Alexander Yu. Aleksandrov

A satellite with an electrodynamic attitude control system is considered. The problem of stabilization of the programmed motion in which the axis of the satellite’s dynamic symmetry is stabilized along the local vertical, and the satellite rotates around this axis is solved. On the basis of the Lyapunov function method, sufficient conditions for asymptotic stability of the stabilized programmed motion in the presence of the perturbing gravitational torque are obtained. These conditions allow a rational choice of the coefficients of parametric control depending on the parameters of the satellite and its orbit.

We develop a perturbative description of vacuum radiative processes in quantum electrodynamics with a prescribed external electromagnetic background capable of producing electron-positron pairs. Since the initial vacuum is then unstable and the in- and out-vacua are inequivalent, radiative observables require a real-time formulation beyond the ordinary in-out approach of vacuum-stable QED. Using the Keldysh-Schwinger-Fradkin nonequilibrium technique, we derive the mean number density of emitted photons through the second nonvanishing order in the fine-structure constant. The leading term, of order α , reproduces the known vertex and tadpole mechanisms, while the complete order- α 2 correction contains interference, loop, and induced-current contributions. We also give an independent derivation based on the spectral decomposition of the identity operator in the in-Fock space, where the photon number density is represented as a sum of squared transition amplitudes and vacuum-disconnected terms are canceled by the optical theorem generalized to an unstable vacuum. In addition, we compute the mean electromagnetic field through order e 3 , including the electromagnetic dressing of the induced vacuum current, and verify it using the corresponding Schwinger-Dyson equations. The final formulas are expressed in terms of exact solutions and propagators of the Dirac equation in the external background and apply to general spacetime-dependent field configurations.

The evolution of the vacuum state in a time-dependent external electric field of arbitrary polarization is investigated within a nonperturbative framework of quantum kinetic equations (QKEs). In our previous work [Phys. Rev. Res. 6, 043009 (2024)], a revised version of the QKEs was derived by using an adiabatic basis constructed from one-particle Hamiltonian eigenfunctions in a spatially homogeneous electric field. In this study, we present an extensive analysis of these equations with particular emphasis on observable quantities. Specifically, we compute momentum-resolved particle yields, the induced electron-positron current, the energy-momentum tensor, and the angular-momentum tensor. We also discuss in detail the charge-renormalization procedure required to remove logarithmic divergences. It is shown that our results are consistent with the previous findings obtained via the Dirac-Heisenberg-Wigner formalism. Our analysis provides a firmer theoretical basis for investigations of nonperturbative effects in strong electric fields.

A group of mobile agents on a straight line is considered. First- and second-order integrators are used as agent models. Decentralized control protocols are proposed that provide both uniform and specified nonlinear uniform (uniform with respect to some function) deployment of agents on a straight-line segment. The construction of these protocols is based on information received by agents about the position of their neighbors, and this information comes not directly, but through auxiliary agents. In addition, there is a constant delay in signals from neighbors and communications between agents can be destroyed and restored at arbitrary instants of time. Using methods of positive systems theory and the Lyapunov–Krasovsky functional method, it is proved that the proposed control algorithms are robust with respect to communication delay and network topology switching.

Two approaches to the problem of triaxial stabilization of a rigid body with the aid of delayed feedback law are considered. The first approach is based on choosing control as a sum of dissipative and restoring torques with a constant delay in the restoring torque. In this case, a special construction of Lyapunov–Krasovskii functional is used to derive exponential stability conditions of the programed regime. In the second approach, the control is constructed without using a dissipative torque. The stabilization is ensured via artificially introducing a delay in the restoring torque, and the proof of the exponential stability is based on the application of the Razumikhin method.