We assess the suitability of quantum and semiclassical initial-value representations (IVRs), exemplified by the coupled coherent states (CCS) method and the Herman-Kluk (HK) propagator, respectively, for modeling the dynamics of an electronic wave packet in a strong laser field, if this wave packet is initially bound. Using Wigner quasiprobability distributions and ensembles of classical trajectories, we identify signatures of over-the-barrier and tunnel ionization in phase space for static and time-dependent fields and the relevant sets of phasespace trajectories to model such features. Overall, we find good agreement with the full solution of the time-dependent Schrödinger equation (TDSE) for Wigner distributions constructed with both IVRs. Our results indicate that the HK propagator does not fully account for tunneling and over-the-barrier reflections. This leads to a dephasing in the time-dependent wave function, which becomes more pronounced for longer times. However, it is able to partly reproduce features associated with the wave packet crossing classically forbidden regions, although the trajectories employed in its construction always obey classical phase-space constraints. We also show that the CCS method represents a fully quantum initial value representation and accurately reproduces the results of a standard TDSE solver. Finally, we show that the HK propagator may be successfully employed to compute the time-dependent dipole acceleration and high-harmonic spectra. Nevertheless, the outcome of the semiclassical computation exhibits disagreements with the TDSE, as a consequence of the previously mentioned dephasing.
With the recently introduced concept of dominant interaction Hamiltonians, we construct numerically as well as analytically the spectrum of high harmonics (HH) generated in electron-ion scattering under an intense laser field. This is achieved by switching the interaction along classical electron trajectories between the integrable cases of the dipole coupled laser field or the ionic potential, depending on which potential is stronger. As a side effect, the intrinsically chaotic character of the dynamics is mapped onto the potential switching sequence while the trajectories become regular. As a consequence, only a few per cent of the trajectories needed in full semiclassical calculations are sufficient to construct the HH spectrum.
We investigate high-order harmonic generation in inhomogeneous media for reduced dimensionality models. We perform a phase-space analysis, in which we identify specific features caused by the field inhomogeneity. We compute high-order harmonic spectra using the numerical solution of the time-dependent Schrödinger equation, and provide an interpretation in terms of classical electron trajectories. We show that the dynamics of the system can be described by the interplay of high-frequency and slow-frequency oscillations, which are given by Mathieu's equations. The latter oscillations lead to an increase in the cutoff energy, and, for small values of the inhomogeneity parameter, take place over many driving-field cycles. In this case, the two processes can be decoupled and the oscillations can be described analytically.
In this paper we report a version of the Coupled Coherent States (CCS) method which is able to accurately compute the HHG spectrum of an electron in a laser field in one dimension by the use of trajectory-guided grids of Gaussian wavepackets. It is shown that by periodic re-projection of the wavefunction and dynamically altering the basis set size, the method can account for a wavefunction which spreads out to cover a large area in phase space while still keeping computational expense low. The HHG spectra obtained show good agreement with those from a time dependent Schrödinger equation solver. We show also that the part of the wavefunction which is responsible for HHG moves along a periodic orbit which is far from that of classical motion. Although this paper is a proof of principle and therefore focussed on a simple one-dimensional system, future generalisations for the multi-electron case are discussed.
In a system of coupled nonlinear oscillators, the breather (or local mode) solution is studied fully quantum mechanically, as well as by a semiclassical initial value representation of the propagator and classical Wigner dynamics. We show that the initial breather state is a superposition of almost degenerate eigenstates. From this simple observation it follows that the breather must decay and revive (i.e., oscillate with energy localization for extended times). Numerical results are shown for a two degree of freedom system. The fact that the semiclassical real-time result reproduces the full quantum one to a large degree, whereas the classical Wigner dynamics based on a similar set of trajectories does not, indicates that the breather oscillation can be viewed as an interference phenomenon.
The Lorentz length contraction for a rod in uniform motion is derived performing two measurements at arbitrary times. Provided that the velocity of the rod is known, this derivation does not require the simultaneous measurement of two events. It thus avoids uncomfortable superluminal relationships. Furthermore, since the observer's simultaneous measurement is not needed in order to observe spatial contraction, this procedure is more akin to the Lorentzian relativity approach and is better suited for more general schemes such as deformed spacetime versions of special relativity. An example of a space contraction measurement from the same rest position in the observer's frame illustrates the procedure.
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