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We propose and develop a general method of numerical calculation of the wave function time evolution in a quantum system which is described by Hamiltonian of an arbitrary dimensionality and with arbitrary interactions. For this, we obtain a general n-order single-step propagator in closed-form, which could be used for the numerical solving of the problem with any prescribed accuracy. We demonstrate the applicability of the proposed approach by considering a quantum problem with non-separable time-dependent Hamiltonian: the propagation of an electron in focused electromagnetic field with vortex electric field component. 

We propose a new method of detecting radiation reaction effects in the motion of particles subjected to laser pulses of moderate intensity and long duration. The effect becomes sizable for particles that gain almost no energy through the interaction with the laser pulse. Hence, there are regions of parameter space in which radiation reaction is actually the dominant influence on charged particle motion.

We model the emission of high energy photons due to relativistic charged particle motion in intense laser-plasma interactions. This is done within a particle-in-cell code, for which high frequency radiation normally cannot be resolved due to finite time steps and grid size. A simple expression for the synchrotron radiation spectra is used together with a Monte-Carlo method for the emittance. We extend previous work by allowing for arbitrary fields, considering the particles to be in instantaneous circular motion due to an effective magnetic field. Furthermore, we implement noise reduction techniques and present validity estimates of the method. Finally, we perform a rigorous comparison to the mechanism of radiation reaction, and find the emitted energy to be in excellent agreement with the losses calculated using radiation reaction. (C) 2015 AIP Publishing LLC.

We consider the Thomson and Compton scattering of high-energy electrons n an intense laser pulse. Our simulations show that energy losses due o radiation reaction cause the emitted radiation to be spread over a roader angular range than the case without these losses included. We xplain this in terms of the effect of these energy losses on the article dynamics. Finally, at ultra-high intensities, i.e. fields with dimensionless parameter a(0)similar to 200, the energy of the ission pectrum is significantly reduced by radiation reaction and also the lassical and QED results begin to differ. This is found to be due to he classical theory overestimating the energy loss of the electrons. uch findings are relevant to radiation source development involving e ext generation of high-intensity laser facilities.

Experimentally detected ultrafast spin avalanches spreading in crystals of molecular (nano) magnets [Decelle et al., Phys. Rev. Lett. 102, 027203 (2009)] have recently been explained in terms of magnetic detonation [Modestov et al., Phys. Rev. Lett. 107, 207208 (2011)]. Here magnetic detonation structure is investigated by taking into account transport processes of the crystals such as thermal conduction and volume viscosity. The transport processes result in smooth profiles of the most important thermodynamical crystal parameters, temperature, density, and pressure, all over the magnetic detonation front, including the leading shock, which is one of the key regions of magnetic detonation. In the case of zero volume viscosity, thermal conduction leads to an isothermal discontinuity instead of the shock, for which temperature is continuous while density and pressure experience jump. It is also demonstrated that the thickness of the magnetic detonation front may be controlled by applying the transverse-magnetic field, which is important for possible experimental observations of magnetic detonation.

We demonstrate that charged particles in a suciently intense standing wave are compressed toward, and oscillate synchronously at, the antinodes of the electric eld. We call this unusualbehaviour `anomalous radiative trapping' (ART). We show using dipole pulses, which oer a pathto increased laser intensity, that ART opens up new possibilities for the generation of radiationand particle beams, both of which are high-energy, directed and collimated. ART also provides a mechanism for particle control in high-intensity quantum-electrodynamics experiments.

The Kelvin-Helmholtz instability in an ionized plasma is studied with a focus on the magnetic field generation via the Biermann battery (baroclinic) mechanism. The problem is solved by using direct numerical simulations of two counter-directed flows in 2D geometry. The simulations demonstrate the formation of eddies and their further interaction and merging resulting in a large single vortex. In contrast to general belief, it is found that the instability generated magnetic field may exhibit significantly different structures from the vorticity field, despite the mathematically identical equations controlling the magnetic field and vorticity evolution. At later stages of the nonlinear instability development, the magnetic field may keep growing even after the hydrodynamic vortex strength has reached its maximum and started decaying due to dissipation.

We obtain a fundamental instability of the magnetization-switching fronts in superparamagnetic and ferromagnetic materials such as crystals of nanomagnets, ferromagnetic nanowires, and systems of quantum dots with large spin. We develop the instability theory for both linear and nonlinear stages. By using numerical simulations we investigate the instability properties focusing on spin avalanches in crystals of nanomagnets. The instability distorts spontaneously the fronts and leads to a complex multidimensional front dynamics. We show that the instability has a universal physical nature, with a deep relationship to a wide variety of physical systems, such as the Darrieus-Landau instability of deflagration fronts in combustion, inertial confinement fusion, and thermonuclear supernovae, and the instability of doping fronts in organic semiconductors.

Quantum turbulence (QT) generated by the Rayleigh-Taylor instability in binary immiscible ultracold 87Rb atoms at zero temperature is studied theoretically. We show that the quantum vortex tangle is qualitatively different from previously considered superfluids, which reveals deep relations between QT and classical turbulence. The present QT may be generated at arbitrarily small Mach numbers, which is a unique property not found in previously studied superfluids. By numerical solution of the coupled Gross-Pitaevskii equations we find that the Kolmogorov scaling law holds for the incompressible kinetic energy. We demonstrate that the phenomenon may be observed in the laboratory.

Anisotropy effects for spin avalanches in crystals of nanomagnets are studied theoretically with the external magnetic field applied at an arbitrary angle to the easy axis. Starting with the Hamiltonian for a single nanomagnet in the crystal, two essential quantities characterizing spin avalanches are calculated: the activation and Zeeman energies. The calculation is performed numerically for a wide range of angles and analytical formulas are derived within the limit of small angles. The anisotropic properties of a single nanomagnet lead to anisotropic behavior of the magnetic deflagration speed. Modifications of the magnetic deflagration speed are investigated for different angles between the external magnetic field and the easy axis of the crystals. Anisotropic properties of magnetic detonation are also studied, which concern, first of all, the temperature behind the leading shock and the characteristic time of spin switching in the detonation.