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By viewing the electron as a wavepacket in the positive energy spectrum of the Dirac equation, we are able to achieve a much clearer understanding of its behavior under weak electromagnetic fields. The intrinsic spin magnetic moment is found to be established from the self-rotation of the wavepacket. A non-canonical structure is also exhibited in the equations of motion due to non- Abelian geometric phases of the Dirac spinors. The wavepacket energy can be expressed simply in terms of the kinetic, electrostatic, and Zeeman terms only. This can be transformed into an effective quantum Hamiltonian by a novel scheme, and reproduces the Pauli Hamiltonian with all-order relativistic corrections.
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We analyze the two-dimensional photoelectrons momentum distribution of Ar atom ionized by midinfrared laser pulses and mainly concentrate on the energy range below 2Up. By using a generalized quantum trajectory Monte Carlo (GQTMC) simulation and comparing with the numerical solution of time-dependent Schrodinger equation (TDSE), we show that in the deep tunneling regime, the rescattered electron trajectories plays unimportant role and the interplay between the intracycle and inter-cycle results in a ring-like interference pattern. The ring-like interference pattern will mask the holographic interference structure in the low longitudinal momentum region. When the nonadiabatic tunneling contributes significantly to ionization, i.e., the Keldysh parameter 1, the contribution of the rescattered electron trajectories become large, thus holographic interference pattern can be clearly observed. Our results help paving the way for gaining physical insight into ultrafast electron dynamic process with attosecond temporal resolution.
Kinematical aspects of pion decay $pi to mu u$ is studied, with neutrino mixing taken into account. An attempt is made to derive the transition probability for such a sequence of processes: a $pi^+$ produced at $(vec{x}_{pi},t_{pi})$ with momentum $vec{p}_{pi}$ decays into a $mu^+$ and a $ u_{mu}$ somewhere in space-time and then the $mu^+$ is detected at $(vec{x}_{mu},t_{mu})$ with momentum $vec{p}_{mu}$ and a $ u_{alpha}$ (a neutrino with flavor $alpha = e$, $mu$, $...$) is detected at $(vec{x}_{ u},t_{ u})$ with momentum $vec{p}_{ u}$. It is shown that (1) if all the particles involved are treated as plane-waves, the energy-momentum conservation would eliminate the neutrino oscillating terms, leaving each mass-eigenstate to contribute separately to the transition probability; (2) if one treats all the particles involved as wave-packets, the neutrino oscillating terms would appear and would be multiplied by two suppression factors, which result from distinction in velocity and in energy between the two interfering neutrino mass-eigenstates. An approximate treatment which takes account of the two complementary features, each of the particles involved propagates along its classical trajectory on the one hand and energies and momenta of the particles involved are conserved during the decay on the other hand, is proposed and similarity and difference between our approach and that of Dolgov et al. are discussed.
Flavor oscillation of traveling neutrinos is treated by solving the one-dimensional Dirac equation for massive fermions. The solutions are given in terms of squeezed coherent state as mutual eigenfunctions of parity operator and the corresponding Hamiltonian, both represented in bosonic creation and annihilation operators. It was shown that a mono-energetic state is non-normalizable, and a normalizable Gaussian wave packet, when of pure parity, cannot propagate. A physical state for a traveling neutrino beam would be represented as a normalizable Gaussian wave packet of equally-weighted mixing of two parities, which has the largest energy-dependent velocity. Based on this wave-packet representation, flavor oscillation of traveling neutrinos can be treated in a strict sense. These results allow the accurate interpretation of experimental data for neutrino oscillation, which is critical in judging whether neutrino oscillation violates CP symmetry.
We consider semiclassical higher-order wave packet solutions of the Schrodinger equation with phase vortices. The vortex line is aligned with the propagation direction, and the wave packet carries a well-defined orbital angular momentum (OAM) $hbar l$ ($l$ is the vortex strength) along its main linear momentum. The probability current coils around momentum in such OAM states of electrons. In an electric field, these states evolve like massless particles with spin $l$. The magnetic-monopole Berry curvature appears in momentum space, which results in a spin-orbit-type interaction and a Berry/Magnus transverse force acting on the wave packet. This brings about the OAM Hall effect. In a magnetic field, there is a Zeeman interaction, which, can lead to more complicated dynamics.
We investigate theoretically electron dynamics under a VUV attosecond pulse train which has a controlled phase delay with respect to an additional strong infrared laser field. Using the strong field approximation and the fact that the attosecond pulse is short compared to the excited electron dynamics, we arrive at a minimal analytical model for the kinetic energy distribution of the electron as well as the photon absorption probability as a function of the phase delay between the fields. We analyze the dynamics in terms of electron wave packet replicas created by the attosecond pulses. The absorption probability shows strong modulations as a function of the phase delay for VUV photons of energy comparable to the binding energy of the electron, while for higher photon energies the absorption probability does not depend on the delay, in line with the experimental observations for helium and argon, respectively.
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