quasi-steady solutions near marginal stability ($1-\gamma_d/\gamma_L\ll 1$) when effective collisions are much larger than the instability growth rate…
We extend our programme of representing the quantum state through exact stand-alone trajectory models to the Dirac equation. We show that the free Dirac equation in the angular coordinate representation is a continuity equation for which…
Trajectory-based methods that propagate classical nuclei on multiple quantum electronic states are often used to simulate nonadiabatic processes in the condensed phase. A long-standing problem of these methods is their lack of detailed…
We give sufficient conditions for the existence of positive travelling wave solutions for multi-dimensional autonomous reaction-diffusion systems with distributed delay. To prove the existence of travelling waves, we give an abstract…