Kinetic simulations of ladder climbing by electron plasma waves

The energy of plasma waves can be moved up and down the spectrum using chirped modulations of plasma parameters, which can be driven by external fields. Depending on whether the wave spectrum is discrete (bounded plasma) or continuous (boundless plasma), this phenomenon is called ladder climbing (LC) or autoresonant acceleration of plasmons. It was first proposed by Barth \textit{et al.} [PRL \textbf{115}, 075001 (2015)] based on a linear fluid model. In this paper, LC of electron plasma waves is investigated using fully nonlinear Vlasov-Poisson simulations of collisionless bounded plasma. It is shown that, in agreement with the basic theory, plasmons survive substantial transformations of the spectrum and are destroyed only when their wave numbers become large enough to trigger Landau damping. Since nonlinear effects decrease the damping rate, LC is even more efficient when practiced on structures like quasiperiodic Bernstein-Greene-Kruskal (BGK) waves rather than on Langmuir waves \textit{per~se}

Synthesising case-study research - ready for the next step?

Within the emerging field of research on education for sustainability (EfS), case studies are an important if not the predominant research approach, although often criticised for its lack of internal and external validity and a tendency to draw conclusions with insufficient rigour. While, basic concerns have been expressed and discussed in an early issue of this journal, main assumption still hold true after more than 10 years of research in the field. Only a few approaches so far have tackled the challenge to provide cross-case comparison and the synthesis of case-study results still remains a research desideratum. In this paper, we argue that developments in the field of qualitative and quantitative meta-analysis in educational science offer a framework, which can be used to overcome that shortcoming. After describing the idea of research synthesis, different types of such a meta-analysis are identified and their potential is discussed for existing case studies in higher EfS. This paper concludes with recommendations for further case-study research in the field

A simple remark on a flat projective morphism with a Calabi-Yau fiber

If a K3 surface is a fiber of a flat projective morphisms over a connected noetherian scheme over the complex number field, then any smooth connected fiber is also a K3 surface. Observing this, Professor Nam-Hoon Lee asked if the same is true for higher dimensional Calabi-Yau fibers. We shall give an explicit negative answer to his question as well as a proof of his initial observation.Comment: 8 pages, main theorem is generalized, one more remark is added, mis-calculation and typos are corrected etc

Many-particle quantum hydrodynamics: Exact equations and pressure tensors

In the first part of this paper, the many-particle quantum hydrodynamics equations for a system containing many particles of different sorts are derived exactly from the many-particle Schrödinger equation, including the derivation of the many-particle continuity equations, many-particle Ehrenfest equations of motion, and many-particle quantum Cauchy equations for any of the different particle sorts and for the total particle ensemble. The new point in our analysis is that we consider a set of arbitrary particles of different sorts in the system. In the many-particle quantum Cauchy equations, there appears a quantity called the pressure tensor. In the second part of this paper, we analyze two versions of this tensor in depth: the Wyatt pressure tensor and the Kuzmenkov pressure tensor. There are different versions because there is a gauge freedom for the pressure tensor similar to that for potentials. We find that the interpretation of all the quantities contributing to the Wyatt pressure tensor is understandable, but for the Kuzmenkov tensor it is difficult. Furthermore, the transformation from Cartesian coordinates to cylindrical coordinates for the Wyatt tensor can be done in a clear way, but for the Kuzmenkov tensor it is rather cumbersome

On the exact rotational and internal Hamiltonian for a non-relativistic closed many-body system

Without applying Born-Oppenheimer approximation, the non-relativistic Hamiltonian can be separated into Hamiltonians for the translation of the center of mass and for the rotational and internal motions of the closed many-body system. This exact rotational and internal Hamiltonian can be expressed in terms of three Euler angles for three independent rotations of the system and the rotated Jacobi coordinates for the internal motions

Trigonometric pulse envelopes for laser-induced quantum dynamics

We relate powers of trigonometric functions to Gaussians by proving that properly truncated cosn functions converge to a Gaussian as n tends to infinity. For an application, we analyse the laser-induced population transfer |X1Σ+ → |A1Πx in a two-level model system of aluminium monochloride (AlCl) with fixed nuclei. We apply linearly x-polarized ultraviolet laser pulses with a trigonometric envelope function, whose square has full width at half-maximum of 2.5 fs and 5.0 fs. Studying population dynamics and optimized laser parameters, we find that the optimal field amplitude for trigonometric pulses with n = 20 and n = 1000 has a relative difference of 1%, which is below experimental resolution

Distinguishing two mechanisms for enhanced ionization of H₂⁺ using orthogonal two-color laser fields

We theoretically study the ionization enhancement of the diatomic molecular ion H2+ at two critical internuclear distances R, using orthogonal two-color laser fields. The polarization of the fundamental infrared laser field and a weak second-harmonic field is parallel and perpendicular to the molecular axis, respectively. It is observed that adding the second-harmonic field raises slightly the first ionization peak at the smaller critical R, whereas it enhances the second one at the larger critical R significantly. We further analyze the observable evidence which distinguishes two underlying mechanisms responsible for the enhanced ionization of H2+: (i) the resonant excitation along with the coherent interference of the ionizing wave packets from the 1sσg and 2pσu states and (ii) the easier ionization from the up-field site of the molecule

The connection between Bohmian mechanics and many-particle quantum hydrodynamics

Bohm developed the Bohmian mechanics (BM), in which the Schrödinger equation is transformed into two differential equations: a continuity equation and an equation of motion similar to the Newtonian equation of motion. This transformation can be executed both for single-particle systems and for many-particle systems. Later, Kuzmenkov and Maksimov used basic quantum mechanics for the derivation of many-particle quantum hydrodynamics (MPQHD) including one differential equation for the mass balance and two differential equations for the momentum balance, and we extended their analysis in a prework (K. Renziehausen, I. Barth in Prog. Theor. Exp. Phys. 2018:013A05, 2018) for the case that the particle ensemble consists of different particle sorts. The purpose of this paper is to show how the differential equations of MPQHD can be derived for such a particle ensemble with the differential equations of BM as a starting point. Moreover, our discussion clarifies that the differential equations of MPQHD are more suitable for an analysis of many-particle systems than the differential equations of BM because the differential equations of MPQHD depend on a single position vector only while the differential equations of BM depend on the complete set of all particle coordinates