Twisted electron in a strong laser wave

Electrons carrying orbital angular momentum (OAM) have recently been discovered theoretically and obtained experimentally that opens up possibilities for using them in high-energy physics. We consider such a twisted electron moving in external field of a plane electromagnetic wave and study how this field influences the electron's OAM. Being motivated by the development of high-power lasers, we focus our attention on a classically strong field regime for which $-e^2 \bar {A^2}/m_e^2 c^4 \gtrsim 1$. It is shown that along with the well-known "plane-wave" Volkov solution, Dirac equation also has the "non-plane-wave" solutions, which possess OAM and a spin-orbit coupling, and generalize the free-electron's Bessel states. Motion of the electron with OAM in a circularly polarized laser wave reveals a twofold character: the wave-packet center moves along a classical helical trajectory with some quantum transverse broadening (due to OAM) existing even for a free electron. Using the twisted states, we calculate the electron's total angular momentum and predict its shift in the strong-field regime that is analogous to the well-known shifts of the electron's momentum and mass (and to a less known shift of its spin) in intense fields. Since the electron's effective angular momentum is conserved in a plane wave, as well as in some more general field configurations, we discuss several possibilities for accelerating non-relativistic twisted electrons by using the focused and combined electromagnetic fields.Comment: to appear in PR

Quantum motion in superposition of Aharonov-Bohm with some additional electromagnetic fields

The structure of additional electromagnetic fields to the Aharonov-Bohm field, for which the Schr\"odinger, Klein-Gordon, and Dirac equations can be solved exactly are described and the corresponding exact solutions are found. It is demonstrated that aside from the known cases (a constant and uniform magnetic field that is parallel to the Aharonov-Bohm solenoid, a static spherically symmetrical electric field, and the field of a magnetic monopole), there are broad classes of additional fields. Among these new additional fields we have physically interesting electric fields acting during a finite time, or localized in a restricted region of space. There are additional time-dependent uniform and isotropic electric fields that allow exact solutions of the Schrodinger equation. In the relativistic case there are additional electric fields propagating along the Aharonov-Bohm solenoid with arbitrary electric pulse shape

On the exact Foldy-Wouthuysen transformation for a Dirac spinor in torsion and other CPT and Lorentz violating backgrounds

We discuss the possibility to perform and use the exact Foldy-Wouthuysen transformation (EFWT) for the Dirac spinor coupled to different CPT and Lorentz violating terms. The classification of such terms is performed, selecting those of them which admit EFWT. For the particular example of an axial vector field, which can be associated with the completely antisymmetric torsion, we construct an explicit EFWT in the case when only a timelike component of this axial vector is present. In the cases when EFWT is not possible, one can still use the corresponding technique for deriving the perturbative Foldy-Wouthuysen transformation, as is illustrated in a particular example in the Appendix

Charged particles in crossed and longitudinal electromagnetic fields and beam guides

We consider a class of electromagnetic fields that contains crossed fields combined with longitudinal electric and magnetic fields. We study the motion of a classical particle (solutions of the Lorentz equations) in such fields. Then, we present an analysis that allows one to decide which fields from the class act as a beam guide for charged particles, and we find some time-independent and time-dependent configurations with beam guiding properties. We demonstrate that the Klein-Gordon and Dirac equations with all the fields from the class can be solved exactly. We study these solutions, which were not known before, and prove that they form complete and orthogonal sets of functions.Comment: 14 page

Aspects of Two-Level Systems under External Time Dependent Fields

The dynamics of two-level systems in time-dependent backgrounds is under consideration. We present some new exact solutions in special backgrounds decaying in time. On the other hand, following ideas of Feynman, Vernon and Hellwarth, we discuss in detail the possibility to reduce the quantum dynamics to a classical Hamiltonian system. This, in particular, opens the possibility to directly apply powerful methods of classical mechanics (e.g. KAM methods) to study the quantum system. Following such an approach, we draw conclusions of relevance for ``quantum chaos'' when the external background is periodic or quasi-periodic in time.Comment: To appear in J. Phys. A. Mathematical and Genera